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Typical Types of Degradation: Motion Blur

Typical Types of Degradation: Motion Blur. Typical Types of Degradation: Atmospheric Turbulence. negligible distortion. Typical Types of Degradation: Uniform Out of Focus Blur. periodic in time. periodic in frequency. Periodic Extension of Signals: Wrong!.

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Typical Types of Degradation: Motion Blur

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  1. Typical Types of Degradation: Motion Blur

  2. Typical Types of Degradation:Atmospheric Turbulence

  3. negligible distortion

  4. Typical Types of Degradation:Uniform Out of Focus Blur

  5. periodic in time periodic in frequency

  6. Periodic Extension of Signals: Wrong!

  7. Periodic Extension of Signals: Correct!

  8. Extension is done by zero-padding

  9. The proof is in the notesbased on the following points • The eigenvalues of a circulant matrix are the DFT values of the signal that forms the matrix. • The eigenvectors of a circulant matrix are the DFT basis functions! • Diagonalisation of the degradation matrix yields the proof circular convolution DFT

  10. 2-D Case

  11. Example • Image 256x256 • Degradation 3x3 • Finally both at least (256+3-1)x(256+3-1)=258x258 and also periodic

  12. Example

  13. NON-BLIND !!

  14. Problems – Suppose there isn’t any additive noise

  15. Problems – Suppose THERE IS ADDITIVE NOISE CAN BE HUGE !!

  16. Pseudo-inverse Filtering with Different Thresholds Observe the ghosts!!!

  17. Pseudo-inverse Filteringin the Presence of Noise

  18. ( ) variance of degraded noiseless signal

  19. ITERATIVE METHODSnew estimate=old estimate+function(old estimate) • There is no need to explicitly implement the inverse of an operator. The restoration process is monitored as it progresses. Termination of the algorithm may take place before convergence. • The effects of noise can be controlled in each iteration. • The algorithms used can be spatially adaptive. • The problem specifications are very flexible with respect to the type of degradation. Iterative techniques can be applied in cases of spatially varying or nonlinear degradations or in cases where the type of degradation is completely unknown (blind restoration).

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