“Deblurring with rank-structured inverse approximations” by Hudachek-Buswell, Matos and Stewart
Conference:
Type(s):
Title:
- Deblurring with rank-structured inverse approximations
Presenter(s)/Author(s):
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.
References:
1. 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.
2. Hansen, P. C., and Jensen, T. K. 2008. Noise propagation in regularizing iterations for image deblurring. Electronic Transactions on Numerical Analysis 31, 204–220.
3. 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.
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