Jensen, Jørgen Arendt

Nikolov, Svetoslav I

Tomov, Borislav Gueorguiev

Modern ultrasound scanners utilize digital beamformers that operate on sampled and quantized echo signals. Timing precision is of essence for achieving good focusing. The direct way to achieve it is through the use of high sampling rates, but that is not economical, so interpolation between echo samples is used. This paper presents a beamformer architecture that combines a band-pass filter-based interpolation algorithm with the dynamic delay-and-sum focusing of a digital beamformer. The reduction in the number of multiplications relative to a linear perchannel interpolation and band-pass per-channel interpolation architecture is respectively 58 % and 75 % beamformer for a 256-channel beamformer using 4-tap filters. The approach allows building high channel count beamformers while maintaining high image quality due to the use of sophisticated intersample interpolation

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Downloaded from orbit.dtu.dk on: Dec 18, 2017Scalable Intersample Interpolation Architecture for High-channel-count BeamformersTomov, Borislav Gueorguiev; Nikolov, Svetoslav I; Jensen, Jørgen ArendtPublished in:Proceedings of the 2011 IEEE International Ultrasonics SymposiumLink to article, DOI:10.1109/ULTSYM.2011.0091Publication date:2011Document VersionEarly version, also known as pre-printLink back to DTU OrbitCitation (APA):Tomov, B. G., Nikolov, S. I., & Jensen, J. A. (2011). Scalable Intersample Interpolation Architecture for High-channel-count Beamformers. In Proceedings of the 2011 IEEE International Ultrasonics Symposium (pp. 381-384). IEEE. DOI: 10.1109/ULTSYM.2011.0091Paper presented at the IEEE International Ultrasonics Symposium, Orlando Florida, 2011:Scalable Intersample Interpolation Architecture for High-channel-count BeamformersBorislav Georgiev Tomov1Svetoslav Ivanov Nikolov2Jørgen Arendt Jensen11Center for Fast Ultrasound Imaging,Biomedical Engineering group, Department of Electrical Engineering, Bldg. 349,Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark2R&D Applications & Technologies, BK Medical, DK-2730 Herlev, DenmarkTo be published in Proceedings of IEEE International Ultrasonics Symposium, Orlando Florida, 2011.Scalable Intersample Interpolation Architecture forHigh-channel-count BeamformersBorislav Georgiev Tomov1, Svetoslav Ivanov Nikolov2 and Jørgen Arendt Jensen11Center for Fast Ultrasound Imaging, Dept. of Elec. Eng. Bldg. 349,Technical University of Denmark, DK-2800 Lyngby, Denmark2R&D Applications & Technologies, BK Medical, DK-2730 Herlev, DenmarkAbstract— Modern ultrasound scanners utilize digital beam-formers that operate on sampled and quantized echo signals.Timing precision is of essence for achieving good focusing. Thedirect way to achieve it is through the use of high sampling rates,but that is not economical, so interpolation between echo samplesis used. This paper presents a beamformer architecture thatcombines a band-pass filter-based interpolation algorithm withthe dynamic delay-and-sum focusing of a digital beamformer. Thereduction in the number of multiplications relative to a linear per-channel interpolation and band-pass per-channel interpolationarchitecture is respectively 58 % and 75 % beamformer for a256-channel beamformer using 4-tap filters. The approach allowsbuilding high channel count beamformers while maintaininghigh image quality due to the use of sophisticated intersampleinterpolation.I. INTRODUCTIONMedical ultrasound imaging is a well-established diagnosticmodality, characterized by short preparation time, lack of sideeffects, portability and a low price compared to other imagingmodalities. The vast majority of commercial ultrasound scan-ners feature a digital beamformer and employ a delay-and-sumfocusing of the digitized echo signals from the tissue [1]. Thequality of the focusing is directly dependent on the timingprecision with which it is done [2].For perfect alignment of the echo signals, echo samples forspecific moments in time must be available from all receivechannels of a beamformer. One way to provide them (withsmall error) is to sample the echo signal at very high frequency,but that is not economical. Another way for achieving focusingprecision is to use interpolation between the input samples.Experiments have been done with linear, polynomial and band-pass filtering interpolation [3]. Linear interpolation is oftenused, since it requires the least amount of hardware comparedto other interpolation techniques.A filter-based interpolation provides much better results thanlinear interpolation, but requires several multiplication opera-tions per sample (several multipliers per input channel). Also,several sets of filtering coefficients must be kept by each filter,and a set is selected for use for each output sample, dependingon its intersample position (the fractional part of the focusingdelay).Using large number of channels in ultrasound beamformersprovides significant benefits, such as higher signal-to-noiseratio, better focusing, and the ability to handle 2-dimensionalarrays that allow 3-dimensional (volume) imaging. In suchτ1 a1τ2 a2 τ3 a3τN−1 aN−1τN aNFocal point(scatterer)Array elements Delay lines Apodization coefficientsAdderFig. 1. Delay-and-sum focusing.beamformers, filter-based interpolation would require linearlyincreasing amounts of logic and memory for its implementa-tion.This paper presents methods for combining the filter-basedinterpolation with the focusing and summing logic, thusgreatly reducing the computational and the coefficient storagedemands in high channel count systems. The principles andthe beamformer architectures are presented in Section II, andan image quality comparison to a conventional architecture ispresented in Section III.II. COMPUTATIONAL ALGORITHMA. Digital beamformer operationA digital beamformer samples and quantizes the receivedecho signals using analog-to-digital converters (ADCs) andsubsequently applies weights on the samples across the chan-nels. Samples are picked from each channel according to adelay profile for the target output sample, and summed. Theprinciple is illustrated in Fig. 1. For an I-channel beamformer,the output samples are summed as follows:so(n) =I∑i=1si(i, dN (i, n))w(i, n) (1)where si is the sampled echo signal signal, i is a channelindex, n is the sample index, w is a weighting coefficient anddN is an input sample index, calculated as the rounded to aninteger part of flight time converted in clock cycles of thesampling frequency fs:d(i, n) =fs(pf (i, n) + pr(i, n))c(2)0 2 4 6 8 10 12 14 16−1−0.500.51FilterCoefficient value0 2 4 6 8 10 12 14 16 18−1−0.500.51Signal valueSignal0 2 4 6 8 10 12 14 16−2−1012Result valueResultSample indexFig. 2. Filtering of an upsampled signal: The differently colored subsets ofthe filter coefficients create the identically colored output samples.where pf is the distance between the beam origin and thecurrent focal point, pr is the distance between the focal pointand the receiving element, and c is the speed of sound. Thismethod only picks out the nearest neighbor sample and leadsto large sidelobes in the point spread function [3]. Some formfor interpolation is, thus, needed.B. Intersample interpolation through filtrationA signal can be upsampled by inserting zeros between con-secutive input samples. Applying a bandpass filter on the resultgenerates an upsampled output stream containing samples fortime instances between those of the samples of the input signal(Fig. 2). The bandpass filter can be split into coefficient sets,which are used to selectively produce inter-sample values.Filtering with such coefficient sets is used for implementingsub-sample timing precision in a digital beamformer. Everyinput channel of the digital beamformer has its own filter blockwith selectable coefficient sets (illustrated in Fig. 3). A high-channel-count beamformer would require a large number ofmultipliers and RAM for storing of these identical groups offilter sets.On each beamformer channel, a filter is applied on the inputsamples once per output sample. For channel i out of I totalchannels, the operation isso(i, n) =K∑k=1si(i, j(k, dN (i, n)))g(k,MF (i, n)) (3)where k is a filter coefficient index in a K-tap filter, so is anoutput sample, si is an input sample, n is an output sampleindex, j is a local sample index for the current filtrationoperation, dN is the integer part of the focusing index, and g isa filter coefficient. MF is a filter set index, which depends onthe fractional part of the d(i, n), as calculated in 2. Whenprecision of 1P of a sampling interval is desired, MF cansamplesinputFilterWeightingbeamformer channeloutputsamplesFig. 3. FIR-filter-interpolation beamformer.take values between 1 and P , thus selecting one out of thenecessary P interpolation filters.A focused sample sfo consists of the sum of apodizedchannel contributions:sfo(n) =I∑i=1so(i, n)w(i, n) (4)where w is a channel weighting coefficient, whose magnitudedepends on the channel index and the depth from which theecho samples arrive.By substituting so from (3), the expression for the focusedsample becomessfo(n) =I∑i=1K∑k=1(si(i, j(k, dN (i, n)))g(k,MF (i, n)))w(i, n)(5)For every subset of channels [ib : ie] for which the filter setindexes MF =M are the same, the expression describing thesum for that subset issfo(n) =ie∑i=ibK∑k=1(si(i, j(k,MF (i, n)))g(k,M))w(i, n) ==K∑k=1g(k,M)ie∑i=ibsi(i, j(k, dF (i, n)))w(i, n)(6)The whole set of channels can be divided into the mentionedsubsets, though some subsets will consist of only one channel.UpsamplingWeightingFilter output samplesinputsamplesAdder treebeamformer channelFig. 4. Beamformer architecture utilizing non-uniform upsampling before summing across channels and filtration.0 5 10 15 20 2500.0050.010.015Focal depth, λDelay,sFig. 5. Example for focusing delay development for the center element (gray)and an outer element (black) of a phased array transducer.C. Filtration of the sum of non-uniformly upsampled inputstreamsWe suggest an architecture that moves the filtration after thesum across channels, using a tree-like pipelined adder struc-ture, operating at a higher frequency (illustrated on Fig. 4).The signal from each input channel is upsampled P times,where P is the number of subsample positions that provide adesired timing precision. The intersample interpolation filters,used in a per-channel filtration, here are combined back intothe filter from which they are made, and that one is applied onthe sum of upsampled input streams at the output sample rate.Whenever the focusing demands it, an upsampled input streamis delayed or advanced relative to the others by a sample. Thisintroduces an error in the filtration, as the non-zero sampleson the affected stream will not be equally spaced, and theirfiltration will not be made using filter coefficients belongingto the same interpolating filter.A focusing index development is illustrated in Fig. 5. Itshows that for the element at the image line origin, thefocusing indexes grow in a straight line, meaning that theintersample distance (in time) stays the same. The filtrationof that sample stream does not introduce errors. The non-uniform upsampling is required for elements for which thedelay curve is not a straight line. The error has a randomnature, as every imperfection may add or subtract from theDepth, mmPer−channel interpolation−5 −4 −3 −2 −1 0 1 2 3 4 51010.51111.51212.5Depth, mmLateral distance, mmCombined interpolation−5 −4 −3 −2 −1 0 1 2 3 4 51010.51111.51212.5Fig. 6. Contour plot of the point spread function for depth of 1 cm, withisolines at -6, -20, -40, and -60 dB relative to the peak.ideal filtration result.III. RESULTSThe effect of the error, introduced by non-uniform upsam-pling, is investigated by simulating ultrasound imaging withField II [4], [5] of three point reflectors, placed 1, 4, and 7cm away from a 128-element λ-spaced 7 MHz linear array,emitting a 2-cycle pulse at the transducer center frequency.The transmit focal point is at depth of 4 cm. Dynamic receivefocusing is used with Hamming apodization and expandingaperture with an F-number of 2. An image consisting of 48lines was created. Contour plots of the point reflector imagesare shown in Fig. 6 for depth of 1 cm, in Fig. 7 for depthof 4 cm, and in Fig. 8 for depth of 7 cm. Black, red, greenand gray isolines indicate levels of -6, -20, -40, and -60 dBrelative to the peak. Per-channel interpolation and combinedinterpolation are compared.For a 256-channel beamformer using 4-tap interpolationfilters and 1/16th intersample precision, the length of theDepth, mmPer−channel interpolation−4 −3 −2 −1 0 1 2 3 439.84040.240.440.640.8Depth, mmLateral distance, mmCombined interpolation−4 −3 −2 −1 0 1 2 3 439.84040.240.440.640.8Fig. 7. Contour plot of the point spread function for depth of 4 cm, withisolines at -6, -20, -40, and -60 dB relative to the peak.Depth, mmPer−channel interpolation−5 −4 −3 −2 −1 0 1 2 3 4 569.57070.571Depth, mmLateral distance, mmCombined interpolation−5 −4 −3 −2 −1 0 1 2 3 4 569.57070.571Fig. 8. Contour plot of the point spread function for depth of 7 cm, withisolines at -6, -20, -40, and -60 dB relative to the peak.combined filter will be 64 coefficients (requiring 64 multi-pliers or multiplication operations). In all cases, a multiplieris necessary for each channel for implementing apodization(weighting). Linear interpolation requires two multiplicationsper channel per output sample. The combined architecturerequires 256 + 64 = 320 multiplications per output sampleversus 256*(2+1) = 768 when using per-channel linear inter-polation (58.3 % savings) and 256*(4+1) = 1280 when usingper-channel bandpass interpolation (75 % savings). For a 1024-channel design, the savings are correspondingly 64.6 % (1088vs. 3072) and 78.7 % (1088 vs. 5120).IV. DISCUSSIONThe introduced error through non-uniform upsampling islargest in the situation where the intersample distance differsmost to that for the channel at the beam origin. The errordecreases as the delay profile of a channel straightens andstarts approaching the straight line that is the delay profile ofthe center channel (illustration in Fig. 5). The use of expandingaperture and windowing means leads to avoiding the situationswith worst-case injected error. The simulation shows verysmall deterioration in PSF, mainly in low depths.V. CONCLUSIONThe post-delay band-pass interpolation provides the preci-sion of band-pass interpolation, combined with computationalrequirements that are much lower than those of linear in-terpolation, making it suitable for use in high-channel-countbeamformers.ACKNOWLEDGMENTThis work was supported by grant 9700883, 9700563 and26-04-0024 from the Danish Science Foundation and by B-KMedical Aps. This project is also supported by grant 024-2008-3 from the Danish Advanced Technology FoundationREFERENCES[1] B. D. Steinberg. Digital beamforming in ultrasound. IEEE Trans.Ultrason., Ferroelec., Freq. Contr., 39:716–721, 1992.[2] S. Holm and K. Kristoffersen. Analysis of worst-case phase quantizationsidelobes in focused beamforming. IEEE Trans. Ultrason., Ferroelec.,Freq. Contr., 39:593–599, 1992.[3] J. Kortbek, H. Andresen, S. Nikolov, and J. A. Jensen. Comparinginterpolation schemes in dynamic receive ultrasound beamforming. InProc. IEEE Ultrason. Symp., pages 1972–1975, 2005.[4] J. A. Jensen. Field: A Program for Simulating Ultrasound Systems. Med.Biol. Eng. Comp., 10th Nordic-Baltic Conference on Biomedical Imaging,Vol. 4, Supplement 1, Part 1:351–353, 1996.[5] J. A. Jensen and N. B. Svendsen. Calculation of Pressure Fields fromArbitrarily Shaped, Apodized, and Excited Ultrasound Transducers. IEEETrans. Ultrason., Ferroelec., Freq. Contr., 39:262–267, 1992.

Scalable Intersample Interpolation Architecture for High-channel-count Beamformers

null Borislav Georgiev Tomov

Svetoslav Ivanov Nikolov

Jorgen Arendt Jensen

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Scalable intersample interpolation architecture for high-channel-count beamformers

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Scalable Intersample Interpolation Architecture for High-channel-count Beamformers

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