Wednesday, April 24, 2013

Sparsity Averaging Reweighted Analysis (SARA) - implementation -

Yves Wiaux just me the following:

Hi Igor,

Matlab code is now available for our Sparsity Averaging Reweighted Analysis (SARA) algorithm on github: https://github.com/basp-group/sopt

While the first SARA paper (http://arxiv.org/abs/1205.3123, published in MNRAS) deals with astronomical imaging, a second article (http://arxiv.org/abs/1208.2330, accepted in IEEE SPL) discusses SARA performance relative to the state of the art for generic compressive imaging in the context of the theory of CS with redundant dictionaries. Implementation relies on the Douglas-Rachford proximal splitting algorithm.

Fast C implementation is on its way, in particular dealing with high-dimensional continuous Fourier sampling, and of interest both for radio-interferometric and magnetic resonance imaging.

May I ask you to post this on Nuit Blanche?

Regards

Yves

Yves Wiaux, Ph.D., Researcher
Signal Processing Labs,
EPFL, Lausanne, Switzerland
&
University of Geneva / Lausanne University Hospital
Sure Yves. here are the attendant papers:

Sparsity Averaging for Compressive Imaging by Rafael E. Carrillo, Jason D. McEwen, Dimitri Van De Ville, Jean-Philippe Thiran, Yves Wiaux

We discuss a novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries, based on the observation that natural images exhibit strong average sparsity over multiple coherent frames. We test our prior and the associated algorithm, based on an analysis reweighted $\ell_1$ formulation, through extensive numerical simulations on natural images for spread spectrum and random Gaussian acquisition schemes. Our results show that average sparsity outperforms state-of-the-art priors that promote sparsity in a single orthonormal basis or redundant frame, or that promote gradient sparsity. Code and test data are available at this https URL

Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging by R. E. Carrillo, J. D. McEwen, Y. Wiaux
We propose a novel algorithm for image reconstruction in radio interferometry. The ill-posed inverse problem associated with the incomplete Fourier sampling identified by the visibility measurements is regularized by the assumption of average signal sparsity over representations in multiple wavelet bases. The algorithm, defined in the versatile framework of convex optimization, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We show through simulations that the proposed approach outperforms state-of-the-art imaging methods in the field, which are based on the assumption of signal sparsity in a single basis only.

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