MMSE Approximation For Sparse Coding Algorithms Using Stochastic Resonance


D. Simon, J. Sulam, Y. Romano, Y. M. Lu, and M. Elad, “MMSE Approximation For Sparse Coding Algorithms Using Stochastic Resonance,” IEEE Transactions on Signal Processing, vol. 67, no. 17, 2019.


Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a sparse prior. Various nonlinear algorithms are available to approximate the solution of such problems.

In this work, we suggest enhancing the performance of sparse coding algorithms by a deliberate and controlled contamination of the input with random noise, a phenomenon known as stochastic resonance. This not only allows for increased performance, but also provides a computationally efficient approximation to the Minimum Mean Square Error (MMSE) estimator, which is ordinarily intractable to compute. We demonstrate our findings empirically and provide a theoretical analysis of our method under several different cases.

arXiv:1806.10171 [eess.SP]

Last updated on 08/22/2019