need of edge detection in deblurring an image

i am trying a project titled "blind and semiblind deblurring of natural images".

their it is mentioned that deblurring method is based on two simple facts

1)in natural image leading edges are sparse 2)edges of the blurred image are less sparse than those of sharp image because they occupy wider area.

i want to know what relationship does this edge detection has with the deblurring the image.. whether its related to know the PSF.. i have no idea about it. kindly help to develop a stratergy

Answer 1

[Image Analyst]

Trying to see how this relates to MATLAB....you can use conv2() to experiment with different convolution kernels. Note how kernels (PSFs) with all positive numbers blur the image while you need negative numbers to sharpen the image or find edges. Have fun experimenting...

[Max]

thanx image analyst:)

a cost function is given to minimize there

C(x,h)=1/2||y-h*h||^2+lambda . R[f(x)]

y is the blurred image

h is the psf

x is the original image

R is regularizer function

f(x) is the set of edge detected image obtained from rotating four sets of edge detection filters

an algorithm is given to minimize.

Initialization

1)set h to the identity operator

2)set x equal to y

3)set lambda and q to the initial value.

optimization loop

4)find the new x estimate :x=argminx C(x,h)

5)find a new h estimate h=argminh C(x,h)

6)set lambda and q to the next value in sequence

7)if lambda >lambdamin go back to step 4,, otherwise stop.

now the thing is the equation C(x,h) given to minimize is a least square problem.. hence i am not abble to understand where to start thius work