Nonconvex compressive sensing reconstruction for tensor using structures in modes

Abstract

This paper focuses on the reconstruction of a tensor captured using Compressive Sensing (CS). Instead of processing the signals via vectorization as is done in conventional CS, in tensor CS high dimensional signals are kept in their original formats, which benefits hardware implementation and eases memory requirements. In addition, more structures exist in a tensor along its various dimensions than in its vectorized format. Utilizing these various structures, this paper proposes a general reconstruction approach for tensor CS. Employing the proximity operator of a nonconvex norm function, a special case for a tensor with low rank and sparse structures is elaborated, which is shown to outperform the state-of-art tensor CS reconstruction methods when applied to magnetic resonance imaging and hyper-spectral imaging.