Typical Types of Degradation: Motion Blur

How does motion blur occur ?

• A camera works by exposing a sheet of light sensitive film to a scene, for a short period of time.

• The light from the scene, hitting the film, causes the film to change chemically, and eventually results in a picture representation of the scene.

• This is known as an exposure.• If the scene changes during that exposure, a blurred image will result, since light

from many scenes hit the film.

Typical Types of Degradation:Atmospheric Turbulence

0025.0 k

001.0k 00025.0 k

negligible

distortion

Typical Types of Degradation:Uniform Out of Focus Blur

periodic in frequency periodic in time

Periodic Extension of Signals: Wrong!

Periodic Extension of Signals: Correct!

Extension is done by zero-padding

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

2-D Case

Example

• Image 256x256

• Degradation 3x3

• Finally both at least

(256+3-1)x(256+3-1)=258x258

and also periodic

Example

NON-BLIND !!

Problems – Suppose there isn’t any additive noise

Problems – Suppose THERE IS ADDITIVE NOISE

CAN BE HUGE !!

Pseudo-inverse Filtering with Different Thresholds

Observe the ghosts!!!

Pseudo-inverse Filteringin the Presence of Noise

),()),(),((

),(),(

),(),(),()),(),((

22

22

vuYvuCvuH

vuHvuF

vuYvuHvuFvuCvuH

( )

variance of degraded noiseless signal

ITERATIVE METHODS

new 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).