Estimating the probability of the presence of a signal of interest in multiresolution single- and multiband image denoising

• Published in: IEEE transactions on image processing Vol. 15; no. 3; pp. 654 - 665
• Main Authors: Pizurica, A., Philips, W.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01-03-2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Additive white noise; Algorithms; Applied sciences; Bands; Bayesian analysis; Bayesian estimation; Color; color and multispectral images; Computer Simulation; Conditioning; Detection, estimation, filtering, equalization, prediction; Exact sciences and technology; Gaussian; generalized likelihood ratio; Image analysis; Image denoising; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image resolution; Information analysis; Information Storage and Retrieval - methods; Information, signal and communications theory; Miscellaneous; Models, Statistical; Noise; Noise reduction; Probability; Signal analysis; Signal and communications theory; Signal processing; Signal resolution; Signal, noise; Spatial resolution; Telecommunications and information theory; Wavelet; Wavelet domain; wavelets; Bayes estimation; Performance evaluation; Bayesian estimation; AWGN; Subband decomposition; Multispectral detection; Image processing; Threshold detection; Noise reduction; Likelihood ratio; generalized likelihood ratio; Adaptive method; Multiresolution analysis; Color image; Laplacian; Mean square error; Multiple image; Probabilistic assessment; color and multispectral images; wavelets; Signal processing; Bayes methods; Image denoising
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2005.863698

We develop three novel wavelet domain denoising methods for subband-adaptive, spatially-adaptive and multivalued image denoising. The core of our approach is the estimation of the probability that a given coefficient contains a significant noise-free component, which we call "signal of interest". In this respect, we analyze cases where the probability of signal presence is 1) fixed per subband, 2) conditioned on a local spatial context, and 3) conditioned on information from multiple image bands. All the probabilities are estimated assuming a generalized Laplacian prior for noise-free subband data and additive white Gaussian noise. The results demonstrate that the new subband-adaptive shrinkage function outperforms Bayesian thresholding approaches in terms of mean-squared error. The spatially adaptive version of the proposed method yields better results than the existing spatially adaptive ones of similar and higher complexity. The performance on color and on multispectral images is superior with respect to recent multiband wavelet thresholding.