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C. R. Acad. Sci. Paris, t. 2, Série IV, p. 1113–1130, 2001 Physique appliquée/Applied physics (Biophysique/Biophysics) DOSSIER IMAGERIE ACOUSTIQUE ET OPTIQUE DES MILIEUX BIOLOGIQUES OPTICAL AND ACOUSTICAL IMAGING OF BIOLOGICAL MEDIA Adaptive diagnostic ultrasonic imaging Gary C. NG a , Gregg E. TRAHEY b a ATL Ultrasound, A. Philips Medical Systems Company, 22100 Bothell-Everett Highway, Bothell, WA 98021, USA b Department of Biomedical Engineering, 136 Hudson Hall, Duke University, Durham, NC 27708, USA E-mail: [email protected]; [email protected] (Reçu le 9 juin 2001, accepté le 28 juillet 2001) Abstract. Medical ultrasonic imaging systems assume a constant, fixed acoustic propagation velocity in tissue. This assumption allows the focusing of ultrasonic pulses in a simple way with transducer arrays with electronic delay lines. However, soft tissue acoustic velocities actually range from 1350 m/s to 1725 m/s, and the basic focusing procedure fails to obtain high quality images on some patients. Here we describe different adaptive techniques that allow focusing through such inhomogeneous tissues. 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS imaging / ultrasound / acoustic / adaptive technique / focusing / speckle / resolution Focalisation adaptative en imagerie ultrasonore Résumé. Les techniques d’imagerie ultrasonore médicale reposent sur l’hypothèse d’un milieu de propagation uniforme ou la vitesse du son est constante. Cette hypothèse permet de focaliser des impulsions ultrasonores à partir de réseau de transducteurs en simulant électroniquement l’effet d’une lentille. En fait les tissus mous ont des célérités ultrasonores qui varient de 1350 m/s à 1725 m/s et les techniques de focalisation classiques ne permettent pas d’obtenir de bonnes images sur certains patients. Nous décrivons ici différentes techniques de focalisation adaptative qui permettent de focaliser les faisceaux ultrasonores en milieu inhomogène. 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS imagerie / ultrasons / acoustique / technique adaptative / focalisation / tavelure / résolution 1. Background Medical ultrasonic imaging systems assume a constant, fixed acoustic propagation velocity, typically 1540 m/s in tissue. This assumption allows the simple calculation of the time delays applied to pulses transmitted from elements on the transducer array and to echoes received at these elements. These delays are used to electronically steer and focus both the transmitted and received ultrasonic waves to a series of locations. Echoes received from a 2D raster of these locations are combined to form an ultrasonic image. The acoustic velocity is also used to calibrate the scale of the ultrasonic image. Soft tissue acoustic velocities actually range from 1350 m/s to 1725 m/s. An ultrasonic pulse travelling from the transducer to the liver would traverse the skin (1625 m/s), subcutaneous and pararenal fat Note présentée par Guy LAVAL. S1296-2147(01)01258-6/FLA 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés 1113

Adaptive diagnostic ultrasonic imaging

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Page 1: Adaptive diagnostic ultrasonic imaging

C. R. Acad. Sci. Paris, t. 2, Série IV, p. 1113–1130, 2001Physique appliquée/Applied physics(Biophysique/Biophysics)

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IMAGERIE ACOUSTIQUE ET OPTIQUE DES MILIEUX BIOLOGIQUES

OPTICAL AND ACOUSTICAL IMAGING OF BIOLOGICAL MEDIA

Adaptive diagnostic ultrasonic imagingGary C. NG a, Gregg E. TRAHEY b

a ATL Ultrasound, A. Philips Medical Systems Company,22100 Bothell-Everett Highway,Bothell, WA 98021, USA

b Department of Biomedical Engineering, 136 Hudson Hall, Duke University, Durham, NC 27708, USAE-mail: [email protected]; [email protected]

(Reçu le 9 juin 2001, accepté le 28 juillet 2001)

Abstract. Medical ultrasonic imaging systems assume a constant, fixed acoustic propagation velocityin tissue. This assumption allows the focusing of ultrasonic pulses in a simple way withtransducer arrays with electronic delay lines. However, soft tissue acoustic velocitiesactually range from 1350 m/s to 1725 m/s, and the basic focusing procedure failsto obtain high quality images on some patients. Here we describe different adaptivetechniques that allow focusing through such inhomogeneous tissues. 2001 Académiedes sciences/Éditions scientifiques et médicales Elsevier SAS

imaging / ultrasound / acoustic / adaptive technique / focusing / speckle / resolution

Focalisation adaptative en imagerie ultrasonore

Résumé. Les techniques d’imagerie ultrasonore médicale reposent sur l’hypothèse d’un milieude propagation uniforme ou la vitesse du son est constante. Cette hypothèse permet defocaliser des impulsions ultrasonores à partir de réseau de transducteurs en simulantélectroniquement l’effet d’une lentille. En fait les tissus mous ont des célérités ultrasonoresqui varient de1350 m/s à 1725 m/s et les techniques de focalisation classiques nepermettent pas d’obtenir de bonnes images sur certains patients. Nous décrivons icidifférentes techniques de focalisation adaptative qui permettent de focaliser les faisceauxultrasonores en milieu inhomogène. 2001 Académie des sciences/Éditions scientifiqueset médicales Elsevier SAS

imagerie / ultrasons / acoustique / technique adaptative / focalisation / tavelure /résolution

1. Background

Medical ultrasonic imaging systems assume a constant, fixed acoustic propagation velocity, typically1540 m/s in tissue. This assumption allows the simple calculation of the time delays applied to pulsestransmitted from elements on the transducer array and to echoes received at these elements. These delaysare used to electronically steer and focus both the transmitted and received ultrasonic waves to a series oflocations. Echoes received from a 2D raster of these locations are combined to form an ultrasonic image.The acoustic velocity is also used to calibrate the scale of the ultrasonic image.

Soft tissue acoustic velocities actually range from 1350 m/s to 1725 m/s. An ultrasonic pulse travellingfrom the transducer to the liver would traverse the skin (1625 m/s), subcutaneous and pararenal fat

Note présentée par Guy LAVAL .

S1296-2147(01)01258-6/FLA 2001 Académie des sciences/Éditions scientifiques et médicales Elsevier SAS. Tous droits réservés 1113

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G.C. NG, G.E. Trahey OPTICAL AND ACOUSTICAL IMAGING OF BIOLOGICAL MEDIA

Figure 1. (a) Received echoes from a point target are measured by each element of the transducer array. Focal delaysare applied, after which received echoes at each channel are aligned. The aligned echoes are summed in phase. (b) Plotof echo amplitude from the point target, after beamform summation of the per channel received echoes, as the transmit

beam is swept laterally across the point target.

(1400 m/s), muscle (1575 m/s), blood (1575 m/s), and liver (1600 m/s) [1]. In order to accurately focuspulses from each transducer element at a point in the liver, each tissue’s acoustic velocity and thicknessalong the acoustic path of each element must be known.

Figures 1and 2 show the ideal and realistic situations for ultrasonic imaging with an array transducer.In the ideal situation shown in figure 1a, the acoustic velocity is uniformly 1540 m/s. In this case, acousticpulses from each element arrive at the focus simultaneously and echoes from a target at the focus, afterpassing through the delay circuits in the beamformer, are summed in phase to form a bright image at thatpoint. Summing the echoes in phase results in the narrowest possible image, or best spatial resolution of thetarget, and the largest target amplitude. This is illustrated in figure 1b, the lateral plot of the summed targetamplitudes after beam formation. In the more realistic situation, shown in figure 2a, ultrasonic signalstravelling to and from the array elements encounter tissue layers with differing acoustic velocities. Asa result, ultrasonic waves travelling from transducer elements to the focal point and back through thebeamformer delay circuitry are not summed in phase. The target echoes are, as a result, weaker and theimage of the target is blurred. The lateral plot of amplitudes from a point target in the presence of a mediumwith differing velocities are shown in figure 2b.

In addition to the ultrasonic pulse timing errors caused by variations in the acoustic velocity of tissues,variable tissue acoustic attenuation can also degrade the resolution of an ultrasonic image.

2. Mathematical description of focusing and aberration

A simple mathematical framework can be provided to describe focusing and phase aberration by lookingonly at wave propagation on receive, and by considering only the echoes from a point target. If a pointtarget located at (x0, y0, z0) is insonified by a transmit pulse, p(t, x, y, z), the echoes from the target can be

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Figure 2. (a) Received echoes from a point target are measured by each element of the transducer array, focused, andsummed in the same manner as in figure 1a. In the presence of an aberrating layer, the received echoes at each channel

are not aligned. The misaligned echoes are summed out of phase. (b) Plot of echo amplitude from the point target,after beamform summation of the per channel received echoes, as the transmit beam is swept laterally across the pointtarget. Notice that the target echo amplitude is diminished, and the main lobe is wider and broken up into two parts.

The widening and break-up of the main lobe implies that the spatial resolution is degraded.

written as:

s(t, x, y, z) =R0p(t, x0, y0, z0)exp(j(2πf/c)r)

r(1)

Here, s(t, x, y, z) is the backscattered signal, R0 is the coefficient of reflection of the target, p(t, x0, y0, z0)is the transmitted pressure field evaluated at the point target position, f is the frequency of the insonifyingwave, c is the acoustic velocity in the medium, and r is the radial distance from the target. The term in theexponent is called the phase spectrum of the signal, and in this case, describes a spherically diverging phasefront emanating from the target. The 1/r term accounts for the decrease in echo amplitude with spreadingof the acoustic field away from the target. If the receive transducer array has N elements located at spatialpositions from (x1, y1, z1) to (xN , yN , zN), the pressure field measured at element i is given by:

s(t, xi, yi, zi) =R0p(t, x0, y0, z0)exp

(j(2πf/c)

√(x0 − xi)2 + (y0 − yi)2 + (z0 − zi)2

)√(x0 − xi)2 + (y0 − yi)2 + (z0 − zi)2

(2)

The term in the square root is the radial distance from the point target to each element on the receive array.To focus the received echoes, a focal time delay, ∆τ , equal to:

∆τi = −1c

√(x0 − xi)2 + (y0 − yi)2 + (z0 − zi)2 (3)

is applied to each element. A time delay in the time domain is related to a phase shift in the frequencydomain. As such, a delay of ∆τi results in a linear phase shift of exp(j 2πf∆τi) in the phase spectrumof the received echo at element i. Figure 1ashows the echoes measured by each element upon receiving

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the divergent wavefront from the point target. After application of focal time delays, ∆τi, the relative timedelays between the received echoes are removed, and all the echoes are now in phase.

The underlying assumption in determining the focal delays is that the acoustic velocity in the medium isa constant, c. However, in an aberrating medium, c actually varies with spatial location. The pressure fieldmeasured at each receive position becomes:

saberrated(t, x, y, z) = s(t, xi, yi, zi) exp(jφ(t, x, y, z)

)(4)

Equation (4) describes any phase aberration in its most general form, and the term in the exponent can applyto any sort of acoustic velocity distortion. In a later section, several assumptions will be presented whichcan simplify the φ(t, x, y, z) term. For now, it is important to observe that application of the focal delaysaccording to equation (3) removes the geometric components, but leaves the exp(jφ(t, x, y, z)) unaffected.This residual phase error implies that the received echoes between elements are not in phase despite theapplication of focal delays. It is this misalignment that results in a degradation of the target resolution andtarget amplitude as shown in figure 2aand 2b.

In addition to phase and amplitude distortions, spatially variable attenuation can also be present in themedium. In such a medium, the pressure field on receive becomes:

saberrated(t, x, y, z) =A(x, y, z)s(t, xi, yi, zi) exp(jφ(t, x, y, z)

)(5)

The difference between equations (4) and (5) is the presence of a spatially variable attenuation term inequation (5). Both the phase distortion term, exp(jφ(t, x, y, z)), and the attenuation term, A(f, x, y, z), canresult in changes in the amplitude and pulse shape of the unaberrated echoes, s(t, xi, yi, zi). Later, we willshow how both of these components can be estimated and removed.

3. Evidence for and models of ultrasonic image quality degradation resulting from interveningtissue layers

Evidence of tissue-induced distortion and degradation of ultrasonic images have been reported sincethe first 2D imaging systems were introduced and such effects became observable. Compound B-modescanners, introduced in the early 1970s, experienced significant losses in image quality when imagesacquired from various transducer positions were averaged using an assumed fixed acoustic velocity. Insuch imaging systems, variations from the assumed acoustic velocity caused misregistrations in the imagesto be averaged and a resultant loss in resolution. Modern diagnostic scanners can also suffer gross imagedistortions resulting from tissue acoustic velocity variations. Figure 3shows an example of such a distortion.

In most clinical applications, tissue-induced degradation of ultrasonic images is subtle and difficult tocharacterize. There is significant disparity among studies [2–13] attempting to measure the nature andmagnitude of such degradation. Various methods have been used in these studies to characterize theacoustic velocity distortions present in different parts of the body. One method, called the pulse echomethod, involves using a single transducer array for both transmit and receive, as in conventional ultrasonicimaging. A focused pulse is transmitted into the tissue, and echoes from targets in the field are measuredby each element of the same array on receive. Any geometric focal delays between the echoes measuredat different elements are removed. The remaining time shifts between the elements represent an estimateof the time delay distortion incurred during the receive propagation path. The advantage of the pulse echomethod is that it mimics the way regular B-mode imaging is done, and allows access for making aberrationmeasurements over a wide range of tissue types and locations. However, since point targets are not alwayspresent in the body, measured echoes are typically generated by clusters of small, sub-resolution, diffusedscatterers. While echoes from point targets are the same when measured at different receive elements,echoes from diffused scatterers vary in pulse shape across the array leading to poorer time delay estimates

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(a) (b)

Figure 3. The images show a liver (A), inferior vena cava (IVC) (B), and aorta (C). The left image was taken with noaberrations introduced. The right image was made with a 1D rippled aberrating layer between the transducer array andthe subject. Notice that the image brightness is reduced, and visualization of the borders of the hepatic veins (indicated

by white arrows), as well as the aorta, is compromised.

than echoes from point targets. As such, other methods like two transducer through-transmission methodshave also been used. In the through-transmission method, one transducer (often a single element) servesas the transmit point source, while a transducer array, positioned on the opposite side, acts as the receiver.However, such a method can only be used where access for placement of two opposing transducers ispossible, such as in the breast.

Different groups [2–13] have reported aberration measurement results over a broad range of values. Forexample, measured time shift distortions in the breast have ranged from as little as 7 to 8 ns [14], whichis a small fraction of a wavelength, to as much as 66.8 ns [15], which approaches half a wavelength. Forlarge time shift distortions approaching half of a wavelength, significant out of phase cancellation betweenreceived echoes at each channel can occur, with concomitant loss of acoustic signal. The disparity in thereported measurements likely arise from differences in the treatment of the tissue type (for example, in vivoversus excised tissue slabs in a water tank), the measurement techniques used, as well as patient-to-patientvariability.

Several models of tissue aberration are commonly used to represent the sources of image qualitydegradation. The simplest model of tissue aberration is a deviation from the expected average acousticvelocity. However, even this type of error can cause a significant loss in image resolution and degrade theimage calibration. For example, if the acoustic velocity is 5% lower than expected, tissues at 4.0 cm fromthe transducer will be displayed at 4.2 cm. On a typical ultrasonic scanner, this error would also lower theimage resolution and brightness by more than a factor of two [16].

The near field thin phase screen model, shown in figure 4a, allows tissue velocity variations at thetransducer face and generates simple time shift distortions in transmitted and received wavefronts. Lookingat time shift distortions using equation (4), the effect of different time shifts is to impose linear phase shiftson the phase spectrum of the received echo. Therefore, if ∆τi is the time shift distortion at element i, thevalues of φ(f, x, y, z) are constrained under this model to be φ(f, x, y, z) = 2πf∆τi. This simple type ofaberration can generate subtle or dramatic losses in image quality, depending on the magnitude of the timingerrors caused by the phase screen and the rate at which these errors vary across the transducer face [17].If the thin phase screen is moved away from the transducer (a mid-range phase screen), the time shiftedwavefront can propagate further, from just after the thin phase screen to the transducer. Interference that

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(a) (b)

Figure 4. (a) The near field thin phase screen model of aberration. The aberrating layer applies a time shift distortionto the received echoes measured at each element position but do not otherwise distort the measured pulse shape. (b)

The distributed model of aberration. The aberrating layer has some thickness, and the phase distortions imposed by theaberrator can vary with range. The distributed aberrator can also be present some distance away from the transducer.

Propagation of the distorted pulse immediately after passage through the aberrator to the transducer results in changesin the measured pulse shape at the transducer in addition to time shift distortions.

arises from propagation causes the shape of the received waveforms at the transducer array to vary withelement position. Finally, designating a phase screen as ‘thin’ implies that there is no range component tothe aberrator. If the aberrator is distributed in range, different phase distortions are imposed successively,and interference effects due to propagation exist both within the aberrator, and from the aberrator to thetransducer. With both the mid-range aberrator and the distributed aberrator, the phase distortion is trulyan arbitrary function of the spatial location (x, y, z), and cannot be simply described as linear phase shiftsat different elements. The presence of attenuation means that the A(f, x, y, z) term in equation (5) is notsimply a constant and results in modulation of the wavefront amplitude independent of the phase distortionspredicted by any of the aberrator models. Table 1describes seven increasingly complex tissue aberrationmodels and their effect on the amplitude and shape (phase) of waves travelling from points on the ultrasonictransducer to the tissue, and back. Undoubtedly, the most sophisticated model, which describes three-dimensional variations in both the acoustic velocity and attenuation of tissue, is the most accurate. Thesimpler models allow easier mathematical representations of tissue and may account for the most significantsources of image quality degradation. The distributed aberrator models allow tissue velocity variations tooccur throughout the propagation path.

A radio-frequency (RF) plot of the received echoes measured at each element can allow for bettervisualization of the effects of the different types of aberrators. The received echoes measured at eachelement of a 64 element transducer array in simulation, after application of receive focal delays, are shownin figure 5a. Gray levels are used to display the acoustic pressure amplitude of the field. The white regionsin the figures indicate regions of compression in the received pressure field, while the black regions markareas of rarefaction. The vertical axis is the element number, while the horizontal axis is time. If a horizontalslice is taken through a certain element number, and the amplitude of the gray levels is plotted against time,the resultant plot is a time limited sinusoidal burst representing the received echo at that element. In theabsence of any sort of acoustic velocity distortion, the received echoes at each element are mutually alignedafter application of receive focal delays. If a near field thin phase screen is placed directly in front ofthe transducer array, the received echoes show relative time shifts with respect to each other, even afterreceive focusing. The received echoes are shown in figure 5b. However, no pulse shape distortions areobserved from one element to the next. Finally, if the same thin phase screen is moved out to 40 mm fromthe transducer, thereby creating a mid-field thin phase screen, both time shift distortions and pulse shapedistortions are seen in the individual element received echoes. This is seen in figure 5c.

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Table 1.Summary of different models for phase aberration in the medium, and how these models account for anywaveform amplitude distortions and phase distortions in an aberrating medium. The gross velocity and near field thin

phase screen are the easiest aberration models to characterize and correct for since only a time shift estimate isrequired between elements. A distributed aberration in an attenuating medium is the most challenging model to

characterize since both distributed phase aberrations and attenuation by the medium can change the pulse shape (phaseand timing) of the received echoes at each element.

Aberrator model Aberrator position Amplitude distortion Phase distortion

Gross velocityerror

Entire volume imaged Shape of received waveform at eachreceive element position is unchanged

Time shift (linear phasedistortion) of the waveform ateach element

Near field thinphase screen

One layer in front ofthe transducer

Shape of received waveform isunchanged

Time shift (linear phasedistortion) of the waveform ateach element

Near field thinphase screen withattenuation

One layer in front ofthe transducer

Shape of received waveform isunchanged. Amplitude of thewaveform at each element scaled bythe attenuation of the aberrator at thatelement position

Time shift (linear phasedistortion) of the waveform ateach element

Mid-range thinphase screen

One layer betweenthe transducer and thetarget

Waveform shape variations caused bypropagation of the phase distortedwave from aberrator to transducer

Phase distortion of waveformat each element can varynon-linearly with frequency

Mid-range thinphase screen withattenuation

One layer betweenthe transducer and thetarget

Waveform shape variations caused by1) propagation of the phase distorted

wave2) amplitude modulation from

attenuation

Phase distortion of waveformat each element can varynon-linearly with frequency

Distributedaberrator

Multiple layersthrough an extendedrange

Waveform shape variations caused by1) phase distortion of medium at

various range locations2) propagation of distorted wave to

transducer

Phase distortion of waveformat each element can varynon-linearly with frequency

Distributedaberrator withattenuation

Multiple layersthrough an extendedrange

Waveform shape variations caused by1) phase distortion of medium at

various range locations2) propagation of distorted wave to

transducer3) amplitude modulation from

attenuation

Phase distortion of waveformat each element can varynon-linearly with frequency

4. Methods of aberration correction

Adaptive imaging may be defined as any change in the characteristics of the imaging system introducedto reduce the image degradation caused by a specific path. Ultrasonographers routinely compensate forlocal variations in tissue attentuation by varying the overall and local receiver amplifier gains to provideadequate and uniform image brightness.

Adaptive imaging in this paper refers to an automated adjustment of the aiming amplitude and/or shapeof ultrasonic signals transmitted and received from individual transducer elements. All adaptive ultrasonicimaging systems must employ the three following steps; first, acoustic pulses are sent to selected tissueregions and echoes are received from these regions; second, echoes are analyzed to estimate the tissue-induced pulse distortions at each transducer element and; third, the tissue is imaged with pulse transmission

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(a) (b)

(c)

Figure 5. Received echoes measured at each elementafter application of receive focal delays. The graylevels represent acoustic pressure amplitude, with

areas of compression marked in white, and areas ofrarefaction indicated by black. (a) is the result in amedium with a known acoustic velocity. All the

received echoes are time aligned with each other. (b) isthe result in a medium with a near field thin phase

screen. The received echoes are identical to each otherin shape but are no longer time aligned after focusing.(c) shows the received echoes with a mid-range thinphase screen. In addition to time shifts, the received

echoes also show element to element variability.

and echo processing at each element modified to compensate for the measured pulse distortions. Adaptivealgorithms differ in their approaches to the second and third steps.

4.1. Time shift compensation techniques

The conceptually most straightforward adaptive imaging method measures the difference in echo arrivaltime between each pair of neighboring elements using cross-correlation or similar pattern-matchingmethods. These differences are then integrated across the array to create an arrival time error profile. Theinverse of this profile is then applied to subsequent pulse transmissions and echo reception to implementadaptive imaging. This method, introduced by Flax and O’Donnell in 1988 [18] and known as the nearestneighbor correlation method, assumes and can compensate for a gross velocity error or thin phase screenmodel of phase aberration. Variations of this method include arrival time measurements between echoesfrom non-neighboring elements or from groups of elements to construct arrival time error profiles [19,20].

A second method, introduced by Trahey and Smith in 1988 [21,22] and known as the speckle brightnessmethod, sums the echoes from element(s) to be corrected with echoes from a larger region on the transducerarray. Echo sums are formed at a range of timing relationships (i.e. echo delays) and the delay at which theecho sum is brightest (largest) is used to form an arrival time error estimate for that element(s). The processis repeated over all elements and the resulting arrival time estimate is used to adjust the timing of individualelement transmissions and receptions. Variations of this approach use a metric besides echo brightness (i.e.echo intensity) or vary the number or geometry of element groups whose echoes are summed [17,23,24].The speckle brightness algorithms, like the nearest neighbor correlation methods, account only for arrivaltime variations described by the first two tissue models in table 1.

Both the nearest neighbor and speckle-brightness algorithms are limited in the accuracy to which theycan estimate arrival time variations across the array. The errors in these estimates are high for larger arrivaltime variations and can severely degrade the performance of these adaptive imaging methods [25].

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4.2. Backpropagation of received pressure field

Liu and Waag [26] describe an adaptive imaging method, which accounts for a mid-field aberrator. Thealgorithm assumes a thin phase screen at some axial distance from the transducer. The received acousticpulses at each element are stored and, in software, backpropagated by calculating the pressure field at eachaxial distance from the transducer. The distance at which the backpropagated pulses from each elementare most similar is taken to be the distance where the aberrating screen is located. The relative time shiftsbetween these pulses at this distance are then estimated in the same manner as Flax and O’Donnell [18].

4.3. Time reversal focusing

Time reversal focusing was first proposed by Mallart and Fink [27] as a method of correcting for anyphase aberrations present in the propagation medium. This technique makes use of acoustic reciprocity andthe invariance of the acoustic wave equation under a time reversal operation. The acoustic wave equationin a lossless medium is given by:

∇2p=1c2∂2p

∂t2(6)

where p is the pressure, c is the acoustic velocity, and t is time. Since the temporal derivative, ∂t issecond order, both p(x, y, z, t) and its time reversed pair, p(x, y, z,−t), are solutions to the equation, i.e.equation (6) is invariant with time reversal. This technique is conceptually similar to optical phase conjugatemirrors, since time reversal and phase conjugation are related by a Fourier transform. The first step of timereversal involves transmitting a short omni-directional burst from a transducer array. The echoes from anypoint targets in the field propagate through the aberrating medium and are then measured by the array(now used in receive mode). The second step requires that the received echoes be re-transmitted from thesame array in a last-in, first-out manner. This is the process of time reversal. The re-transmitted signalsrepresent the focal delays and pulse shapes which result in optimal focusing at the location of the pointtarget in the presence of the aberrating medium. Another way of looking at it is this: if the phase distortionimposed by the aberrating medium is exp[jφ(f, x, y, z)], re-transmission of the time reversed receivedechoes is equivalent to pre-distorting the transmit signal with a phase response of exp[−jφ(f, x, y, z)]. It isimportant to note that time reversal corrects only for the phase distortion and not any attenuation distortion(the A(f, x, y, z) term in equation (5)). However, Wu et al. [28] have demonstrated experimentally thatin a weakly attenuating media, time reversal focusing operation can indeed correct for any aberrations.The advantage of time reversal focusing is that, unlike the methods that perform time shift compensation,time reversal does not require that the aberrator be confined to a thin layer near the transducer array. Thedisadvantage of time reversal focusing is that it requires point targets whereas time shift compensationtechniques can use either point targets or speckle targets. In the presence of multiple point targets, the timereversal process can be iterated and will result in focusing on the most reflective point target to the exclusionof the other targets [29]. To overcome this limitation, the DORT technique [30] can be used to allowfocusing on targets other than the brightest. The DORT technique consists of eigenvector decomposition ofthe received echoes from the multiple point targets. Each spatially resolved target can be represented as aneigenvector and focusing on a particular target can be accomplished by re-transmission of just its associatedeigenvector.

4.4. Time reversal focusing with attenuation compensation

In a more strongly attenuating medium, an additional first temporal derivative term is added toequation (6). This implies that while acoustic reciprocity is still valid, the time reversal operation isno longer invariant in an attenuating medium. Practically, this means that time reversal focusing in anattenuating medium will still maximize the acoustic pressure field at the focus, but the side-lobe levelsaway from the focus may be sub-optimal [31]. To correct for the effects of attenuating medium, time

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reversal focusing is carried out with attenuation compensation [31]. With this technique, the amplitude ofthe received echoes from point targets in the medium is measured at every element. During re-transmission,the amplitude of the transmit signal at each element is scaled by the inverse of the received echo amplitudeat that element. Any element-to-element variation in amplitude on receive is corrected by the inverse ofthis variation on the re-transmit. If time reversal focusing can be thought of as a phase conjugate filter,then time reversal focusing with attenuation compensation, can be viewed conceptually as an inversefilter that corrects for an attenuating layer close to the transducer array in addition to the phase distortionthroughout the medium. Comparisons were made between time reversal focusing, time reversal focusingwith attenuation compensation and true inverse filtering through the skull by Tanter et al. [31]. Addingattenuation compensation to time reversal gave improved side lobe suppression compared to time reversalfocusing alone, and resulted in point spread functions in the focal plane that were similar (up to a −20 dBlevel) to those obtained with true inverse filtering.

5. Adaptive imaging as a linear filtering operation

5.1. Introduction to linear filters

Many of the adaptive imaging methods described above may be understood and classified by consideringthem as an independent filter applied to pulses transmitted from each element and to echoes received at thatelement.

The term filter refers to a set of operations, implemented in either hardware or software, which can beapplied to a signal to either suppress undesired signal characteristics (e.g. noise, directional interference) orenhance desired signal components. Filters are needed because the desired signal is often corrupted whenit is generated, or when it is propagated through a distorting channel. Areas in which digital filters are usedextensively to compensate for channel distortion effects include the equalization of telephone channels [32],and the elimination of coherent interference from multipath propagation in sonar [33]. The problem of phaseaberration can likewise be categorized as a channel distortion effect, where the channel is the transmit–receive path of acoustic signals from the transducer through human tissue, and the distortion arises fromvelocity inhomogeneities in tissue. In this section, a general framework is provided for describing adaptiveimaging techniques as linear filtering operations with different types of digital filters.

Finite Impulse Response (FIR) filters belong to a general class of systems, which have responses thatare time-limited when the inputs to the systems are also time-limited. In comparison, Infinite ImpulseResponse (IIR) systems have responses that are not time-limited even when time limited system inputsare used, because these systems are recursive in nature. Following the notation used in Oppenheim andSchafer [34], the impulse response, h(n), of an FIR system can be described as:

h(n) =M∑

k=0

bkδ[n− k] ={bn, 0 � n�M0, otherwise

(7)

Here, n is used to denote discrete time samples, and bn is the response of the system at different discretetime samples, M is the time duration over which a response is obtained, and δ denotes the Dirac deltafunction. The filtering operation is illustrated in figure 6.

In figure 6, each ∆ represents a single sample delay. Since the structure of the filter is similar to thatof a tapped delay line, each delayed sample of x(n) is referred to as a ‘tap’, and the associated filtercoefficient, bk , as the ‘tap weight’. The total number of taps, M , which is also the length of the FIR filter,is known as the ‘mask length’ of the filter. For an input of x(n), the output of an FIR system is:

y(n) =M∑

k=0

bkx(n− k) (8)

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Figure 6. Filtering of input signal x(n)with a five-tap FIR filter.

The frequency response of this system, H(f), is given by:

H(f) =M∑

k=0

bk e−j 2πfk (9)

Alternatively, the frequency response can be written as the product of a magnitude response and a phaseresponse:

H(f) =∣∣H(f)

∣∣ exp(jφ(f)

)(10)

The filter coefficients, bn, in equation (8) are related to equation (9) by taking the inverse Fourier transformof the frequency response:

bn =W (n)[

12π

∫ π

−π

[∣∣H(f)∣∣ exp

(jφ(f)

)]exp(j 2πfn)df

], 0 � n�M (11)

Here, W (n) is used to denote the windowing function used to time-limit the inverse Fourier transform suchthat the number of filter coefficients, bn corresponds to the desired filter mask length. By manipulating themagnitude and phase response of H(f), FIR filters can be used to shape both the magnitude and phaseresponse of an input signal, x(n). Since the effect of an aberrating medium is to distort the phase spectrumof the signal, the ability of FIR filters to manipulate the input signal phase spectrum is particularly importantin adaptive imaging.

5.2. Matched filters

Range and velocity estimates in pulse-echo systems are frequently compromised by the addition of noisein the propagation channel. The filter applied to such noisy signals and which results in a maximizationof signal-to-noise power ratio the received signal is known as a matched filter. In the presence of additivewhite noise with constant power spectrum across all frequencies, the discrete-time received signal, r(n) is:

r(n) = s(n) +w(n) (12)

where s(n) is the uncorrupted desired signal, and w(n) is the noise incurred in the propagation path. Theoptimal matched filter in this case is an FIR filter with an impulse response [35]:

h(n) ={s∗(M − n), n <M0, n >M

(13)

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The impulse response is given by a time-reversed version of the desired signal, where ∗ denotes takingthe complex conjugate if s(n) is complex. The output is the autocorrelation of the function of the signalto which the filter is matched, in this case, s(n). Equivalently, in the frequency domain, the output signal,Y (f), is given by:

Y (f) =H(f)(S(f) +W (f)

)=

[S∗(f) exp(j 2πfM)

]S(f) +

[S∗(f) exp(j 2πfM)

]W (f)

=∣∣S(f)

∣∣2 exp(j 2πfM) (14)

The cross power spectrum between S∗(f) and W (f) is zero since the noise and signal are uncorrelated.In the presence of channel distortion, a priori knowledge of the desired signal for construction of the

matched filter is frequently lacking. Additionally, the channel distortion itself behaves like a filter, and thereceived signal is the convolution of the original signal with the impulse response of the channel. In thefrequency domain, the received signal, R(f), in the presence of channel distortion, Hd(f), is given by:

R(f) = S(f)Hd(f) = S(f)A(f) exp(−jφ(f)

)(15)

A(f) is the magnitude distortion imposed by the channel and φ(f) is the frequency-dependent phasedistortion. To estimate the matched filter, a reference signal in the form of a delta pulse is transmittedinto the medium, and the received signal is measured. The matched filter which leads to optimal signal-to-noise ratio in this case is the time-reverse of the received signal in the time domain. In the frequencydomain, the matched filter is written as:

H(f) = H∗d(f) =A(f) exp

(jφ(f)

)(16)

where Hd(f) denotes the estimate of the underlying channel distortion, Hd(f). If the estimate is exact, i.e.Hd(f) =Hd(f), the resultant signal after filtering with this estimated matched filter is:

Y (f) = S(f)Hd(f)H∗d(f) = S(f)A2(f) (17)

The important thing to note in equation (17), is that filtering the signal with the estimated matched filterresults in elimination of the phase spectral distortion, but a squaring of the amplitude distortion.

5.3. Inverse filter

To fully eliminate the channel distortion using a compensating FIR filter, an inverse filter is required. Forthe same channel distortion described in previous sections, the frequency response of the inverse filter isgiven by:

H(f) =1

Hd(f)=

1A(f) exp(−j 2πfϕ(f))

(18)

and the output of the received signal after application of the inverse filter is:

Y (f) = S(f)Hd(f)1

Hd(f)= S(f) (19)

In theory, an inverse filter leads to the elimination of both magnitude and phase spectral distortions bythe channel. However, an inverse filter is often not realizable practically, since the presence of zeroes inthe magnitude spectrum of the channel distortion function implies that the response of the inverse filterat these frequencies is infinite. Additionally, at frequencies where Hd(f) is small, the inverse filter has aresponse that is large. Any noise present at these frequencies will be amplified to very large magnitudes

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by the inverse filter. As such, the frequency range over which an inverse filter can be applied is often bandlimited to regions where Hd(f) is large. In regions whereHd(f) is small, it is assumed that the effect of thechannel distortion at these frequencies is negligible, and is left uncorrected by the inverse filter. The choiceof frequency ranges over which to derive and apply the inverse filter is rather arbitrary, and the design ofthe inverse filter involves weighing the noise immunity of the filter against the degree to which the channeldistortion is corrected for.

5.4. Time shift compensation as a phase shifting FIR filter

In the previous sections, the various algorithms used for estimating phase aberrations, and their relativemerits, were described. In this section, the focus is not on the estimation of the time shifts but in theprocess with which these estimates are used to compensate for the arrival time fluctuations (for the sakeof simplicity of notation, the spatial variables (x, y, z) are not shown in subsequent equations althoughthe aberrating medium can still vary over spatial position). If the compensating time shift estimate for thereceived signal at element i is τi, the signal, si(n) is time delayed by τi such that the corrected signal,yi(n), is given by si(n− τi). This time shift compensation process may be described mathematically as:

yi(n) = si(n− τi) = si(n) ∗ δ(n− τi) =M∑

k=0

bksi(n− k), bk ={

1 at k = τi0, otherwise

(20)

Comparing equation (20) to equation (8), used in describing the linear filtering process with an FIR filter, itcan be seen that time shifting the receive signal at the ith element is equivalent to filtering si(t) with an FIRfilter of mask length, M , in which all the filter coefficients, except for one, are zeroes. The single non-zerocoefficient has unity magnitude, and its position is given by the estimated time shift, τi. The mask lengthis calculated from the maximum range of time shifts desired divided by the time interval between samples.In the frequency domain, the effect of time shift compensation on the frequency spectrum of the receivedsignal, Si(f), can be described as:

Yi(f) = Si(f)Hi(f) = Si(f) exp(−j 2πτi) (21)

Time shifting of the received signal imposes a linear phase tilt on the spectrum of the received signal. Thegradient of the linear phase tilt is given by −2πτi. As such, time shift compensation is an FIR filteringprocess with a single degree of freedom where the position of the single real, unity-magnitude, filtercoefficient is selected within the mask length of the filter to impose different linear phase shifts on thereceived echo.

5.5. Time reversal focusing as a matched filter

Time reversal focusing, described earlier, can correct for any phase spectral distortions imposed bya distributed aberrating medium. However, time reversal focusing can also be thought of as a two-stepmatched filter operation applied on transmit within the FIR filter framework used here. This description isdiagrammed in the frequency domain in figure 7for a single element case. The response for an entire arrayof elements can then be constructed from the single element description through a process of superpositionof the single element responses. The initial transmitted signal, S(f) is distorted by the aberrating mediumwith the transfer function Hd(f) (= A(f) exp(−j 2πfφ(f))), such that the target is insonified with anaberrated pulse, that has a frequency response S(f)Hd(f). The echo from the target propagates throughthe aberrating medium again, and the signal measured by the receive aperture is S(f)[Hd(f)]2. The timereversal and retransmission of the received signal is equivalent to a matched filtering operation on transmitwith an FIR filter with complex filter coefficients and having the frequency response:

H(f) =(S(f)

[Hd(f)

]2)∗(22)

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Figure 7. Time reversal focusing as a matched filter applied on the transmitted signal. The transmittted signal from anelement, denoted S(f), propagates through an aberrating medium, modeled with transfer function Hd(f) to thetarget. The echoes from the target propagate through the medium and are received by the element. The received

echoes are time reversed, which in the frequency domain is a phase conjugation operation, (S(f)[Hd(f)]2)∗, andre-transmitted. The received echoes from the target when insonified by the re-transmitted signal is given as

(S(f)[Hd(f)]2)∗[Hd(f)]2.

In the second iteration, when the time reversed pulse is retransmitted into the aberrating medium, the targetis insonified with a transmitted acoustic signal:

(S(f)

[Hd(f)

]2)∗Hd(f) = S∗(f)A3(f) exp

(j 2πfφ(f)

)(23)

The received signal in this second iteration is:

(S(f)

[Hd(f)

]2)∗(Hd(f)

)2 = S∗(f)A4(f) (24)

The application of the matched filter on transmit has led to the elimination of the phase spectral distortion,φ(f), imposed by the aberrating medium, although any amplitude variations are emphasized. It is importantto note here that there are actually two sources of amplitude variations in the received signals from anaberrating medium. Attenuation in the propagating path of the acoustic pulse is one source of amplitudevariation, and is described by theA(f) term. Interference between acoustic signals that are out of phase witheach other form the second source of amplitude variations. The simplest example of amplitude variationsfrom interference is the total cancellation of two echoes of identical pulse shape, but with a phase differenceof a half wavelength, when these echoes are summed across a receive aperture. Time reversal corrects for theamplitude variations due to interference, but actually emphasizes the amplitude variations due to attenuativepath characteristics. Hence, a weakly attenuating medium, in which A(f) ∼= 1, is required for time reversal.

5.6. Time reversal focusing with attenuation compensation as inverse filtering

Time reversal focusing with attenuation compensation provides a technique that closely approximatesinverse filtering. If we assume that the attenuation present is a near field thin attenuator, all it does is scale thereceived echoes at each element. The attenuation function, A(f), is therefore constant with frequency, i.e.A(f) =A0. This can be seen within the linear filtering framework presented here. Equation (22) describesthe re-transmitted signal used for time reversal. With attenuation compensation, the re-transmitted signalbecomes:

H(f) =(S(f)

[1A0

Hd(f)]2)∗

(25)

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If we repeat the same steps as in equations (23) and (24) for the second iteration of transmit and receive,we get the following received signal:

(S(f)

[1A0

Hd(f)]2)∗(

Hd(f))2 = S∗(f) (26)

The received signal in equation (26) lacks an A(f) term, meaning that attenuation compensation on there-transmitted signal has been corrected for the attenuative path characteristics.

5.7. Summary of adaptive imaging techniques

Table 2.Summary of FIR filter descriptions of adaptive imaging algorithms.

Technique Characteristics of single channel FIR filter Type of aberration correction

Time shift compensation Single unity-magnitude filter coefficient atposition τi within M tap positions

Time shift of entire signal, or linearphase tilt in frequency domain

Time reversal focusing(matched filter)

Single FIR filter of M taps. Filter coefficientsare the time reverse of the received signal

Pulse shape distortion from interferenceand phase spectral distortion but notpulse shape distortion from attenuation

Time reversal withattenuation compensation(inverse filter)

Single FIR filter of M taps. Filter coefficientsare the time reverse of the received signalscaled by the inverse of the receivedamplitude

Pulse shape distortion frominterference, phase spectral distortionsand attenuation

6. Transducer arrays for adaptive imaging

Most ultrasonic scanners utilize 1D array transducers, typically with 128 active transmitting and receivingelectronic channels. Multiplexers are often used to sequentially address collections of 128 elements in alarger array, either to ‘walk’ the active array across a field-of-view or to combine echoes from sequentiallyaddressed elements to form high-resolution images. 1D arrays rely on an acoustic lens to focus beams in theelevation dimension and rely on electronic timing of transmitted and received pulse to focus beams in thelateral dimension. Recently, several manufacturers have introduced 2D arrays of the style shown in figure 8.These arrays are designed to improve the focusing of beams in the elevation dimension by providing someelectronic focusing in that dimension. The timing of pulses applied to elements is identical for elementsaxisymmetric about the array center in the elevation dimension. These elements can be wired together inorder to reduce the number of electronic channels required to address these elements.

Successful adaptive imaging requires that array elements be small enough in both dimensions toadequately sample the distortions in the echo wavefront. Elements which are large with respect to thespatial variations in the echo wavefront will integrate these distortions and degrade the ability to measureand adaptively compensate for them. Most researchers have measured effective rates of spatial variation inwavefronts distorted by tissue in the range from 0.2–0.5 cycles/mm. Adequate sampling of such distortionswould require element smaller than 1 mm in both dimensions. Currently, typical 1D arrays have elementheights of 3–10 mm and typical 2D arrays have element heights of 1–2 mm. Thus, the geometry of current2D arrays is likely to be suitable for adaptive imaging. However, the wiring together of symmetricallypaired elements, as shown figure 8b, would not be acceptable for adaptive imaging.

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(a) (b)

Figure 8. The array geometry shown in (a) is that of a 1D array. There are multiple elements sampling the azimuthaldimension, but only a single element in elevation. The element is much thinner in azimuth than in elevation. Focusingin elevation is achieved through a physical lens, and electronic time delay adjustments are not possible. The 2D array

geometry is shown in (b). The number of elements is much higher in azimuth than elevation, but the limited number ofelements in elevation still allows for electronic time delay adjustments for coarse elevation focusing and aberration

correction.

7. Current status of adaptive ultrasonic imaging systems

There are currently no commercially available adaptive ultrasonic imaging systems. The first real-timeadaptive imaging system was constructed in 1990 in a research phased array scanner at Duke Universityand implements the speckle-brightness algorithm on a 32-element, 3.1 MHz phased array scanner. Althoughthis system achieved impressive improvements in kidney and liver image quality when synthetic aberratinglayers were applied to the transducer, no aberrations were measured by the system during normal clinicalscanning. This is likely due to the relatively crude 80 ns precision of the timing delay quantization ofthe system and the use of a 1D array [36]. Using a modified speckle brightness algorithm, researchersat Siemens Medical Systems [37] have recently implemented a quasi-real time adaptive imaging systemon a 128 channel, 7.5 MHz array with very precise (8 ns) time delay quantization. The system showsdramatic image quality improvements in phantoms with synthetic aberrators, but more subtle effects in

(a) (b)

Figure 9. Examples of image quality improvement in ultrasound images using and adaptive imaging systemdeveloped at General Electric Medical Systems (Rigby et al. [38]). The corrected images (center, (a) and (b)) showsignificantly better definition of blood vessels and organ boundaries compared to the corresponding control images(left, (a) and (b)). The diagrams on the right identify the organs imaged. The corrected images also show improved

image brightness in the boxed regions indicated.

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normal clinical scanning. The authors attribute these limited clinical results to the use of a 1D transducerarray and the complexity of backscatter from tissues. Researchers at General Electric Medical Systems andthe University of Michigan [38] have recently introduced a quasi-real time adaptive scanner implementedon a 6 × 96, two-dimensional 3.5 MHz array. The system used a modified version of the nearest neighborcorrelation algorithm, called the beam sum-channel correlation method. This system is the first reportedreal-time adaptive system implemented on a 2D array and the initial results show impressive image qualityimprovements from adaptive imaging of the abdomens of adult males. Although this prototype systemhas significant limitations in its number of active channels (128 vs. 576 addressable elements) and in itsimaging rates, it demonstrates the potential of future adaptive imaging systems. Figure 9shows examplesof the image quality improvement realized by the General Electric system.

8. Future of adaptive ultrasonic imaging systems

Work at a number of academic and industry research laboratories has demonstrated the potential ofmarked improvement of ultrasonic image quality using adaptive imaging methods. Successful clinicalimplementation of real-time adaptive ultrasonic imaging will require the construction of scanners withfar more computational power than existing systems to implement even the simplest adaptive techniques.In addition, adaptive imaging will likely only yield significant clinical impact when systems’ active channelcounts greatly exceed the typical value today of 128 channels. Finally, adaptive imaging will require theavailability of high frequency 2D arrays which currently only exist in research laboratories.

Fortunately, the decreasing costs of computational circuitry and the increased sophistication andautomation of ultrasonic transducer fabrication techniques will likely make possible the commercialavailability of adaptive imaging systems within the next decade.

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