1208.2330 (Rafael E. Carrillo et al.)

Sparsity Averaging for Compressive Imaging    [PDF]

Rafael E. Carrillo, Jason D. McEwen, Dimitri Van De Ville, Jean-Philippe Thiran, Yves Wiaux

We propose a novel regularization method for sparse image reconstruction from compressive measurements. The approach relies on the conjecture that natural images exhibit strong average sparsity over multiple coherent frames. The associated reconstruction algorithm, based on an analysis prior and a reweighted $\ell_1$ scheme, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We test our prior and the associated algorithm through extensive numerical simulations for spread spectrum and Gaussian acquisition schemes suggested by the recent theory of compressed sensing with coherent and redundant dictionaries. 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. We also illustrate the performance of SARA in the context of Fourier imaging, for particular applications in astronomy and medicine.

View original: http://arxiv.org/abs/1208.2330