Distributed Convolutional Sparse Coding

We consider the problem of building shift-invariant representations for long signals in the context of distributed processing. We propose an asynchronous algorithm based on coordinate descent called DICOD to efficiently solve the `1minimization problems involved in convolutional sparse coding. This algorithm leverages the weak temporal dependency of the convolution to reduce the interprocess communication to a few local messages. We prove that this algorithm converges to the optimal solution and that it scales with superlinear speedup, up to a certain limit. These properties are illustrated with numerical experiments and our algorithm is compared to the state-of-the-art methods used for convolutional sparse coding.