AM-FM Image Analysis based on Sparse Coding Frequency Separation Approach

We propose here an extension to images of a sparse coding frequency separation method. The approach is based on a 2D multicomponent amplitude modulation (AM)-frequency modulation (FM) image modeling, where the 2D monocomponent parts are obtained by sparse approximations that are solved with matching pursuits. For synthetic images, a separable dictionary is built, while a patch-based dictionary learning method is adopted for real images. In fact, the total variation (TV) norm is applied on patches to select the decomposition modes with highest TV-norm, doing so yields to an interesting image analysis tool that properly separates the image frequency contents. The proposed approach turns out to share the same behaviors with the well known empirical mode decomposition (EMD) method. Obtained results are encouraging for feature and texture analysis, and for image denoising as well.