A CURE for noisy magnetic resonance images: Chi-square unbiased risk estimation

TL;DR

This paper introduces a new unbiased risk estimation method for denoising magnetic resonance images modeled as noncentral chi-square variables, leading to improved algorithms for image enhancement.

Contribution

It derives an unbiased mean-squared error expression for estimators of noncentral chi-square parameters and applies it to develop effective denoising algorithms for MRI data.

Findings

Algorithms outperform state-of-the-art methods on simulated data.

Effective in denoising actual magnetic resonance images.

Computationally tractable and adaptable to different transforms.

Abstract

In this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chi-square random variable. We then consider the task of denoising squared-magnitude magnetic resonance image data, which are well modeled as independent noncentral chi-square random variables on two degrees of freedom. We consider two broad classes of linearly parameterized shrinkage estimators that can be optimized using our risk estimate, one in the general context of undecimated filterbank transforms, and another in the specific case of the unnormalized Haar wavelet transform. The resultant algorithms are computationally tractable and improve upon state-of-the-art methods for both simulated and actual magnetic resonance image data.