Conference Paper

Chi-square unbiased risk estimate for denoising magnitude MR images

DOI: 10.1109/ICIP.2011.6115745 Conference: 18th IEEE International Conference on Image Processing, ICIP 2011, Brussels, Belgium, September 11-14, 2011
Source: DBLP


In this article we develop Stein-type results for unbiased estimation of the risk associated with parametric estimators of the noncentrality parameter of chi-squared random variables on two degrees of freedom. These results allow for estimator adaptivity, and thus can be used to optimize the parameters of a broad class of typical denoising functions, subject only to weak smoothness assumptions. We show how to apply these results to the problem of enhancing magnitude magnetic resonance images, which are known to be corrupted by Rician noise. As an example, we propose a transform-domain point-wise estimator based on linear expansion of thresholds. Finally, we apply this estimator to synthetic and real image data in conjunction with the undecimated Haar wavelet transform, and conclude that it is able to outperform previous wavelet-based techniques and compares favorably with a more recent approach based on non-local means.

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Available from: Florian Luisier, Feb 04, 2015
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    • "Wavelet-based method of de-noising makes the wavelet and scaling coefficients biased.In order to make the scaling coefficients independent of the signal, chi-square distribution method is employed[8] [24].This method is problematic as it introduces characteristics artifacts, and becomes difficult to assure the scale and becomes difficult to assure the scale and threshold of the wavelet. iv. "
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    • "Yet, similar to the additive white Gaussian (SURE) and Poisson (PURE) noise cases, it is also possible to derive a Stein-like unbiased estimate for non-central chi-square distributed data. Such an unbiased estimate of the expected MSE has been recently introduced in [10] and termed CURE. For any estimator f (y) satisfying some smoothness constraints, CURE is given by "
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    • "We conclude in Section V with denoising experiments conducted on simulated and actual magnitude MR images, and evaluations of our methods relative to the current state of the art. Note that a subset of this work (mainly part of Section III) has been accepted for presentation at the 2011 IEEE International Conference on Image Processing [28]. "
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    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.
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