Adaptive sparsity reconstruction method for ultrasonic images based on compressive sensing

This paper proposes an improved backtracking-based adaptive orthogonal matching pursuit (OMP) algorithm (IBAOMP) and applies it to ultrasonic RF echoes signals. We first model the residual signal of an ultrasonic image with a Gaussian-like distribution to analyse the relationship between BAOMP thresholding and sparsity. Then we improve the BAOMP algorithm by a variable atoms selecting thresholding to avoid possible wrong match and residual increase in upper iterations of BAOMP. The proposed IBAOMP triggers the calibration of enrolled atom candidates to avoid the quasi-periodic mismatch of residual signals and upgrades the atommatch rate. We compare IBAOMP with other greedy algorithms for the biomedical ultrasonic image and 1D sparse signals. Numerical experiments demonstrate that the proposed IBAOMP algorithm can obviously prevent the residual rebounds for the biomedical ultrasonic image reconstruction and increase the exact recovery probability by 26% in comparison to BAOMP for Gaussian sparse signal.