Multiresolution Analysis with Pulses

Abstract

Multiresolution analysis has recently received considerable attention in relation to wavelets. The word “multiresolution” is appropriate in so far as wavelets are local in some sense, and therefore have exponentially decaying impulse response. In image processing it is clear that edges and impulses yield undesirable synthetic features in partially reconstructed images from linear multiscale decompositions. Median decompositions are regarded as better in practice, but computational complexity and lack of theory are problems. An alternative, from mathematical morphology is possible, yielding results demonstrably similar to the median decomposition, but computationally simpler, and having a strong theory for deriving qualitative and quantitative properties.