Improved VC-based signal denoising

Signal denoising is closely related to function estimation from noisy samples. Vapnik-Chervonenkis (VC) theory provides a general framework for estimation of dependencies from finite samples. This theory emphasizes model complexity control according to the structural risk minimization inductive principle, which considers a nested set of models of increasing complexity (called a structure), and then selects an optimal model complexity providing minimum error for future samples. Cherkassky and Shao (1998) applied the VC-theory for signal denoising and estimation. This paper extends the original VC-based signal denoising to practical settings where a (noisy) signal is oversampled. We show that in such settings one needs to modify analytical VC bounds for optimal signal denoising. We also present empirical comparisons between the proposed methodology and standard VC-based denoising for univariate signals. These comparisons indicate that the proposed denoising methodology yields superior estimation accuracy and more compact signal representation for various univariate signals.