Compressive sensing for ultrasound RF echoes using a-Stable Distributions

This paper introduces a novel framework for compressive sensing of biomedical ultrasonic signals based on modelling data with stable distributions. We propose an approach to ℓ_p norm minimisation that employs the iteratively reweighted least squares (IRLS) algorithm but in which the parameter p is judiciously chosen by relating it to the characteristic exponent of the underlying alpha-stable distributed data. Our results show that the proposed algorithm, which we prefer to call S±S-IRLS, outperforms previously proposed ℓ₁ minimisation algorithms, such as basis pursuit or orthogonal matching pursuit, both visually and in terms of PSNR.