Adaptive blind image deblurring and denoising

Blind image deblurring aims to reconstruct the original image from its blurred version without knowing the blurring mechanism. This is a challenging ill‐posed problem because there are infinitely many possible solutions. The ill‐posedness is further exacerbated if the blurring mechanism depends on the pixel location. In the literature, commonly used methods often assume that the blur is location invariant and estimate the blurring mechanism before restoring the image. In this article, we propose a blind image deblurring and denoising method that directly restores the image and allows the blur to change over locations. A major feature of the proposed method is that it detects blurry pixels using a neighborhood size that optimizes the detection power, and it removes the blur and noise by using as many sharp pixels as possible. Theoretically, we establish that our image estimate is consistent as the image resolution improves, an asymptotic property many existing deblurring methods lack. Numerically, we demonstrate our method's superior performance over state‐of‐the‐art methods in simulated experiments. Applications to real data also show that the proposed method works well.