Blind image deconvolution using a robust GCD approach

S. Unnikrishna Pillai, B. Liang
1999 IEEE Transactions on Image Processing  
In this paper, we study the problem of image deblurring which arises in Image Processing and Computer Graphics. More precisely, we study the deblurring of a blurred image in one and two dimensions. We propose a new, fast, based on matrices of special form, method, deblurring the initial blurred image in a stable way, reducing per one order the required computational complexity. For this purpose we modify the algorithm proposed in [3] in order to take advantage of the special form of Toeplitz
more » ... form of Toeplitz matrices that we use. Through the study of the error analysis of our method we prove its stability using orthogonal transformations. Known algorithms approaching the problem using Discrete Fourier Transformations (DFT) [1, 2] are sensitive in numerical computations. We compare our method with these ones, concluding to useful results, which concern both the stability as the complexity of the algorithms. The proposed procedures are tested using real examples. [2] Raymond A. Heindl, Fourier Transform, Polynomial GCD, and Image Restoration, Master Thesis, Department of Mathematical Sciences, Clemson University (2005) . [3] D. Triantafyllou and M. Mitrouli, On rank and null space computation of the generalized Sylvester matrix, Numer.
doi:10.1109/83.743863 pmid:18267476 fatcat:fwslbne7rfhyjk33ezd7rhubky