Abstract
The inverse problem of image restoration to remove noise and blur in an observed image was extensively studied in the last two decades. For the case of a known blurring kernel (or a known blurring type such as out of focus or Gaussian blur), many effective models and efficient solvers exist. However when the underlying blur is unknown, there have been fewer developments for modelling the so-called blind deblurring since the early works of You and Kaveh (1996) and Chan and Wong (1998). A major challenge is how to impose the extra constraints to ensure quality of restoration. This paper proposes a new transform based method to impose the positivity constraints automatically and then two numerical solution algorithms. Test results demonstrate the effectiveness and robustness of the proposed method in restoring blurred images.
Highlights
Among image preprocessing problems is the reconstruction of an image from a given degraded image, such as images corrupted by noise [1, 2] or blur [3, 4] or images with missing or damaged portions [5]
We focus on image deblurring in the blind case where the blur operator is unknown
We have presented a total variation based blind deconvolution model with solution positivity achieved by implicit transforms and two solution algorithms for reconstructing a deblurred image along with its blur kernel
Summary
Among image preprocessing problems is the reconstruction of an image from a given degraded image, such as images corrupted by noise [1, 2] or blur [3, 4] or images with missing or damaged portions [5]. Such tasks have been widely studied in the last few decades; see [6] for decoupling noise and blur modeling, [7] for imposing box constraints, [8] for a fast iterative solver for noise and blur modeling, and [9, 10] for general surveys.
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