This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# ImageDeconvolve

 ImageDeconvolvegives a deconvolution of image using kernel ker.
• The deconvolution kernel is given as a numerical matrix or as an image and cannot be larger than image in any dimension.
• The kernel represents the point spread function, which is assumed to model the blur present in the image.
• ImageDeconvolve always gives an image of type of the same dimensions as image.
• The deconvolution kernel must have a single channel or the same number of color channels as the image.
• Possible settings specifying spectral deconvolution methods are:
 "DampedLS" damped least squares, generalized Tikhonov regularization "Tikhonov" Tikhonov regularization method "TSVD" truncated singular value decomposition "Wiener" Wiener deconvolution
• For spectral deconvolution methods, a regularization parameter p can be given with a setting Method. For non-negative deconvolution kernels in which the sum of all elements is equal to 1, the regularization parameter is typically in the range from 0 to 1.
• With a setting Method, separate regularization parameters can be given for each color channel.
• The following settings for the Method option specify iterative deconvolution methods:
 "Hybrid" Tikhonov-Golub-Kahan bidiagonalization regularization "RichardsonLucy" Richardson-Lucy iterative deconvolution "SteepestDescent" modified residual norm steepest descent
• The and methods always return non-negative pixel values.
• Iterative deconvolution methods typically provide better results than spectral methods but are computationally more expensive. By default, preconditioned versions of the iterative methods are used. Preconditioning can be disabled by setting Method->{"method", "Preconditioned"-> False}, resulting in slower convergence.
• The classical Richardson-Lucy deconvolution method does not use preconditioning.
• ImageDeconvolve also supports an iterative method that effectively implements an iterative total variation regularization algorithm.
• The following suboptions can be specified with a setting Method:
 "NoiseModel" "Gaussian" noise model "Regularization" Automatic regularization parameter
• Possible settings for are , , or .
• The maximum number of iterations to be tried when using iterative deconvolution methods can be controlled with the MaxIterations option. The default setting is MaxIterations.
• ImageDeconvolve takes a Padding option. The default setting is . Spectral deconvolution methods do not depend on the choice of padding.
Restore a blurred image:
Deblur a Snellen chart:
The point spread function can be given as an image:
Restore a blurred image:
 Out[1]=

Deblur a Snellen chart:
 Out[1]=

The point spread function can be given as an image:
 Out[1]=
 Scope   (2)
Remove Gaussian blur:
Remove out-of-focus blur:
 Options   (4)
Comparison of spectral deconvolution methods:
Comparison of iterative deconvolution methods:
Iterative methods with preconditioning:
Total variation method with explicit regularization parameter:
 Applications   (1)
Guess an appropriate PSF for removing motion blur:
Even a small amount of noise in a blurred image can reduce the quality of reconstruction:
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