Image compression based on a multi-directional map-dependent algorithm

This work is devoted to the construction of a new multi-directional edge-adapted compression algorithm for images. It is based on a multi-scale transform that is performed in two steps: a detection step producing a map of edges and a prediction/multi-resolution step which takes into account the information given by the map. A short analysis of the multi-scale transform is performed and an estimate of the error associated to the largest coefficients for a piecewise regular function with Lipschitz edges is provided. Comparisons between this map-dependent algorithm and different classical algorithms are given.