Adaptive Markov Models for Information-Theoretic Empirical-Bayesian MRI Denoising

This paper presents a novel framework for denoising magnetic resonance images. The framework relies on adaptive Markov-random-field (MRF) image models that we infer nonparametrically from the corrupted input data itself. The proposed denoising method produces an optimal reconstruction based on principles in empirical-Bayesian estimation and information theory. Given the corrupted input data and the knowledge of the Rician noise model, the Bayesian-denoising method bootstraps itself by estimating the uncorrupted-signal Markov statistics, by optimizing an informationtheoretic metric using the expectation-maximization (EM) algorithm. It then employs the inferred uncorrupted-signal Markov statistics as an adaptive prior in a Bayesian-denoising process at each pixel. Furthermore, it proposes a novel Bayesian-inference algorithm on MRFs incorporating entropy reduction, namely iterated conditional entropy reduction (ICER). The results demonstrate that the method denoises conservatively while ensuring the preservation of most of the important features in brain-MR images. Qualitative and quantitative comparisons with the state of the art clearly depict the advantages of the proposed method. Adaptive Markov Models for Information-Theoretic Empirical-Bayesian MRI Denoising Suyash P. Awate and Ross T. Whitaker Abstract This paper presents a novel framework for denoising magnetic resonance images. The framework relies on adaptive Markov-random-field (MRF) image models that we infer nonparametrically from the corrupted input data itself. The proposed denoising method produces an optimal reconstruction based on principles in empirical-Bayesian estimation and information theory. Given the corrupted input data and the knowledge of the Rician noise model, the Bayesian-denoising method bootstraps itself by estimating the uncorrupted-signal Markov statistics, by optimizing an information-theoretic metric using the expectation-maximization (EM) algorithm. It then employs the inferred uncorrupted-signal Markov statistics as an adaptive prior in a Bayesian-denoising process at each pixel. Furthermore, it proposes a novel Bayesian-inference algorithm on MRFs incorporating entropy reduction, namely iterated conditional entropy reduction (ICER). The results demonstrate that the method denoises conservatively while ensuring the preservation of most of the important features in brain-MR images. Qualitative and quantitative comparisons with the state of the art clearly depict the advantages of the proposed method.This paper presents a novel framework for denoising magnetic resonance images. The framework relies on adaptive Markov-random-field (MRF) image models that we infer nonparametrically from the corrupted input data itself. The proposed denoising method produces an optimal reconstruction based on principles in empirical-Bayesian estimation and information theory. Given the corrupted input data and the knowledge of the Rician noise model, the Bayesian-denoising method bootstraps itself by estimating the uncorrupted-signal Markov statistics, by optimizing an information-theoretic metric using the expectation-maximization (EM) algorithm. It then employs the inferred uncorrupted-signal Markov statistics as an adaptive prior in a Bayesian-denoising process at each pixel. Furthermore, it proposes a novel Bayesian-inference algorithm on MRFs incorporating entropy reduction, namely iterated conditional entropy reduction (ICER). The results demonstrate that the method denoises conservatively while ensuring the preservation of most of the important features in brain-MR images. Qualitative and quantitative comparisons with the state of the art clearly depict the advantages of the proposed method.