30-05-2013, 04:56 PM
Algebraic Approach to Restoration
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The objective of image restoration is to estimate an original
image f from a degraded image g and some knowledge or
assumptions about H and n.
Algebraic approach seeks an estimate of f, denoted , that
minimizes a predefined criterion of performance.
To demonstrate the overall concept, the least square criterion
function will be used.
The least square criterion function can be used in two
different ways:
Unconstrained approach,
Constrained approach.
Removal of Blur Caused by Uniform Linear Motion:
Consider the problem of restoring an image that has been
blurred by uniform linear motion.
This problem is chosen because of its practical implication
and the fact that it lends itself well to an analytical formulation.
Solution of the uniform blurring case also demonstrates how
zeros of H(u,v) can be handled computationally.
Suppose that an image f(x,y) undergoes planar motion and
that x0(t) and y0(t) are time varying components of motion in
the x and y direction respectively.
Also assume the shutter opening and closing takes place
instantaneously.
Supposing the optical imaging process is also perfect, it will
isolate the effect of image motion.