  This paper seeks to combine dictionary learning and hierarchical image
representation in a principled way. To make dictionary atoms capturing
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. The cascade allows collaborative
reconstructions at different resolutions using the same dimensional dictionary
atoms. Our jointly learned dictionary comprises atoms that adapt to the
information available at the coarsest layer where the support of atoms reaches
their maximum range and the residual images where the supplementary details
progressively refine the 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 more flexible and accurate representations using much less number of
coefficients. Its computational efficiency stems from encoding at the coarsest
resolution, which is minuscule, and encoding the residuals, which are
relatively much sparse. Our extensive experiments on multiple datasets
demonstrate that this new method is powerful in image coding, denoising,
inpainting and artifact removal tasks outperforming the state-of-the-art
techniques.
