Dictionary learning with weighted stochastic gradient descent

A vector signal can be sparsely represented by a linear combination of small number of atoms in a dictionary. Many works focused on finding this dictionary by adopting a learning point-of-view. We present a new dictionary learning method with Weighted Stochastic Gradient Descent (WSGD). We construct a novel cost function by introducing a weighting matrix and solve this problem by stochastic gradient descent. It is demonstrated from synthetic experiments that our method have a good performance in signal representation capability and the ability to recover the original dictionary.