Image Denoising using a Novel Frobenius Norm Filter for a Class of Noises

In this paper, we present a novel Frobenius Norm Filter (FNF), which is a spatially selective noise filtration technique in the wavelet subband domain. We address the issue of denoising of images corrupted with additive, multiplicative, and uncorrelated noise. The proposed nonlinear filter is an adaptive order statistic filter functioning on the L^2 space, which modulates itself according to the noise level. We have applied the comparative Frobenius Norm under a given window set and pixel connectivity for removal of noise. We prove the existence of a minimizer, and its convergence, of our specialized filter. We present a comparative study between FNF and certain standard filters, and find that our method is capable of reducing large noise blotches, and is an adequate preprocess to improving the quality of segmentation and facilitating the feature extraction process. We obtained better restoration results, especially when the images were highly corrupted and having a high noise density.