Discrete multiscale wavelet shrinkage and integrodifferential equations
Stephan Didas, Gabriele Steidl, Joachim Weickert · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2008
We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with respect to their denoising quality by numerical experiments.