Consistent Blind Image Deblurring Using Jump-Preserving Extrapolation

Blind image deblurring (BID) aims to estimate the true image from blurred observations when the blurring mechanism described by a point spread function (PSF) cannot be completely specified beforehand. This is a challenging ill-posed problem because there are infinitely many solutions even in cases when the PSF is location invariant. In reality, however, blurring often cannot be accurately described by a location-invariant PSF and the ill-posedness of the BID problem would be further exacerbated. In this article, we propose a novel BID methodology, which allows the PSF to change over locations. The true image is estimated by our jump-preserving extrapolation (JPEX) technique. The proposed method classifies the pixels in a blurred image into two categories: blurry pixels and sharp pixels. The key idea of JPEX is to remove blur involved in blurry pixels using nearby sharp pixels. Theoretical justifications show that the proposed method is statistically consistent. Numerical experiments with both simulated and real images demonstrate that it works well in applications. The comparison with state-of-the-art methods favors the proposed approach as well.