  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. 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. The
proposed method adds controlled noise to the input and estimates a sparse
representation from the perturbed signal. A set of such solutions is then
obtained by projecting the original input signal onto the recovered set of
supports. We present two variants of the described method, which differ in
their final step. The first is a provably convergent approximation to the
Minimum Mean Square Error (MMSE) estimator, relying on the generative model and
applying a weighted average over the recovered solutions. The second is a
relaxed variant of the former that simply applies an empirical mean. We show
that both methods provide a computationally efficient approximation to the MMSE
estimator, which is typically intractable to compute. We demonstrate our
findings empirically and provide a theoretical analysis of our method under
several different cases.
