A post-beamforming 2D pseudoinverse filter for coarsely sampled ultrasound arrays

Beamforming artifacts due to coarse discretization of imaging apertures represent a significant barrier toward the use of array probes in high frequency ultrasound (HFUS) applications. In this paper, we present a new design approach for two-dimensional (2D) regularized Pseudoinverse filters suitable for restoring imaging contrast in systems employing coarsely sampled arrays. The approach is based on a discretized 2D imaging model for linear arrays, and the imaging operator can be represented with a block Toeplitz matrix with the blocks them-selves being Toeplitz. With sufficiently large grid size in the axial and lateral directions, it is possible to replace this Toeplitz-block block Toeplitz (TBBT) operator with its circulant-block block circulant (CBBC) equivalent. This leads to a computationally-efficient implementation of the regularized Pseudoinverse filtering approach using the 2D fast Fourier transform (FFT). Using FIELD II, we present simulation data of the 2D point spread functions (PSFs) and a cyst phantom for imaging systems employing linear arrays with fine and coarse sampling of the imaging aperture. The 6-dB axial and lateral dimensions of the PSF, the main-lobe grating-lobe ratio (MGR) and contrast ratio (CR) are computed for the coarsely-sampled array with different levels of regularization to demonstrate the trade off between contrast and spatial resolutions. These results demonstrate approximate sigmoid functions with respect to log₁₀β which reveals a smooth, well-behaved regularization process of this algorithm.