Cascade residuals guided nonlinear dictionary learning

In this paper, we aim to extend dictionary learning onto hierarchical image representations in a principled way. To achieve dictionary atoms capture additional information from extended receptive fields and attain improved descriptive capacity, we present a two-pass multi-resolution cascade framework for dictionary learning and sparse coding. This cascade method allows collaborative reconstructions at different resolutions using only the same dimensional dictionary atoms. The jointly learned dictionary comprises atoms that adapt to the information available at the coarsest layer, where the support of atoms reaches a maximum range, and the residual images, where the supplementary details refine progressively a reconstruction objective. The residual at a layer is computed by the difference between the aggregated reconstructions of the previous layers and the downsampled original image at that layer. Our method generates flexible and accurate representations using only a small number of coefficients. It is computationally efficient since it encodes the image at the coarsest resolution while yielding very sparse residuals. Our extensive experiments on multiple image coding, denoising, inpainting and artifact removal tasks demonstrate that our method provides superior results.