Weighted Tensor Least Angle Regression for Solving Sparse Weighted Multilinear Least Squares Problems

Sparse weighted multilinear least-squares is a generalization of the sparse multilinear least-squares problem, where prior information about, e.g., parameters and data is incorporated by multiplying both sides of the original problem by a typically diagonal weights matrix. However, the introduction of arbitrary diagonal weights would result in a non-Kronecker least-squares problem that could be very large to store or solve practically. In this paper, we generalize our recent Tensor Least Angle Regression (T-LARS) algorithm to efficiently solve either L0 or L1 constrained multilinear least-squares problems with arbitrary diagonal weights for all critical values of their regularization parameter. To demonstrate the validity of our new Weighted Least Angle Regression (WT-LARS) algorithm, we used it to successfully solve three different image inpainting problems by obtaining sparse representations of binary-weighted images.