Multiresolution Analysis with Pulses
Carl Rohwer · Birkhäuser Basel eBooks · 2002
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. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.