An Adaptive Contourlet HMM–PCNN Model of Sparse Representation for Image Denoising

Abstract

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 expectationmaximization 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.

A combined HMM–PCNN model in the contourlet domain for image data compression

“…Moreover, we modulated the image data to match the HMM-PCNN model. Finally, we verified the effectiveness of the hybrid HMM-PCNN in contourlet model part [40] through an image compression application with the well-known SPIHT algorithm: its performance is better than that of the SPIHT contourlet coding. PCNN https://doi.org/10.1371/journal.pone.0236089.g016…”

“…Simialr to the configuration in [40], we set V E and α E are set as V E = 1 − G, α E = G for the adaptive PCNN model.…”

“…On the contrary, the state probability produced by the learning procedure is also taken into consideration in our method, which makes it a two-stage selection: the area with saliency is first selected and then the significant coefficients are transmitted in the area. In reality, the first stage can be Reprinted from [40] and [53] under a CC BY license, with permission from IEEE publisher, original copyright 2019, OSA publisher, original copyright 2014, respectively. https://doi.org/10.1371/journal.pone.0236089.g014…”

“…The idea of considering human visual features for MGA can best be realized in image data compression applications. For this reason, we would like to report the result of research on image data compression of combined HMM/PCNN model in the contourlet domain, which is based on the previous research [40].…”

“…Hybrid HMM-PCNN model in the contourlet domain for the SPIHT algorithm, where CHMM denotes the HMM in the contourlet domain. Reprinted from[40] under a CC BY license, with permission from IEEE publisher, original copyright 2019.…”