IEEE Trans Image Process. 2012 Aug;21(8):3454-66. doi: 10.1109/TIP.2012.2191565. Epub 2012 Apr 5.
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.
在本文中，我们推导出了与卡方随机变量的非中心参数的连续可微估计量相关的期望均方误差的无偏表达式。然后，我们考虑对平方幅度磁共振图像数据进行去噪的任务，这些数据很好地建模为两个自由度上的独立非中心卡方随机变量。我们考虑了两类广泛的线性参数化收缩估计量，可以使用我们的风险估计进行优化，一种是在未分解滤波器组变换的一般情况下，另一种是在未归一化 Haar 小波变换的特定情况下。得到的算法在计算上是可行的，并且优于大多数模拟和实际磁共振图像数据的最先进方法。
