Image Restoration Algorithm Based on Regularization and Adaptation
We propose to add a special summand (stabilizer) to the original Tikhonov regularization algorithm; this regularizer includes a specially adapted function to the solution characteristics for the problem of image restoration. This approach to approximation of non-smooth functions based on our new technique for choosing interpolation points. As a result, the approximate solutions have better accuracy and images become more deblured. Moreover, it becomes possible to keep small objects and contours in complex scenes by incorporation of background knowledge about their location or structure into the regularization procedure.
KeywordsImage reconstruction Non-smooth solution Adaptive method Ill-posed problem Tikhonov regularization Fredholm integral equation Numerical method
The author would like to express special gratitude to Prof. V.V. Vasin from the Institute of Mathematics and Mechanics UB RAS. This work was supported by Russian Foundation for Basic Research, project no. 12-01-00106. I would like to thank the colleagues from AIST Program and Organizing Committees for their helpful advice and guidance in the paper preparations and supported by the Program of Presidium RAS N 15 (project 12-P-1-1023).
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