14-08-2012, 03:14 PM
Image Deconvolution By Richardson Lucy Algorithm
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Abstract
In our project we have tried to restore an image degraded by presence of noise
by applying Richardson Lucy Algorithm. Computer implementation of this algorithm
is our main aim. Besides we have shown that this algorithm is nothing but an EM
Algorithm. In our project we have considered gray images only.
Introduction:
Restoration of digital images from their degraded measurement has always been a problem of
great interest. A specific solution to the problem of image restoration is generally determined
by the nature of degradation phenomena. So it is highly dependent on the nature of the
noise present there. Given the noise function, one can use the Richardson-Lucy Algorithm
to restore the degraded image. This algorithm was introduced by W.H. Richardson (1972)
and L.B. Lucy (1974).
What is an Image:
An image is nothing but a huge collection of numbers known as pixels. In particular a gray
image is an image in which the value of each pixel is a single sample, that is it carries only
intensity information. So a pixel in a given image is just the intensity at that particular
point. The pixel value is a number between 0 and 1 (both inclusive). 0 denotes the total
absence (i.e. black) and 1 denotes the total presence (i.e. white).
Point Spread Function:
The Point Spread Function describes the response of an imaging system to a point source
or point object. Following is an example of a PSF:
Computer Implementation:
Suppose, we are given a square image of size M ×M. Then there is a total of M2 pixels.
For each of the pixels, we have to apply the algorithm. To compute the denominator of (2),
we have to run a loop over all M2 pixels. This denominator is to be calculated for each of
the M2 terms in the outer most sum of (2). So, for a single iteration step, complexity will
be M2 ×M2 ×M2 = M6. Now, even a small image is of 256 × 256 or 512 × 512. So, first
we have to reduce the complexity.