Convergence Gain in Compressive Deconvolution: Application to Medical Ultrasound Imaging

The compressive deconvolution (CD) problem represents a class of efficient models that is appealing in high-resolution ultrasound image reconstruction. In this paper, we focus on designing an improved CD method based on the framework of a strictly contractive Peaceman–Rechford splitting method (sc-PRSM). By fully excavating the special structure of ultrasound image reconstruction, the improved CD method is easier to implement by partially linearizing the quadratic term of subproblems in the CD problem. The resulting subproblems can obtain closed-form solutions. The convergence of the improved CD method with partial linearization is guaranteed by employing a customized relaxation factor. We establish the global convergence for the new method. The performance of the method is verified via several experiments implemented in realistic synthetic data and in vivo ultrasound images.