Denoising techniques in adaptive multi-resolution domains with applications to biomedical images.

Variational mode decomposition (VMD) is a new adaptive multi-resolution technique suitable for signal denoising purpose. The main focus of this work has been to study the feasibility of several image denoising techniques in empirical mode decomposition (EMD) and VMD domains. A comparative study is made using 11 techniques widely used in the literature, including Wiener filter, first-order local statistics, fourth partial differential equation, nonlinear complex diffusion process, linear complex diffusion process (LCDP), probabilistic non-local means, non-local Euclidean medians, non-local means, non-local patch regression, discrete wavelet transform and wavelet packet transform. On the basis of comparison of 396 denoising based on peak signal-to-noise ratio, it is found that the best performances are obtained in VMD domain when appropriate denoising techniques are applied. Particularly, it is found that LCDP in combination with VMD performs the best and that VMD is faster than EMD.