1. Constrained Least Squares Filtering
Team 15 R
黃得源

2. Introduction – Inverse Filtering
Image Degradation
G(u,v) = H(u,v) F(u,v)
F(u,v) = G(u,v)/H(u,v)
Image Degradation with noise
N(u,v)/H(u,v) could easily dominate the estimated image

3. Improvement Wiener Filtering Sn(u,v) & Sf(u,v) must be known
K = Sn(u,v)/Sf(u,v),
Sn(u,v) = |N(u,v)|2
Sf(u,v) = |F(u,v)|2
Sn(u,v) & Sf(u,v) must be known
Sn(u,v) the power spectrum of the noise,
Sf(u,v) the power spectrum of the original image

4. Improvement – Cons. Constrained Least Squares Filtering Constrain:
P(u,v) is the fourier transform of the Laplacian operator
Constrain:
|g – H |2 = |η|2
R(u,v) = G(u,v) – H(u,v)
Adjust γfrom the constrain – by Newton-Raphson root-finding
Apply algorithm from Prof. Hsien-Sen Hung(洪賢昇)
但是power spectrum of the noise

5. The Project Implementation in Matlab Collaborate with an other group
Constrained Least Squares Filtering
Collaborate with an other group
They would implement
Wiener Filter
Inverse Filter
Geometric Mean Filter
Define Blur & Noise Function
Compare the results of filters

6. Reference
Andrews, H. C., and Hunt, B. R. Digital Image Restoration, Prentice Hall, Englewood Cliffs, N. J. [1977].
Wiener, N. Extrapolation, Interpolation, and Smoothing of Stationary Time Series, the MIT Press, Cambridge, Mass. [1942].
R. Woods, R. Gonzalez, Digital Image Processing (2nd Edition)
M.Bilgen, H.S. Hung, Constrained least-squares filtering for noisy images blurred by random point spread function, Optical Engineering, June. 1994