Blind Estimation of Noisy Images via Fuzzy Matching-Pursuits

This paper presents an original application of fuzzy logic to restoration of images affected by white noise, possibly nonstationary and/or signal dependent. Space-varying linear MMSE estimation is stated as a problem of matching pursuits, in which the estimator is obtained as an expansion in series of a finite number of non-orthogonal prototype estimators, fitting the spatial features of the different statistical classes encountered, e.g. edges and textures. Such estimators are calculated in a fuzzy fashion through an automatic training procedure. The space-varying coefficients of the expansion are stated as degrees of fuzzy membership of a pixel to each of the estimators. Besides the fact that neither "a priori" knowledge of the noise model is required nor a particular signal model is assumed, a performance comparison highlights the advantages of the proposed approach. Results on simulated noisy versions of Lenna show a steady SNR improvement of almost 2.5 dB over Kuan's LLMMSE filtering and of 2 dB over wavelet thresholding, irrespective of noise model and intensity.