A Unifying Approach to Inverse Problems of Ultrasound Beamforming and Deconvolution

Beamforming is an essential step in the ultrasound image formation pipeline and has recently attracted growing interest. An important goal of beamforming is to increase the image spatial resolution, or in other words to narrow down the system point spread function. In parallel to beamforming approaches, deconvolution methods have also been explored in ultrasound imaging to mitigate the adverse effects of PSF. Unfortunately, these two steps have only been considered separately in a sequential approach. Herein, a novel framework for unifying beamforming and deconvolution 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 advantage of the alternating direction method of multipliers 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. Furthermore, the superiority of the proposed approach in comparison with the sequential approach as well as each of the other beamforming and deconvolution approaches alone is also shown. Results demonstrate that our approach combines the advantages of both methods and offers ultrasound images with superior resolution and contrast.