A Computationally Efficient Non-Linear Beamformer Based on pth Root Signal Compression for Enhanced Ultrasound B-Mode Imaging
Résumé
Background, Motivation and ObjectiveTo improve quality of focused ultrasound images, the non-linear Filtered-Delay Multiply And Sum (F-DMAS) beamformer (DOI: 10.1109/TMI.2014.2371235) was recently proposed as an alternative to the common Delay And Sum (DAS). Given the higher computational cost as compared to DAS, in this paper we propose a simplified version of FDMAS, which consists in applying DAS to the square root of the RF signals, followed by squaring and band-pass filtering. The lowered computational cost allows the use of the proposed beamformer in high frame-rate imaging, such as ultrafast imaging, or in 3D imaging. Besides, we generalize the method to the pth root case, referred to as F-DAS1/p.Statement of Contribution/MethodsTo reconstruct one image line, the DAS beamformer performs the sum of the N received and delayed RF signals (si). F-DMAS instead computes the sum of the signed square roots of the (N2-N)/2 cross-products of si pairs. The cross-products, representing the aperture auto-correlation function, are responsible for the better resolution, while square roots preserve signal dimensionality. The F-DMAS algebraic formulation can be rearranged as the difference between the squared sum of the signed square roots of si, and the sum of the absolute values of si. The proposed F-DAS1/2 computes the squared sum of the signed square roots of si, thus approximating F-DMAS by eliminating the second term of the difference, which is shown to be negligible. The same formulation is used for F-DAS1/p, by computing the sum of the signed pth roots of si and the pth power of the resulting output.Results/DiscussionPoint Spread Functions (PSFs) and cyst phantom images were simulated using DAS, F-DMAS, F-DAS1/2, F-DAS1/3, and a 192-element linear array with 12 MHz excitation signals. In F-DMAS and F-DAS1/p, RF beamformed data were band-pass filtered to select the frequency band shifted by non-linear operations. Performance equivalence between F-DAS1/2and F-DMAS is demonstrated by a normalized mean squared error of RF-images lower than 1%, and very similar PSF profiles and Contrast-to-Noise Ratios. Moreover, as p increases, the main lobe width decreases, side lobes are reduced (Figure 1) and the cyst Contrast Ratio is enhanced (DAS: -43.6 dB, F-DAS1/2: -62.7 dB, F-DAS1/3: -76.1 dB). The proposed FDAS1/p has thus proved to achieve the same or better performance as F-DMAS with a lower computational cost.