Dictionary learning of convolved signals

Assuming that a set of source signals is sparsely representable in a given dictionary, we show how their sparse recovery fails whenever we can only measure a convolved observation of them. Starting from this motivation, we develop a block coordinate descent method which aims to learn a convolved dictionary and provide a sparse representation of the observed signals with small residual norm. We compare the proposed approach to the K-SVD dictionary learning algorithm and show through numerical experiment on synthetic signals that, provided some conditions on the problem data, our technique converges in a fixed number of iterations to a sparse representation with smaller residual norm.

• Type: Journal
• Year: 2011
• Where: ICASSP
• Authors: Daniele Barchiesi, Mark D. Plumbley
• Keywords: ICASSP 2011, Residual Norm, Signal Processing, Smaller Residual Norm, Sparse Representation