Flexible Multi-layer Sparse Approximations of Matrices and Applications
This addresses computational bottlenecks in signal processing and machine learning applications, though it appears incremental as it builds on existing non-convex optimization methods.
The paper tackles the high computational cost of applying linear operators in high-dimensional signal processing and machine learning by introducing an algorithm that approximately factorizes matrices into few sparse factors, demonstrating experimental improvements on problems like image denoising and inverse problems.
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the complexity of applying linear operators in high dimension by approximately factorizing the corresponding matrix into few sparse factors. The approach relies on recent advances in non-convex optimization. It is first explained and analyzed in details and then demonstrated experimentally on various problems including dictionary learning for image denoising, and the approximation of large matrices arising in inverse problems.