Convolutional Matching Pursuit and Dictionary Training

Here, {W,Z} are the dictionary and the coefficients, respectively, and zk is the kth column of Z. K, q, and λ are user selected parameters controlling the power of the model. More recently, many models with additional structure have been proposed. For example, in [9, 2], the dictionary elements are arranged in groups and the sparsity is on the group level. In [3, 5, 7], the dictionaries are constructed to be translation invariant. In the former work, the dictionary is constructed via a non-negative matrix factorization. In the latter two works, the construction is a convolutional analogue of 1.2 or an l variant, with 0 < p < 1. In this short note we work with greedy algorithms for solving the convolutional analogues of 1.1. Specifically, we demonstrate that sparse coding by matching pursuit and dictionary learning via K-SVD [1] can be used in the translation invariant setting.