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Topic 9 - Image Restoration

Topic 9 - Image Restoration. Department of Physics and Astronomy. DIGITAL IMAGE PROCESSING Course 3624. Professor Bob Warwick. Restoring a Blurred Image.

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Topic 9 - Image Restoration

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  1. Topic 9 - Image Restoration Department of Physics and Astronomy DIGITAL IMAGE PROCESSING Course 3624 Professor Bob Warwick

  2. Restoring a Blurred Image

  3. In image restoration an attempt is made to reconstruct a degraded image by using "a priori" knowledge of the degradation process. Consider the following system: 9.1 Image Degradation Model See detailed notes demonstrating that for a linear, position invariant system....

  4. 9.2 The System Filter Measured Image 'Ideal' Image PSF Noise FT of Measured Image FT of 'Ideal' Image System Filter FT of Noise Where the SYSTEM FILTER H(u,v) is the FT of the PSF h(x,y) EXAMPLES OF DIFFERENT TYPES OF SYSTEM FILTER (in 1-d & 2-d) (a) Uniform 1-d Blurring (eg due to "camera shake") (b) Gaussian PSF (eg due to atmospheric turbulence)

  5. Degradation due to Camera Shake or Motion Blur

  6. Imaging in Astronomy:Atmospheric effects can cause "poor seeing"

  7. Different Types of System Filter cont. Systems with Diffraction Limited PSFs Rectangular Aperture Circular Aperture Airy Disk Dist. 1.75 % The angular resolution of a telescope is often quoted as the radius of the first minimum in the Airy pattern: nb for the eye

  8. System Filter of a Diffraction-Limited Imager The aperture distribution (in units of wavelength λ) scaled by flens amplitude intensity (PSF) auto-correlation How are the aperture distribution and the system filter related?

  9. The Original HST-System Filter PSF System Filter

  10. 9.2 Image Restoration - The Inverse Filter FT of Measured Image FT of 'Ideal' Image System Filter FT of Noise How can the 'Ideal' Image F(u,v)  f(x,y) be restored? The required process is a DECONVOLUTION in the presence of noise – (which is tricky!!). Inverting the equation we get: But since the second term depends on a statistical variable for which we may (at best) know only the average properties, then we are left to calculate an estimate: This is the INVERSE FILTER recipe. We assume "a priori" knowledge of H(u,v), obtained perhaps as the FT of the image of a point source (ie, the PSF). The best approach is to use the Inverse Filter only where H(u,v)>>0.

  11. Image Restoration Example

  12. Image Restoration Example

  13. 9.3 The Wiener Restoration Filter The WIENER FILTER provides a method of restoring images are both blurred and noisy in a more robust fashion than the INVERSE FILTER. The filter has the form: Here the K(u,v) term "copes" with the zeros in H(u,v). An "optimum" choice is K(u,v) = noise power/signal power, but this quantity is general not known in detail. Implementation: Generally some value/form for K(u,v) is estimated or guessed. For example: (a) K(u,v) = constant, where the value might be chosen interactively or iteratively. (b) Determine an approximate form for K(u,v) from inspection of the input data G(u,v). I

  14. Image Restoration Example - I

  15. Image Restoration Example - II

  16. Some Comparisons u  The operation of the Wiener Filter: (a) In the absence of blur H  1 (ie, low-pass in character) (b) In the absence of noise K  0 (ie, high-pass in character)

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