  Sparse signal representations based on linear combinations of learned atoms
have been used to obtain state-of-the-art results in several practical signal
processing applications. Approximation methods are needed to process
high-dimensional signals in this way because the problem to calculate optimal
atoms for sparse coding is NP-hard. Here we study greedy algorithms for
unsupervised learning of dictionaries of shift-invariant atoms and propose a
new method where each atom is selected with the same probability on average,
which corresponds to the homeostatic regulation of a recurrent convolutional
neural network. Equiprobable selection can be used with several greedy
algorithms for dictionary learning to ensure that all atoms adapt during
training and that no particular atom is more likely to take part in the linear
combination on average. We demonstrate via simulation experiments that
dictionary learning with equiprobable selection results in higher entropy of
the sparse representation and lower reconstruction and denoising errors, both
in the case of ordinary matching pursuit and orthogonal matching pursuit with
shift-invariant dictionaries. Furthermore, we show that the computational costs
of the matching pursuits are lower with equiprobable selection, leading to
faster and more accurate dictionary learning algorithms.
