Compressive sensing for ultrasound RF echoes using a-Stable Distributions

Abstract

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 ℓ(1) minimisation algorithms, such as basis pursuit or orthogonal matching pursuit, both visually and in terms of PSNR.

Reconstruction of compressively sampled ultrasound images using dual prior information

“…We achieved that by observing that for alpha-stable signals, which do not possess finite second-or higher-order moments, the minimum dispersion criterion [11] can be defined as an alternative to the classical minimum mean square error for Gaussian signals. This leads to a least p norm estimation problem, an approach that we have shown to enhance the reconstruction of heavy-tailed RF signals from their measurement projections [2]. Here, our approach to RF signal reconstruction still relies on SαS-IRLS [2] but is implemented in the frequency domain as in [4] and modified (following [8]) to incorporate information on the support of RF signals.…”

“…In [2] we have devised a principled strategy for choosing the optimal p by relating the p norm minimisation to the actual SαS statistics of the RF signals. We achieved that by observing that for alpha-stable signals, which do not possess finite second-or higher-order moments, the minimum dispersion criterion [11] can be defined as an alternative to the classical minimum mean square error for Gaussian signals.…”

“…In this contribution, we further extend our techniques described in [2,4] by supplementing the prior information available to an p norm minimisation algorithm with the support of the RF echoes in the frequency domain. In ultrasound applications the latter can be easily inferred through knowledge of the acquisition frequency and transducer bandwidth.…”

“…On the other hand, the effect of the random sampling pattern on the reconstruction quality, when working in the frequency domain (k-space) was studied in [3]. This was further exploited in [4] for the design of a US reconstruction technique similar to [2] but operating in the Fourier domain.…”

“…In particular, in [2], we introduced a novel framework for CS of biomedical ultrasonic signals based on modeling data with symmetric alpha-stable (SαS ) distributions. Then, we proposed an p norm-based minimization approach that employed the iteratively reweighted least squares (IRLS) algorithm, but in which the parameter p was judiciously chosen by relating it to the characteristic exponent of the underlying This work was partially funded by the CS-ORION (PIAP-GA-2009-251605) grant within the 7th Framework Program of the European Community alpha-stable distributed data.…”