Tensor Least Angle Regression for Sparse Representations of Multidimensional Signals.

Neural Computation
Ishan WickramasinghaSherif S Sherif

Abstract

Sparse signal representations have gained much interest recently in both signal processing and statistical communities. Compared to orthogonal matching pursuit (OMP) and basis pursuit, which solve the L0 and L1 constrained sparse least-squares problems, respectively, least angle regression (LARS) is a computationally efficient method to solve both problems for all critical values of the regularization parameter λ. However, all of these methods are not suitable for solving large multidimensional sparse least-squares problems, as they would require extensive computational power and memory. An earlier generalization of OMP, known as Kronecker-OMP, was developed to solve the L0 problem for large multidimensional sparse least-squares problems. However, its memory usage and computation time increase quickly with the number of problem dimensions and iterations. In this letter, we develop a generalization of LARS, tensor least angle regression (T-LARS) that could efficiently solve either large L0 or large L1 constrained multidimensional, sparse, least-squares problems (underdetermined or overdetermined) for all critical values of the regularization parameter λ and with lower computational complexity and memory usage than Kronecker-OMP....Continue Reading

References

Feb 20, 2003·Neural Computation·Kenneth Kreutz-DelgadoTerrence J Sejnowski
Apr 1, 2006·Proceedings of the National Academy of Sciences of the United States of America·David L Donoho, Michael Elad
Dec 13, 2006·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Michael Elad, Michal Aharon
Jul 26, 2013·Journal of Digital Imaging·Kenneth ClarkFred Prior

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