Over the last several decades, magnetic resonance imaging (MRI) technology has benefited from a variety of technological developments resulting in increased resolution, signal-to-noise ratio (SNR), and acquisition speed. However, fundamental trade-offs between resolution, speed, and SNR combined with scientific, clinical, and financial pressures to obtain more data more quickly, result in images that still exhibit significant levels of noise. In particular, the need for shorter acquisition times, such as in dynamic imaging, often undermines the ability to obtain images having both high resolution and high SNR. Furthermore, the efficacy of higher-level, post processing of MR images, including tissue classification and organ segmentation, that assume specific models of tissue intensity (e.g., homogeneous), are sometimes impaired by even moderate noise levels. Hence, denoising MR images remains an important problem. From a multitude of statistical and variational denoising formulations proposed, no particular one appears as a clear winner in all relevant aspects, including the reduction of randomness and intensity bias, structure and edge preservation, generality, reliability, automation, and computational cost.
This paper presents a novel framework for denoising MR images that relies on the adaptive Markov-random-field (MRF) image model described in [9,5]. The work in this paper is a significant modification of our previous approach in [8]. The key idea in the modeling approach is to adapt or infer the model from the corrupted input data itself and subsequently process the data based on the infer model. The proposed denoising method produces an optimal reconstruction based on principles in empirical-Bayesian estimation [141,140] and information theory. The method bootstraps itself by estimating the uncorrupted-signal Markov statistics, using an information-theoretic optimality metric, from the corrupted input data and the knowledge of the Rician noise model. It then employs the inferred uncorrupted-signal Markov statistics as an adaptive prior in a Bayesian denoising process at each pixel. In this way, it avoids the need of imposing ad hoc prior models. Furthermore, it proposes a novel iterative Bayesian-inference algorithm on MRFs that incorporates entropy reduction on posterior PDFs. We call this new approach as iterated conditional entropy reduction (ICER). The results demonstrate that the method denoises conservatively while ensuring the preservation of most of the important features in the brain MR images. Qualitative and quantitative comparisons with the state of the art clearly depict the advantages of the proposed method.