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IPCV >> Image Enhancement and Restoration > imdeconvl2

imdeconvl2

Deconvolution with L2 Regularization

Syntax

imout = imdeconvl2(imin,psf,lambda)

Parameters

imin :

Source Image

f :

Blur function

lamda :

Regularization parameter

imout :

Deblurred Image

Description

Deconvolution is obtained by dividing the Fourier transform of :

$[f^\star(\omega) = \frac{\hat y(\omega)}{\hat h(\omega)} = \hat f_0(\omega) + \hat w(\omega)/{\hat h(\omega)}]$

To avoid this explosion, we consider a simple regularization.

$[f^{\star} = \text{argmin}_f \: \|y-\Phi f\|^2 + \lambda \|f\|^2]$

Since the filtering is diagonalized over Fourier, the solution is simply computed over the Fourier domain as:

$[\hat f^\star(\omega) = \frac{\hat y(\omega) \hat h(\omega)}{ \|\hat h(\omega)\|^2 + \lambda }]$

Examples

S = imread(fullpath(getIPCVpath() + "/images/balloons_gray.png"));
S = im2double(S);
h = fspecial('motion',25,45);
S2 = imfilter(S,h,'circular');
imshow(S2);
S3 = imdeconvl2(S2,h,0);
scf;imshow(S3);

See also

Authors

Bibliography

1. Advanced Signal, Image and Surface Processing, Ceremade, Université Paris-Dauphine


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