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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.
Unambiguous detection of signals superimposed on unknown trends is difficult for unevenly spaced data. Here, we formulate the Discrete Chi-square Method (DCM) that can determine the best model for many signals superimposed on arbitrary polynomial tre
Spatial prediction of weather-elements like temperature, precipitation, and barometric pressure are generally based on satellite imagery or data collected at ground-stations. None of these data provide information at a more granular or hyper-local re
Recent evidence has shown that structural magnetic resonance imaging (MRI) is an effective tool for Alzheimers disease (AD) prediction and diagnosis. While traditional MRI-based diagnosis uses images acquired at a single time point, a longitudinal st
Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability model for thi
Under-representation of certain populations, based on gender, race/ethnicity, and age, in data collection for predictive modeling may yield less-accurate predictions for the under-represented groups. Recently, this issue of fairness in predictions ha