title: A CURE for noisy magnetic resonance images: chi-square unbiased risk estimation.
abstract: n this article we derive an unbiased expression for the expected mean-squared error associated with continuously differentiable estimators of the noncentrality parameter of a chisquare 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 most state-of-the-art methods for both simulated and actual magnetic resonance image data.
authors.forename: Florian
authors.initials: F
authors.lastname: Luisier
authors.forename: Thierry
authors.initials: T
authors.lastname: Blu
authors.forename: Patrick J
authors.initials: PJ
authors.lastname: Wolfe
mesh_terms: D000465:Algorithms; D016009:Chi-Square Distribution; D003627:Data Interpretation, Statistical; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008279:Magnetic Resonance Imaging / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D059629:Signal-To-Noise Ratio; D058067:Wavelet Analysis