Department of Electrical and Computer Engineering, Michigan State University, East Lansing, MI 48824-1226, USA.
IEEE Trans Image Process. 1999;8(5):666-78. doi: 10.1109/83.760334.
Many imaging systems rely on photon detection as the basis of image formation. One of the major sources of error in these systems is Poisson noise due to the quantum nature of the photon detection process. Unlike additive Gaussian white noise, the variance of Poisson noise is proportional to the underlying signal intensity, and consequently separating signal from noise is a very difficult task. In this paper, we perform a novel gedankenexperiment to devise a new wavelet-domain filtering procedure for noise removal in photon imaging systems. The filter adapts to both the signal and the noise, and balances the trade-off between noise removal and excessive smoothing of image details. Designed using the statistical method of cross-validation, the filter is simultaneously optimal in a small-sample predictive sum of squares sense and asymptotically optimal in the mean-square-error sense. The filtering procedure has a simple interpretation as a joint edge detection/estimation process. Moreover, we derive an efficient algorithm for performing the filtering that has the same order of complexity as the fast wavelet transform itself. The performance of the new filter is assessed with simulated data experiments and tested with actual nuclear medicine imagery.
许多成像系统依赖光子探测作为图像形成的基础。这些系统中的一个主要误差源是由于光子探测过程的量子性质而导致的泊松噪声。与加性高斯白噪声不同，泊松噪声的方差与潜在的信号强度成正比，因此从噪声中分离信号是一项非常困难的任务。在本文中，我们进行了一个新的思维实验，设计了一种新的小波域滤波程序，用于去除光子成像系统中的噪声。该滤波器自适应于信号和噪声，并在噪声消除和图像细节过度平滑之间取得平衡。该滤波器使用交叉验证的统计方法设计，在小样本预测均方和意义上同时是最优的，在均方误差意义上是渐近最优的。该滤波过程可以简单地解释为联合边缘检测/估计过程。此外，我们推导出一种用于执行滤波的有效算法，其复杂度与快速小波变换本身相同。新滤波器的性能通过模拟数据实验进行评估，并通过实际核医学图像进行测试。
