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Center for Nonlinear Studies |
Total Variation (TV) regularization is a successful approach to a wide variety of image restoration problems, including denoising and deblurring. While this has been a very active area of research over the past decade, optimal selection of the regularization parameter has received surprisingly little attention. A number of optimal parameter selection methods have been developed in the context of Tikhonov regularization, but the TV functional is somewhat more difficult to deal with, and extension of these methods to TV regularization is non-trivial. We have implemented existing parameter selection methods, such as the Discrepancy Principle which is based on the variance of the given noise, Correlation Approach which tries to find out the parameter giving the minimum correlation between the restored image and noise, and Max(SNR) Approach which tries to maximize the SNR functional that is expressed in term of the parameter. We have extended the L-Curve and Unbiased Predictive Risk Estimator (UPRE) method to the TV functional. I will compare these approaches, concentrating on three types of restoration problems: denoising, deblurring with well-posed kernel and deblurring with ill-conditioned kernel.
Host: Brendt Wohlberg