DiCoDiLe: Distributed Convolutional Dictionary Learning.

Convolutional dictionary learning (CDL) estimates shift invariant basis adapted to represent signals or images. CDL has proven useful for image denoising or inpainting, as well as for pattern discovery on multivariate signals. Contrarily to standard patch-based dictionary learning, patterns estimated by CDL can be positioned anywhere in signals or images. Optimization techniques consequently face the difficulty of working with extremely large inputs with millions of pixels or time samples. To address this optimization problem, we propose a distributed and asynchronous algorithm, employing locally greedy coordinate descent and a soft-locking mechanism that does not require a central server. Computation can be distributed on a number of workers which scales linearly with the size of the data. The parallel computation accelerates the parameter estimation and the distributed setting allows our algorithm to be used with data that do not fit into a single computer's RAM. Experiments confirm the theoretical scaling properties of the algorithm. This allows to demonstrate an improved pattern recovery as images grow in size, and to learn patterns on images from the Hubble Space Telescope containing tens of millions of pixels.