A CURE for Noisy Magnetic Resonance Images: Chi-Square Unbiased Risk Estimation

In this paper, 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 (MR) image data, whic...

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Bibliographic Details
Published in:IEEE transactions on image processing 2012-08, Vol.21 (8), p.3454-3466
Main Authors: Luisier, F., Blu, T., Wolfe, P. J.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Biological and medical sciences
Chi-Square Distribution
Computerized, statistical medical data processing and models in biomedicine
Data Interpretation, Statistical
Detection, estimation, filtering, equalization, prediction
Estimation
Exact sciences and technology
filterbank transform
Humans
image denoising
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Information, signal and communications theory
magnetic resonance (MR) imaging
Magnetic Resonance Imaging - methods
Medical management aid. Diagnosis aid
Medical sciences
Noise reduction
Pattern Recognition, Automated - methods
Random variables
Reproducibility of Results
Rician channels
Rician noise
Sensitivity and Specificity
Signal and communications theory
Signal processing
Signal, noise
Signal-To-Noise Ratio
Telecommunications and information theory
unbiased risk estimation
Vectors
Wavelet Analysis
Wavelet transforms
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Summary:In this paper, 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 (MR) 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 the other 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 MR image data.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2012.2191565