投影GSURE在迭代收缩法参数自动调整中的应用
The Projected GSURE for Automatic Parameter Tuning in Iterative Shrinkage Methods
摘要：
线性逆问题在信号和图像处理中非常常见。许多旨在解决此类问题的算法都包含需要调整的未知参数。在这项工作中，我们专注于最佳选择这样的参数，在迭代收缩方法的图像去模糊和图像缩放。我们的工作使用投影广义Stein无偏风险估计（GSURE）确定这些算法的阈值λ和迭代次数K。建议的参数选择处理任何退化算子，包括不适定，甚至矩形。这是通过对预计的预期误差使用GSURE来实现的。我们进一步提出了一个有效的贪婪参数设置方案，调整参数，同时迭代，而不会损害所得到的去模糊性能。最后，我们提供了广泛的比较，传统的方法进行参数选择，显示使用的投影GSURE的优越性。
英文摘要：
Linear inverse problems are very common in signal and image processing. Many algorithms that aim at solving such problems include unknown parameters that need tuning. In this work we focus on optimally selecting such parameters in iterative shrinkage methods for image deblurring and image zooming. Our work uses the projected Generalized Stein Unbiased Risk Estimator (GSURE) for determining the threshold value lambda and the iterations number K in these algorithms. The proposed parameter selection is shown to handle any degradation operator, including ill-posed and even rectangular ones. This is achieved by using GSURE on the projected expected error. We further propose an efficient greedy parameter setting scheme, that tunes the parameter while iterating without impairing the resulting deblurring performance. Finally, we provide extensive comparisons to conventional methods for parameter selection, showing the superiority of the use of the projected GSURE.
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