小波域图像复原111.ppt

小波域图像复原 彭思龙 silong.peng@ia.ac.cn 中科院自动化所 国家专用集成电路设计工程技术研究中心 Image Restoration  Image Restoration  Image Restoration Image Restoration－Degradation model Degradation model (Continous form) Linear vs. Non-linear Many types of degradation can be approximated by linear, space invariant processes Non-linear and space variant models are more accurate Difficult to solve Unsolvable Image Restoration－Degradation model Matrix-Vector representation of image restoration problem: Stack f, g, row-by-row or colon-by-colon to form vector reprsentations of these 2-D variables —— theoretic analysis more easily Image Restoration Image Restoration – Ill-posed Problem Inverse filtering solution H is ill-conditioned which makes image restoration problem an ill-posed problem Solution is not stable: not continuely depend on the observed data g Image Restoration – Ill-posed Problem Another perspective—— Least square solution Image Restoration – Ill-posed Problem Another perspective—— Least square solution (Cont.) Image Restoration For g = Hf + h, the regularization method constructs the solution as u(f, g) describes how the real image data is related to the degraded data. In other words, this term models the characteristic of the imaging system. bv(f) is the regularization term with the regularization operator v operating on the original image f, and the regularization parameter b used to tune up the weight of the regularization term. By adding the regularization term, the original ill-posed problem turns into a well-posed one, that is, the insertion of the regularization operator puts some constraints on what f might be, which makes the solution more stable. Image Restoration MAP (maximum a-posteriori probability) Formulate solution from statistical point of view: MAP approach tries to find an estimate of image f that maximizes the a-posteriori probability