In this paper, we propose a novel model of sparse representation for image denoising that we call an adaptive contourlet hidden Markov model (HMM)-pulse-coupled neural network (PCNN). In this study, we first adopted a contourlet transform to decompose a noisy image to be some subband coefficients of various directions at various scales. The contourlet emulated extremely well the sparse representation performance of human visual perception, such as its multiscale characteristics, geometric features, and bandpass properties. Second, we used an HMM method to create a statistical model that expressed the coefficient relationships in intrabands, interbands, intrascales, and interscales. Then we used an expectation-maximization training algorithm to obtain the state probability. The result included the state, scale, and direction, the position of the coefficient, the noisy image, and the parameter set of the HMM model. Third, we put the state probability into the PCNN model, which could adaptively optimize the parameters of the HMM model and get better coefficients of clean images. Finally, we transformed the image denoising problem into a Bayesian posterior probability estimation problem. We also reconstructed a denoised image based on the clean coefficients obtained from our proposed method. The experimental results show that the contourlet HMM-PCNN model proposed in this paper is superior to the contourlet with hidden Markov tree model and the wavelet threshold method.
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