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# deconvreg() - Image Processing

```J = deconvreg(I, PSF) deconvolves
image I using the regularized filter algorithm,
returning deblurred image J. The assumption is that the image I was
created by convolving a true image with a point-spread function PSF
and possibly by adding noise. The algorithm is a constrained optimum
in the sense of least square error between the estimated and the true
images under requirement of preserving image smoothness. I can be a N-dimensional array.J = deconvreg(I, PSF, NOISEPOWER) where NOISEPOWER is
the additive noise power. The default value is 0.J = deconvreg(I, PSF, NOISEPOWER, LRANGE) where LRANGE is
a vector specifying range where the search for the optimal solution
is performed. The algorithm finds an optimal Lagrange multiplier LAGRA within
the LRANGE range. If LRANGE is
a scalar, the algorithm assumes that LAGRA is given
and equal to LRANGE; the NP value
is then ignored. The default range is between [1e-9 and 1e9].J = deconvreg(I, PSF, NOISEPOWER, LRANGE,
REGOP)  where REGOP is the regularization
operator to constrain the deconvolution. The default regularization
operator is the Laplacian operator, to retain the image smoothness.
The REGOP array dimensions must not exceed the
image dimensions; any nonsingleton dimensions must correspond to the
nonsingleton dimensions of PSF.[J, LAGRA] = deconvreg(I, PSF,...) outputs
the value of the Lagrange multiplier LAGRA in addition
to the restored image J.Note

The output image J could exhibit ringing
introduced by the discrete Fourier transform used in the algorithm.
To reduce the ringing, process the image with the edgetaper function
prior to calling the deconvreg function. For example, I
= edgetaper(I,PSF).```

### Syntax

```J = deconvreg(I, PSF)J = deconvreg(I, PSF, NOISEPOWER)J = deconvreg(I, PSF, NOISEPOWER, LRANGE)J = deconvreg(I, PSF, NOISEPOWER, LRANGE,
REGOP) [J, LAGRA] = deconvreg(I, PSF,...)```

### Example

```I = checkerboard(8);
PSF = fspecial('gaussian',7,10);
V = .01;
BlurredNoisy = imnoise(imfilter(I,PSF),'gaussian',0,V);
NOISEPOWER = V*prod(size(I));
[J LAGRA] = deconvreg(BlurredNoisy,PSF,NOISEPOWER);

subplot(221); imshow(BlurredNoisy);
title('A = Blurred and Noisy');
subplot(222); imshow(J);
title('[J LAGRA] = deconvreg(A,PSF,NP)');
subplot(223); imshow(deconvreg(BlurredNoisy,PSF,[],LAGRA/10));
title('deconvreg(A,PSF,[],0.1*LAGRA)');
subplot(224); imshow(deconvreg(BlurredNoisy,PSF,[],LAGRA*10));
title('deconvreg(A,PSF,[],10*LAGRA)');```