Robust Compressive Spectral Image Recovery Algorithm Using Dictionary Learning and Transform Tensor SVD

This paper proposes a low-rank tensor minimization algorithm to recover a spectral image (SI) from a set of compressed observations. The proposal takes advantage of the transform tensor singular value decomposition (tt-SVD) to promote a low-rank structure on the recovered SI. The methodology has three stages. First, a poor low-rank version of the SI is estimated using the tt-SVD framework with the discrete cosine transform (DCT). Then, an orthogonal transform is learned from the initial estimation using dictionary learning. Finally, an algorithm to find a low-rank approximation of the SI in both, the DCT and the learned transform is introduced. Quantitative evaluation over two databases and two compressive optical systems shows that the proposed method improves the reconstruction quality in up to 10dB as well as it is robust in the presence of noise.