Fast Multi-Resolution Image Operations

A wide class of operations on images can be performed directly in the wavelet domain by operating on coefficients of the wavelet transforms of the images and other matrices defined by the operation. Operating in the wavelet domain enables to perform these operations progressively in a coarse-to-fine fashion, to operate on different resolutions, manipulate features at different scales, and to localize the operation in both the spatial and the frequency domains. Performing such operations in the wavelet domain and then reconstructing the result is more efficient than performing the same operation in the standard direct fashion and reduces the memory footprint