Ultrasound compressive deconvolution with ℓP-Norm prior

It has been recently shown that compressive sampling is an interesting perspective for fast ultrasound imaging. This paper addresses the problem of compressive deconvolution for ultrasound imaging systems using an assumption of generalized Gaussian distributed tissue reflectivity function. The benefit of compressive deconvolution is the joint volume reduction of the acquired data and the image resolution improvement. The main contribution of this work is to apply the framework of compressive deconvolution on ultrasound imaging and to propose a novel `p-norm (1 ≤ p ≤ 2) algorithm based on Alternating Direction Method of Multipliers. The performance of the proposed algorithm is tested on simulated data and compared with those obtained by a more intuitive sequential compressive deconvolution method.