Multilinear Compressive Sensing With Tensor Ring Factorization

Tensor factorization has become a powerful tool for representation and analysis of multi-dimensional data. Low rank tensor factorization can be viewed as a higher order generalization of low-rank matrix factorization, both of which have been used for image and video representation and reconstruction from compressive measurements. In this paper, we present an algorithm for reconstructing images and videos from compressive measurements using tensor ring factorization model. We use a projected gradient descent approach that alternates between gradient descent over a loss function and projection onto a low-rank tensor ring structure. We also present a computationally efficient initialization step for the special case of multilinear compressive sensing. We present simulation results to demonstrate the performance of our algorithm on real images and videos.