ENEE631 Digital Image Processing (Spring'04) Image Restoration Image Restoration Spring ’04 Instructor: Min Wu ECE Department, Univ. of Maryland, College Park www.ajconline.umd.edu (select ENEE631 S’04) [email protected]Based on ENEE631 Based on ENEE631 Spring’04 Spring’04 Section 7 Section 7
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ENEE631 Digital Image Processing (Spring'04) Image Restoration Spring ’04 Instructor: Min Wu ECE Department, Univ. of Maryland, College Park .
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Figure is from slides at Gonzalez/ Woods DIP book website (Chapter 5)
ENEE631 Digital Image Processing (Spring'04) Lec8 – Image Restoration [12]
Handling Noise in DeconvolutionHandling Noise in Deconvolution Inverse filtering is sensitive to noise
– Does not explicitly modeling and handling noise
Try to balance between deblurring 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) ] 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
ENEE631 Digital Image Processing (Spring'04) Lec8 – Image Restoration [21]
Wiener Filter: Issues to Be AddressedWiener Filter: Issues to Be Addressed
Wiener filter’s size– Theoretically has infinite impulse response ~ require large-size DFTs– Impose filter size constraint: find the best FIR that minimizes MSE
Need to estimate power spectrum density of orig. signal– Estimate p.s.d. of blurred image v and compensate variance due to
noise– Estimate p.s.d. from a set of representative images similar to the images
to be restored– Or use statistical model for the orig. image and estimate parameters
– Constrained least square filter ~ see Jain’s Sec.8.8 & Gonzalez Sec.5.9 Optimize smoothness in restored image (least-square of the
rough transitions) Constrain differences between blurred image and blurred
version of reconstructed image Estimate the restoration filter w/o the need of estimating p.s.d.
ENEE631 Digital Image Processing (Spring'04) Lec8 – Image Restoration [24]
Basic Ideas of Blind DeconvolutionBasic Ideas of Blind Deconvolution
Three ways to estimate H: observation, experimentation, math. modeling
Estimate H via spectrum’s zero patterns
– Two major classes of blur (motion blur and out-of-focus)– H has nulls related to the type and the parameters of the blur
Maximum-Likelihood blur estimation
– Each set of image model and blur parameters gives a “typical” blurred output; Probability comes into picture because of the existence of noise
– Given the observation of blurred image, try to find the set of parameters that is most likely to produce that blurred output
Iteration ~ Expectation-Maximization approach (EM) Given estimated parameters, restore image via Wiener filtering Examine restored image and refine parameter estimation Get local optimums
To explore more: Bovik’s Handbook Sec.3.5 (subsection-4, pp136)
“Blind Image Deconvolution” by Kundur et al, IEEE Sig. Proc. Magazine, vol.13, 1996