Multilinear Compressed Sensing using Tensor Least Angle Regression (T-LARS)

Multilinear compressed sensing generalizes the compressed sensing formulation to tensor signals, where the tensor signal is reconstructed using much fewer samples obtained in a sparse domain by solving a multilinear sparse coding problem. The Kronecker-OMP, a generalization of Orthogonal Matching Pursuit (OMP) solves the L0 constrained multilinear sparse least-squares problems. However, with the problem dimensions and the number of iterations, the space and computational cost of Kronecker-OMP increase in the polynomial order. Authors have previously developed a generalized least-angle regression(LARS), known as Tensor Least Angle Regression (T-LARS), with a lower asymptotic space and computational complexity than Kronecker-OMP to efficiently solve both L0 and L1 constrained multilinear sparse least-squares problems. In this paper, we used T-LARS to solve multilinear compressed sensing problems and compared the results with Kronecker-OMP, where the T-LARS is 56 times faster than Kronecker-OMP in reconstructing the 3D PET-CT images using compressed sensing samples.