We explore the unifying connection between kernel regression, Volterra series expansion and multiscale signal decomposition using recent results on function estimation for system identification. We show that using any of these techniques for (non-linear) image processing tasks is (approximately) equivalent. Further, we use the relation between wavelets and independent components of natural images. Kernel methods can be shown to be implicit Volterra series expansions, which are well approximated by wavelets. Wavelets are, in turn, well represented by independent components of natural images. Thus, it can be seen that kernel methods are also near optimal in terms of higher order statistical modeling and approximation of (natural) images. This explains the reason for good results often (perceptually) observed with the use of kernel methods for many image processing problems.
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[v1] 2018-04-19 09:47:02
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