Use estimated signal and noise to adjust step size for image restoration

Image deblurring is a challenging inverse problem, especially when there is additive noise to the observation. To solve such an inverse problem in an iterative manner, it is important to control the step size for achieving a stable and robust performance. We designed a method that controls the progress of iterative process in solving the inverse problem without the need for a user-specified step size. The method searches for an optimal step size under the assumption that the signal and noise are two independent stochastic processes. Experiments show that the method can achieve good performance in the presence of noise and imperfect knowledge about the blurring kernel. Tests also show that, for different blurring kernels and noise levels, the difference between two consecutive estimates given by the new method tends to remain more stable and stay in a smaller range, as compared to those given by some existing techniques. This stable feature makes the new method more robust in the sense that it is easier to select a stopping threshold for the new method to use in different scenarios.