Degradation reduction in optics imagery using Toeplitz structure |
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Authors: | James G Nagy V Paul Pauca Robert J Plemmons Todd C Torgersen |
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Affiliation: | (1) Department of Mathematics, Southern Methodist University, 75275-0156 Dallas, TX;(2) Department of Computer Science, Duke University, 27708 Durham, NC;(3) Department of Mathematics and Computer Science, Wake Forest University, 27109 Winston-Salem, NC;(4) Department of Mathematics and Computer Science, Wake Forest University, 27109 Winston-Salem, NC |
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Abstract: | This paper is concerned with improvement in optical image quality by image restoration. Image restoration is an ill-posed
inverse problem which involves the removal or minimization of degradations caused by noise and blur in an image, resulting
from, in this case, imaging through a medium. Our work here concerns the use of the underlying Toeplitz structure of such
problems, and associated techniques for accelerating the convergence of iterative image restoration computations. Denoising
methods, including total variation minimization, followed by segmentation-based preconditioning methods for minimum residual
conjugate gradient iterations, are investigated. Regularization is accomplished by segmenting the image into (smooth) segments
and varying the preconditioners across the segments. By taking advantage of the Toeplitz structure, our algorithms can be
implemented with computational complexity of onlyO (ln
2 logn), wheren
2 is the number of pixels in the image andl is the number of segments used. Also, parallelization is straightforward. Numerical tests are reported for atmospheric imaging
problems, including the case of spatially varying blur.
Research supported in part by a National Science Foundation Postdoctoral Research Fellowship.
Research sponsored by the U.S. Air Force Office of Scientific Research under grant F49620-97-1-1039.
Research sponsored by the U.S. Air Force Office of Scientific Research under grant F49620-97-1-0139, and by the National Science
Foundation under grant CCR-96-23356.
Research sponsored by the National Science Foundation under grant CCR-96-23356. |
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Keywords: | |
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