A Unifying Approach to Ultrasound Beamforming and Deconvolution Using ADMM

Beamforming is an essential step in the ultrasound image formation pipeline and has attracted growing interest recently. An important goal of beamforming is to improve the quality of the Point Spread Function (PSF), which is far from an ideal Dirac delta function in ultrasound imaging. Therefore, deconvolution as a well-known post-processing method is also used for mitigating the adverse effects of PSF. Unfortunately, these two steps have only been used separately in a sequential approach. Herein, a novel framework for combining both methods in ultrasound image reconstruction is introduced. More specifically, the proposed formulation is a regularized inverse problem including two linear models for beamforming and deconvolution plus additional sparsity constraint. We take benefits of the Alternating Direction Method of Multipliers (ADMM) algorithm to find the solution of the joint optimization problem. The performance evaluation is presented on a set of publicly available simulations, real phantoms, and in vivo data from the Plane-wave Imaging Challenge in Medical UltraSound (PICMUS). Furthermore, the superiority of the proposed approach in comparison with the sequential approach as well as each of other beamforming and deconvolution approaches alone are also shown. Results demonstrate that our approach combines the advantages of both methods and offers ultrasound images with high resolution and contrast.