Footprints and edgeprints for image denoising and compression

Wavelets have been quite successful in compression or denoising applications. To further improve the performance of wavelet based algorithms, we have recently introduced the notion of footprint, which is a data structure which contains all the wavelet coefficients generated by a discontinuity. The combined use of wavelets and footprints leads to very efficient algorithms for compression and denoising of 1D piecewise smooth signals. We extend some of the previous results by presenting a new denoising algorithm, where footprints are chosen adaptively according to the singularity locations. This new algorithm outperforms previously proposed ones. Then, we introduce the notion of edgeprints, which represents a natural extension of footprints to the two dimensional case. First experimental results on the compression of 2D piecewise smooth signals using edgeprints are promising.