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Conclusions
Published in Mario Bertero, Patrizia Boccacci, Christine De Mol, Introduction to Inverse Problems in Imaging, 2021
Mario Bertero, Patrizia Boccacci, Christine De Mol
Step 1 is obvious: it is the basic point for the formulation of the problem of image formation and it can be called the mathematical modeling of the forward problem. In some cases, as in X-ray tomography, this step may be rather easy while it may be very difficult in others (for instance, in the case of emission tomography). In image deconvolution this step is equivalent to the identification of the PSF by means of measurements or to its computation based on a sufficiently accurate model of the imaging system. If one has only a poor knowledge of the PSF one can attempt to improve it by means of methods for blind deconvolution, a term introduced by Stockham, Cannon and Ingebretsen [270] for denoting problems where both the PSF and the object are unknown. One has now at one's disposal many methods of blind deconvolution: spectral methods [270], iterative methods [14] or maximum likelihood methods [186]. The discussion of such methods is beyond the scope of this book.
Comments and concluding remarks
Published in Bertero Mario, Boccacci Patrizia, Introduction to Inverse Problems in Imaging, 2020
Bertero Mario, Boccacci Patrizia
We briefly discuss now the various steps mentioned above. Step 1 is obvious; it is the basic point for the formulation of the problem of image formation. In some cases, as in X-ray tomography, this step may be rather easy while it may be very difficult in others (for instance, in the case of emission tomography). In image deconvolution this step is equivalent to the identification of the PSF by means of measurements or of computations based on a sufficiently accurate model of the imaging system. If one has only a poor knowledge of the PSF one can attempt to improve it by means of methods of blind deconvolution, a term introduced by Stockham, Cannon and Ingebretsen [1] to denote problems where both the PSF and the object are unknown. One has now at one's disposal many methods of blind-deconvolution: spectral methods [1], iterative methods [2] or maximum likelihood methods [3].
Fusion of Blurred Images
Published in Rick S. Blum, Zheng Liu, Multi-Sensor Image Fusion and Its Applications, 2018
Blind deconvolution in its most general form is an unsolvable problem. All methods proposed in the literature inevitably make some assumptions about the PSFs hi and/or the original image u(x, y). Different assumptions give rise to various deconvolution methods. There are two basic approaches to solving the MBD problem. The first one is to separately treat each channel by any single-channel deconvolution method and then to combine the results; the other is to employ deconvolution methods that are multichannel in their nature.
A fractional-order regularization with sparsity constraint for blind restoration of images
Published in Inverse Problems in Science and Engineering, 2021
Shaowen Yan, Guoxi Ni, Jingjing Liu
If both clear image and blur kernel or PSF are unknown, how to reverse from the blurry image f is then a blind deconvolution problem. Blind deconvolution is a very challenging ill-conditioned and ill-posed inverse problem, because it is not only sensitive to image noise but also with infinitely many solutions. These problems originate from many applications such as remote sensing, astronomy, medical image, video cameras and the enhancement of blurred photos. Blind deconvolution methods have been proposed to simultaneously estimate the true image and PSF, such as the IBD and NAS-RIF [6–8]; another successful method is the parametric blind deconvolution method, which supposes PSF can be described by parametric model with one or more unknown parameters [9, 10], as we know that the blind deconvolution is ill-posed, to avoid such problem, some regularization terms are used for solvability.