Ultrasonics 38 (2000) 179–182www.elsevier.nl/locate/ultras

A multirate scan conversion method

C. Fritsch *, M. Parrilla, O. Martınez, D. JimenezInstituto de Automatica Industrial, La Poveda (Arganda), 28500 Madrid, Spain

Abstract

B-mode ultrasonic imaging requires that the acquired polar coordinate ultrasound data be converted to the Cartesian formatused by digital monitors. Image quality depends on the interpolation algorithm used to this purpose. In this work a selectivesampling technique, based on acquiring data at specific points of the scanned area together with a straightforward linearinterpolation step, is proposed. Hardware complexity is avoided, because the interpolation task can be carried out by software inreal time, concurrently with data acquisition. The performances of the proposed approach are analysed with regard to thoseprovided by other algorithms and some implementation issues are addressed. © 2000 Elsevier Science B.V. All rights reserved.

Keywords: Digital ultrasound; Echography; Interpolation; Real time; Scan conversion

1. Introduction system to obtain an ideally exact scan converted image[2,3]. However, this method is impractical owing to the

Pulse-echo B-mode sectorial imaging uses a scan infinite extent of the sinc function.conversion process to map the polar data acquired in Approximate scan conversion methods have beenthe spatial domain to the Cartesian coordinates used by investigated in the search for accuracy, speed and sim-digital monitors. Interpolation is required to avoid arti- plicity. Interpolation with cubic splines yields goodfacts, such as moire effects, which appear when the results [4], although it is computing intensive. A fasterspace is undersampled [1]. The number of ultrasonic method with similar performance is bilinear interpola-beams N is limited by the two-way transit time up to a tion from a set of samples surrounding every pixel,depth R, the ultrasound propagating at velocity c, and although an important hardware support is required toby the required frame rate f by: achieve the computations in real time [5]. The nearest

neighbour interpolation algorithm (NNIA) assigns toN≤c/2Rf. (1)every pixel the value of the nearest sample in the spatial

On the other hand, all the H×V pixels of a screen domain. The method can be software implemented indisplaying a sectorial image of angle h will be completely real time if look-up tables with the correspondencefilled only if the number of equally spaced beams is at (x, y)�(r, w)�(sample index, scan line number) areleast: built. Acceptable images are obtained if a large number

of beams is available, but this is not the usual case; withlow sampling densities, the image quality is poor [6 ].N≥Vh=

Hh

2 sin(h/2), (2)

Application of the NNIA to linearly interpolatedoversampled vectors has been shown to give good imageswhich might come into conflict with Eq. (1). For exam-[7], although it requires a high data bandwidth andple, if h=p/2, H=500, 556 beams are needed, but ifstorage resources. These techniques use uniform sam-R=0.15 m, c=1500 m s−1, f=25 Hz, no more than 200pling of the polar spatial domain. The uniform ladderscan lines will be available and some interpolationalgorithm changes the sampling frequency at every scanprocess is required. The continuous representation of aline, trying to match sample-to-pixel positions. A linearsampled image can be obtained by convolution with ainterpolation in Cartesian coordinates is carried out forsinc function and then resampled in the new coordinateunfilled pixels [8]. The method shows advantages butrequires fast and accurate frequency switching circuits* Corresponding author. Fax: +34-1-871-70-50.

E-mail address: carlos@iai.csic.es (C. Fritsch) which keep phase coherence [9]. Also, interpolation in

0041-624X/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved.PII: S0041-624X ( 99 ) 00044-X

180 C. Fritsch et al. / Ultrasonics 38 (2000) 179–182

Fig. 1. (a) Division in regions; (b) Creation of virtual segments by interpolation.

Cartesian rather than in polar coordinates tends toproduce blocky images.

2. The selective sampling technique (SST )

Ultrasonic information is not isotropic, since reso-lution is usually higher in the radial than in the angulardirection. The proposed SST exploits this fact using ahigh sampling rate. Nevertheless, a moderate data flowis kept by selecting only those data samples which areused either for display or for a simple linear interpola-tion process.

Ideally, the spatial sample positions should matchthe pixel positions, which requires a huge number of Fig. 2. The SST process: samples are selected for assignment (S1) orscan lines, in the order of hV2/2. However, because of for interpolation (S2–S5). Pixels A and C are in region 3, pixel B inthe limited lateral resolution, a smaller number of beams region 2. Q2 and Q3 values are not evaluated.should provide a good approximation, as long as thesampling rate is kept high enough (Eq. (2)). If N beams corresponding ‘near’ pixel. With Dh=h/(N−1), theare uniformly distributed on a sector of h rad and the maximum number of regions in a sector image is givenmaximum acceptable distance from any pixel to a scan by:line is d, all the pixels up to a radius

M=INT+[ log2(V Dh/d ], (4)

rk≤2kd(N−1)/h (3)

where INT+(x) is the first integer greater than x. Forwill have a distance less than 2kd to some scan line. typical values: V<500, Dh<p/200, d>0.5, M≤4 and,Dividing the sector in regions limited by radii at most, there will be seven different interpolating[rk, rk+1], k=1, 2, … (Fig. 1(a)) and creating 2k−1−1 coefficient values. If the same number of look-up tables

equispaced virtual scan segments between each two are built in the display computer with interpolationadjacent real scan lines in every region k (Fig. 1(b)), results, this process is reduced to a memory access, fastthe distance from any pixel to a real or virtual scan line enough for real-time execution. For 8 bit samples, justwill be less than d. Linear interpolation of the values of 0.5 MB of (cheap) main memory is required.real samples in adjacent scan lines yields virtual sample Fig. 3 shows a possible SST architecture. A 1 bitvalues. The interpolation coefficients used for virtualsegment i in region k, i=1, …, 2k−1, are c

ik=i/2k−1 and

1−cik

, respectively. Only those samples which are usedfor interpolation, or those that directly are the nearestneighbour of a pixel are actually acquired. In Fig. 2, thevalue of sample S1 is directly assigned to pixel A, whileS2 and S3 (in region k=2), are used to obtain the valueof Q1=(S2+S3)/2, which is assigned to pixel B. Also,S4 and S5 (in region k=3) are used to obtain the valueof Q4=(S4+3S5)/4, assigned to pixel C; the values of

Fig. 3. Diagram of a SST architecture.Q2 and Q3 are not computed, since they do not have a

181C. Fritsch et al. / Ultrasonics 38 (2000) 179–182

Fig. 4. Reference image of the sponge phantom after oversampling and bilinear interpolation.

recirculating shift register is pre-loaded to select, from a further bilinear interpolation process with doubleprecision floating point arithmetic is used to obtain thethe data flowing out of the A/D, only those samples

that are used for the display and interpolation processes. reference image R (Fig. 4). Pruning the original B-scanby factors p={2, 3, 4, 5} gives the B

psector scans setThe length of the shift register has to be at least equal

to the number of samples needed and can be easily of {257, 171, 129, 103} lines, respectively. Image Gpq

result from Bp

by application of algorithm q: (1) NNIA,implemented with a single chip SRAM with some con-trol logic. A FIFO buffer interfaces the SST logic with (2) BILINear interpolation, (3) STANDARD sampling

(two samples per pixel in the central vector, equivalentthe display computer.to an 8.7 MHz sampling rate) with bilinear interpolationand, (4) SST with d=0.5.

3. Experiments

Experiments were carried out with a sponge phantom4. Results and discussionusing a 5 MHz focused transducer. A total of 513 scan

lines on a 75° sector are acquired at 40 MHz (8 bit, 2KThe signal-to-noise (SNR) power rate for eachsamples per line). The image size is determined by Eq.

method summarised in Table 1 is computed as:(2): H×V=477×392 pixels (477×222, dropping thedelay). Such high sample density (Dh<0.15°, SNR=10 log[∑ (R−G

pq)2/∑R2 ] dB. (5)

Dr<20 mm) would provide a nearly optimal image justBilinear interpolation provides the best performance ifapplying the NNIA. However, for comparison purposesapplied with double precision floating point arithmetic

Table 1 to oversampled A-scan vectors (as with NNIA).SNR (dB) of various methods with different numbers of scan lines However, if applied to the standard sampled vectors the

performance is poor, even lower than that with NNIA.N ( lines) NNIA BILIN STANDARD SSTBy contrast, SST provides an SNR near to that of

257 18.3 27.8 12.2 24.5 bilinear interpolation but with simpler arithmetic.171 15.2 20.6 11.9 19.9 Although not shown, using double precision floating129 12.9 16.6 11.3 16.3 point arithmetic for the SST linear interpolation does103 11.3 14.4 10.7 14.2

not produce any practical improvement (<0.2 dB).

Table 2Number of samples required to form an image with different methods

N ( lines) NNIA and BILIN STANDARD SST

Total ( KS) S/line Total (KS) S/line Total (KS) S/line (ave)

257 526 2048 114 444 131 510171 350 2048 76 444 124 726129 264 2048 57 444 117 909103 211 2048 46 444 112 1084

182 C. Fritsch et al. / Ultrasonics 38 (2000) 179–182

The number of samples required by every method is the display processor, and the simple interpolation pro-cess can be achieved by software in real time using ashown in Table 2. The NNIA and BILIN use a large

amount of data (2048N ) and the standard method, the small set of look-up tables in the main memory of thedisplay processor.smallest amount (444N ). The SST handles a moderate

and rather constant number of samples; although theaverage number of samples per line increases withdecreasing N, the total number of selected samples Acknowledgementdecrease with the number of scan lines.

This work has been supported by CICYT grant nr.TAP97-0662-C02-01.

5. Conclusions

ReferencesA selective sampling technique (SST) for scan conver-

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