### Tensors for Improving Compressed Sensing Reconstruction

#### Abstract

Compressed Sensing (CS) proposes a framework that any signal can be efficiently reconstructed by observing fewer measurements than required by the famous Shannon-Nyquist theorem, the observing signal must be sparse in some transform domain. Many methods have been proposed to further improve the quality of reconstructed images such as Group Sparsity, Structural Group Sparsity, Total-Variation etc. In this paper we unify tensor based approach with compressed sensing to efficiently reconstruct the original signal. Tensor based approach helps in preserving the intrinsic structure of the signal. Two methods of tensor decomposition Tucker and CANDE/PARAFAC (CP) are unified to give the best low-rank representation of the sparse signal.

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