ω- k Algorithm for Sparse-Transmit Sparse-Receive Diverging Beam Synthetic Aperture Transmit Scheme
03 Jun 2020-IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 67, Iss: 10, pp 2046-2056
TL;DR: A fast and efficient frequency–wavenumber algorithm for the sparse DBSAT scheme and an additional novel step of recovering missing frame data due to sparse transmit is introduced, namely, projection onto elliptical sets (POES).
Abstract: In synthetic aperture (SA) imaging reported in the ultrasound imaging literature, typically, the delay and sum (DAS) beamformer is used; however, it is computationally expensive due to the pixel-by-pixel processing performed in the time domain. Recently, the adaptation of frequency-domain beamformers for medical ultrasound SA imaging, particularly to single-element/multielement synthetic transmit aperture (STA/MSTA) schemes, has been reported. In such reports, usually, less attention is paid to reducing system complexity. Recently, a sparse-transmit sparse-receive version of diverging beam-based synthetic aperture technique (DBSAT) was shown to achieve a reduction in system complexity by using fewer parallel receive channels, yet it achieves better quality and higher frame rate than conventional focused beamforming. However, this was also demonstrated using the DAS beamformer. In this work, we aim at achieving a reduction in computational cost, in addition to a reduction in system complexity, by implementing a fast and efficient frequency–wavenumber ( $\omega $ - ${k}$ ) algorithm for the sparse DBSAT scheme. In doing so, an additional novel step of recovering missing frame data due to sparse transmit is introduced, namely, projection onto elliptical sets (POES). The results from this novel combination of $\omega $ - ${k}$ with POES recovery showed that it is feasible to achieve several orders of magnitude faster reconstruction compared with the standard DAS beamforming, without any compromise in the image quality and, in some cases, with improved image quality. The average value of the contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) calculated from cyst at 15-mm depth obtained using the different schemes was 4.94 and 5.73 dB better when $\omega $ - ${k}$ was employed instead of DAS, respectively. In addition, for the sparse data set acquired with a 50% overlap during transmit and 64 active receive elements, DAS reconstruction takes as long as ~647 s, whereas the $\omega $ - ${k}$ algorithm takes only ~2 s when programmed and executed in MATLAB.
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TL;DR: In this article , a sparse-transmit scheme (with only 8 transmits) on Synthetic Transmit Aperture technique (sparse STA) was chosen to evaluate the beamformers ability to generate the high-resolution Ultrasound image.
6 citations
TL;DR: In this paper , the authors proposed two Fourier-domain beamformers (vs1 and vs2) for non-steered diverging wave imaging and an explicit interpolation scheme for virtual-source-based steered divergence wave imaging using a convex probe.
Abstract: Convex probes have been widely used in clinical abdominal imaging for providing deep penetration and wide field of view. Ultrafast imaging modalities have been studied extensively in the ultrasound community. Specifically, broader wavefronts, such as plane wave and spherical wave, are used for transmission. For convex array, spherical wavefront can be simply synthesized by turning all elements simultaneously. Due to the lack to transmit focus, the image quality is suboptimal. One solution is to adopt virtual sources behind the transducer and compound corresponding images. In this work, we propose two novel Fourier-domain beamformers (vs1 and vs2) for nonsteered diverging wave imaging and an explicit interpolation scheme for virtual-source-based steered diverging wave imaging using a convex probe. The received echoes are first beamformed using the proposed beamformers and then interpolated along the range axis. A total of 31 virtual sources located on a circular line are used. The lateral resolution, the contrast ( C ), and the contrast-to-noise ratio (CNR) are evaluated in simulations, phantom experiments, ex vivo imaging of the bovine heart, and in vivo imaging of the liver. The results show that the two proposed Fourier-domain beamformers give higher contrast than dynamic receive focusing (DRF) with better resolution. In vitro results demonstrate the enhancement on CNR: 6.7-dB improvement by vs1 and 5.9-dB improvement by vs2. Ex vivo imaging experiments on the bovine heart validate the CNR enhancements by 8.4 dB (vs1) and 8.3 dB (vs2). In vivo imaging on the human liver also reveals 6.7- and 5.5-dB improvements of CNR by vs1 and vs2, respectively. The computation time of vs1 and vs2, depending on the image pixel number, is shortened by 2-73 and 4-216 times than the DRF.
3 citations
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Additional excerpts
...Prior Work in Frequency-Domain Beamforming: The ω-k algorithm, also referred to as omega-k, range migration, Stolt migration, and so on in various studies, is originated from the field of seismic imaging [13], which was later...
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TL;DR: The paper describes the use of synthetic aperture (SA) imaging in medical ultrasound, where data is acquired simultaneously from all directions over a number of emissions, and the full image can be reconstructed from this data.
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