WienerFilteringforImageRestorationBasicsonImage.ppt

SPIE ITcom 8/01 M. Wu: ENEE631 Digital Image Processing (Spring09) Wiener Filtering for Image Restoration Basics on Image Compression Spring ’09 Instructor: Min Wu  Electrical and Computer Engineering Department, University of Maryland, College Park Overview Last Time: image restoration Power spectral density for 2-D stationary random field A few commonly seen linear distortions in imaging system Deconvolution: inverse filtering, pseudo-inverse filtering Today: Wiener filtering: balance between inverse filtering noise removal Basics compression techniques Handling Noise in Deconvolution Inverse filtering is sensitive to noise Does not explicitly model and handle noise Balance between undo degradation H vs. noise suppression Minimize MSE between the original and restored e = E{ [ u(n1, n2) – u’(n1, n2) ] 2 }, where u’(n1, n2) is a func. of {v(m1, m2) } Best estimate is conditional mean E[ u(n1 , n2) | all v(m1 , m2) ] see EE621; but usually difficult to solve for general restoration (need conditional probability distribution, and estimation is nonlinear in general) Get the best linear estimate instead ? Wiener filtering Consider the (desired) image and noise as random fields Produce a linear estimate from the observed image to minimize MSE EE621 Review: MMSE Baysian parameter estimation – Minimum Mean Squared Error (MMSE) Estimation EE630 Review: Wiener Filtering Want to know the actual values (of the current/interested realization) of a random process {d[n]}, but cannot directly observe it. What we can observe is a process {x[n]} that is statistically related to d[n]. We want to estimate d[n] from x[n]. EE630 Review: Principle of Orthogonality “Orthogonal” in a statistical sense: i.e. the optimal error signal and each observation sample used in the filtering (and also their combinations) are statistically uncorrelated plugging e[n] into the orthogonality principle leads to the normal equation. Wiener Filtering Get the best lin