Fine-Granularity and Spatially-Adaptive Regularization for Projection-Based Image Deblurring

This paper studies two classes of regularization strategies to achieve an improved tradeoff between image recovery and noise suppression in projection-based image deblurring. The first is based on a simple fact that r-times Landweber iteration leads to a fixed level of regularization, which allows us to achieve fine-granularity control of projection-based iterative deblurring by varying the value r. The regularization behavior is explained by using the theory of Lagrangian multiplier for variational schemes. The second class of regularization strategy is based on the observation that various regularized filters can be viewed as nonexpansive mappings in the metric space. A deeper understanding about different regularization filters can be gained by probing into their asymptotic behavior-the fixed point of nonexpansive mappings. By making an analogy to the states of matter in statistical physics, we can observe that different image structures (smooth regions, regular edges and textures) correspond to different fixed points of nonexpansive mappings when the temperature(regularization) parameter varies. Such an analogy motivates us to propose a deterministic annealing based approach toward spatial adaptation in projection-based image deblurring. Significant performance improvements over the current state-of-the-art schemes have been observed in our experiments, which substantiates the effectiveness of the proposed regularization strategies.