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.

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Abstract-This paper presents a novel rotation-invariant image retrieval scheme based on a transformation of the texture information via a steerable pyramid. First, we fit the distribution of the subband coefficients using a joint alpha-stable sub-Gaussian model to capture their non-Gaussian behavior. Then, we apply a normalization process in order to Gaussianize the coefficients. As a result, the feature extraction step consists of estimating the covariances between the normalized pyramid coefficients. The similarity between two distinct texture images is measured by minimizing a rotation-invariant version of the Kullback-Leibler Divergence between their corresponding multivariate Gaussian distributions, where the minimization is performed over a set of rotation angles.Index Terms-Fractional lower-order moments (FLOMs), rotation-invariant Kullback-Leibler divergence (KLD), statistical image retrieval, steerable model, sub-Gaussian distribution.

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