A Nonlocal Maximum Likelihood Estimation Method for Rician Noise Reduction in MR Images

Postacquisition denoising of magnetic resonance (MR) images is of importance for clinical diagnosis and computerized analysis, such as tissue classification and segmentation. It has been shown that the noise in MR magnitude images follows a Rician distribution, which is signal-dependent when signal-to-noise ratio (SNR) is low. It is particularly difficult to remove the random fluctuations and bias introduced by Rician noise. The objective of this paper is to estimate the noise free signal from MR magnitude images. We model images as random fields and assume that pixels which have similar neighborhoods come from the same distribution. We propose a nonlocal maximum likelihood (NLML) estimation method for Rician noise reduction. Our method yields an optimal estimation result that is more accurate in recovering the true signal from Rician noise than NL means algorithm in the sense of SNR, contrast, and method error. We demonstrate that NLML performs better than the conventional local maximum likelihood (LML) estimation method in preserving and defining sharp tissue boundaries in terms of a well-defined sharpness metric while also having superior performance in method error.

I. Introduction

Denoising of magnetic resonance (MR) images remains a critical issue, spurred partly by the necessity of trading-off resolution, signal-to-noise ratio (SNR), and acquisition speed, which results in images that still demonstrate significant noise levels [1]–[7]. Sources of MR noise [8] include thermal noise (from the conductivity of the system's hardware), inductive losses (from the conductivity of the object being imaged), sample resolution, and field-of-view (among others). Understanding the spatial distribution of noise in an MR image is critical to any attempt to estimate the underpinning (true) signal. The investigation of how noise is distributed in MR images (along with techniques proposed to ameliorate the noise) has a long history. It was shown that pure noise in MR magnitude images can be modeled as a Rayleigh distribution [1]. Afterwards, the Rician model [4] was proposed as a more general model of noise in MR images.