Weighted Non-Convex Penalty Minimization for Compressed Ultrasound Signal Reconstruction

The reconstruction of high quality images from a limited number of radio-frequency (RF) measurements is crucial for ultrafast plane wave ultrasound (PWUS) imaging system. The sparse and low rank model can efficiently exploit the correlation between different ultrasound channels. However, the reconstruction strategies derived from sparse models use convex relaxations of the matrix l1 norm to induce sparsity, and convex approximations are widely known to result in biased estimators, which usually underestimates the coefficient amplitudes of RF signals in the frequency domain. In this work, we designed a weighted nonconvex penalty (WNCP) to extract sparsity more strongly than the l1 norm to alleviate the bias issue, aiming at reducing reconstruction errors. An optimization algorithm based on simultaneous direction method of multipliers (SDMM) is proposed to evaluate the effectiveness through in vivo data from PICMUS dataset. Results show the proposed method obtains a B-mode image quality superior to that obtained through our previous method.