Constrained Least Squares Filtering

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Constrained Least Squares Filtering

• Team 15
• R95921037
• ???

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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

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Improvement

• Wiener Filtering
• 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

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Improvement Cons.

• Constrained Least Squares Filtering
• P(u,v) is the fourier transform of the Laplacian
  operator
• Constrain
• g H 2 ?2
• R(u,v) G(u,v) H(u,v)
• Adjust ?from the constrain by Newton-Raphson
  root-finding
• Apply algorithm from Prof. Hsien-Sen Hung(???)

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The Project

• Implementation in Matlab
• 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

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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