Mary Hudachek-Buswell
ABSTRACT
In this presentation, the restoration of images blurred by atmospheric turbulence is examined. The proposal uses a new class of approximations to blurring operators representing Gaussian blur. The Toeplitz matrix representing the blur is transformed into a Cauchy-like (CL) matrix using the FFT. In addition to the CL structure, the transformed matrix has a rank structure. In particular, the off-diagonal blocks have low rank. This class of matrices can be approximated quickly, and the structure can be exploited for fast image restoration.
- Chandrasekaran, S., Gu, M., Sun, X., Xia, J., and Zhu, J. 2007. A superfast algorithm for toeplitz systems of linear equations. SIAM Journal on Matrix Analysis and Applications 29, 4, 1247--1266. Google Scholar
Digital Library
- Hansen, P. C., and Jensen, T. K. 2008. Noise propagation in regularizing iterations for image deblurring. Electronic Transactions on Numerical Analysis 31, 204--220.Google Scholar
- Nagy, J. G., Plemmons, R. J., and Torgersen, T. C. 1996. Iterative image restoration using approximate inverse preconditioning. IEEE Transactions on Image Processing 5, 7 (July), 1151--1162. Google ScholarDigital Library
Index Terms
- Deblurring with rank-structured inverse approximations
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