Comparing interpolation schemes in dynamic receive ultrasound beamforming

In medical ultrasound interpolation schemes are of- ten applied in receive focusing for reconstruction of image points. This paper investigates the performance of various interpolation scheme by means of ultrasound simulations of point scatterers in Field II. The investigation includes conventional B-mode imaging and synthetic aperture (SA) imaging using a 192-element, 7 MHz linear array transducer with λ pitch as simulation model. The evaluation consists primarily of calculations of the side lobe to main lobe ratio, SLMLR, and the noise power of the interpolation error. When using conventional B-mode imaging and linear interpolation, the difference in mean SLMLR is 6.2 dB. With polynomial interpolation the ratio is in the range 6.2 dB to 0.3 dB using 2nd to 5th order polynomials, and with FIR interpolation the ratio is in the range 5.8 dB to 0.1 dB depending on the filter design. The SNR is between 21 dB and 45 dB with the polynomial interpolation and between 37 dB and 43 dB with FIR filtering. In the synthetic aperture imaging modality the difference in mean SLMLR ranges from 14 dB to 33 dB and 6d B to 31 dB for the polynomial and FIR filtering schemes respectively. By using a proper interpolation scheme it is possible to reduce the sampling frequency and avoid a decrease in performance. When replacing linear interpolation with a more advanced interpolation scheme it is possible to obtain a reduction of 18 dB and 33 dB in the SLMLR for the B-mode and SA imaging, respectively, and an improvement in SNR of 24 dB. I. INTRODUCTION In medical ultrasound receive focusing is a core signal processing element used for reconstruction of image points from the received transducer signals in both conventional and synthetic aperture imaging. In the delay-and-sum beamformer a sample is selected from each of the receive channels corresponding to the echo of the image point target. The sample index is based on the total transmit-receive time-of- flight. Due to the continuous nature of the time-of-flight, it will not necessarily lie at the discrete time indices of the sampled channel data. Thus, some form of interpolation is needed and this heavily influences the image quality and the hardware complexity for implementation. By using a proper interpolation scheme it is possible to reduce the sampling frequency or to improve performance. The investigation in this paper is based on the work of Henrik Andresen (1) and quantifies the change in performance as a function of interpolation type applied by means of ultrasound simulations of point scatterers in Field II (2). This paper introduces the beamformation toolbox, BFT2 which is used in the investigation. BFT2 (3),(4), developed at CFU is written in C and has a Matlab program interface. It performs dynamic receive focusing and offers choices between static or dynamic apodization and various interpolation schemes. The interpolation schemes investigated include linear, polynomial, and upsampling and FIR filtering. Various order polynomials and FIR filters are investigated. II. DESCRIPTION The investigation in this paper on the influence of the choice of interpolation scheme includes conventional B-mode imaging and synthetic aperture imaging (SAI). The ultrasound RF signals for the investigation is created using Field II and the beamforming is performed with BFT2. From a reference data set an evaluation data set is created, which is used for the evaluation. For the evaluation the point-spread function, PSF is useful when observing the characteristics of different imaging modalities. It is highly affected by the type of transmit-receive focusing used, and is, thus, also affected by the interpolation in receive beamforming. The lateral part of the PSF is especially interesting in terms of spatial distribution and amplitude of the side-lobe energy, which again directly affects the image contrast. The evaluation and comparison of interpolation schemes is done by partly observing the lateral PSF and quantizing the main-lobe and side-lobe energy distribution in terms of the full-width-half-maximum, FWHM and the side-lobe-main-lobe-ratio, SLMLR and partly by the noise power of the interpolation error. The FWHM and the SLMLR are calculated in the horizontal plane at the depth of each of the point scatterers and compared to the case where the reference data is used. A. Simulation setup The ultrasound RF signals for the investigation is created us- ing Field II with a 192-element, 7 MHz linear array transducer with λ pitch as simulation model and a 3-cycle sinusoid as excitation. The simulation is based on point scatterers placed at a depth of 10 mm to 80 mm with 5 mm between each, placed along the center of the transducer. A reference RF data set has been created using a sampling frequency of 1 GHz and linear interpolation and the evaluation RF data set is created by decimating the reference data (picking out samples) to a sampling frequency of 40 MHz. Two data sets are created. One by using conventional B-mode imaging, and one by using