Parallel image restoration using surrogate constraint methods
Journal of Parallel and Distributed Computing
EURASIP Journal on Applied Signal Processing
Total variation minimizing blind deconvolution with shock filter reference
Image and Vision Computing
Estimating the 3D direction of a translating camera from a single motion-blurred image
Pattern Recognition Letters
Image enhancement for fluid lens camera based on color correlation
IEEE Transactions on Image Processing
Restoration of images with piecewise space-variant blur
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Space-variant deblurring using one blurred and one underexposed image
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Contourlet domain multiband deblurring based on color correlation for fluid lens cameras
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
Smoothing and regularization with modified sparse approximate inverses
Journal on Image and Video Processing - Special issue on iterative signal processing in communications
Variational deblurring of images with uncertain and spatially variant blurs
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Non-uniform Deblurring for Shaken Images
International Journal of Computer Vision
Modeling and synthesis of aperture effects in cameras
Computational Aesthetics'08 Proceedings of the Fourth Eurographics conference on Computational Aesthetics in Graphics, Visualization and Imaging
Shift-invariant approximations of structured shift-variant blurring matrices
Numerical Algorithms
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Restoration of images that have been blurred by the effects of a Gaussian blurring function is an ill-posed but well-studied problem. Any blur that is spatially invariant can be expressed as a convolution kernel in an integral equation. Fast and effective algorithms then exist for determining the original image by preconditioned iterative methods. If the blurring function is spatially variant, however, then the problem is more difficult. In this work we develop fast algorithms for forming the convolution and for recovering the original image when the convolution functions are spatially variant but have a small domain of support. This assumption leads to a discrete problem involving a banded matrix. We devise an effective preconditioner and prove that the preconditioned matrix differs from the identity by a matrix of small rank plus a matrix of small norm. Numerical examples are given, related to the Hubble Space Telescope (HST) Wide-Field/Planetary Camera. The algorithms that we develop are applicable to other ill-posed integral equations as well.