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# deconvreg() - Image Processing

### Syntax

### Example

### Output / Return Value

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### Reference

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).

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,...)

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)');