ListDeconvolve

ListDeconvolve[ker,list]

gives a deconvolution of list using kernel ker.

Details and Options

  • The arguments ker and list in ListDeconvolve[ker,list] can be real numerical arrays of any rank, and ker cannot be larger than list in any dimension.
  • The following options can be given:
  • Method "DampedLS"deconvolution method to be used
    Padding"Reversed"padding to use for values beyond the original data
    MaxIterations10number of iterations to try
  • If the elements of list are exact numbers, ListDeconvolve begins by applying N to them.
  • For a full documentation of available settings, see the reference page for ImageDeconvolve.

Examples

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Basic Examples  (2)

Create a 2D array and convolve it with a Gaussian kernel:

Deconvolve the array:

Deconvolve a 3D array:

Options  (2)

Method  (2)

Deconvolve a signal with different levels of regularization:

Use various methods to deconvolve a piecewise constant signal:

Applications  (2)

Deconvolve a piecewise constant signal that was blurred and corrupted by additive noise:

Deconvolve a cellular automaton list:

Properties & Relations  (2)

ListDeconvolve is an approximate inverse of ListConvolve:

ImageDeconvolve can be used to deblur images:

Possible Issues  (1)

Zero regularization values give rise to ringing artifacts:

Neat Examples  (1)

This generates blurry and noisy data:

Compute 30 iterations of the Richardson–Lucy algorithm:

Visualize the restoration process. The red dots show the original values of the signal:

Wolfram Research (2010), ListDeconvolve, Wolfram Language function, https://reference.wolfram.com/language/ref/ListDeconvolve.html.

Text

Wolfram Research (2010), ListDeconvolve, Wolfram Language function, https://reference.wolfram.com/language/ref/ListDeconvolve.html.

CMS

Wolfram Language. 2010. "ListDeconvolve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ListDeconvolve.html.

APA

Wolfram Language. (2010). ListDeconvolve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListDeconvolve.html

BibTeX

@misc{reference.wolfram_2024_listdeconvolve, author="Wolfram Research", title="{ListDeconvolve}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ListDeconvolve.html}", note=[Accessed: 25-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_listdeconvolve, organization={Wolfram Research}, title={ListDeconvolve}, year={2010}, url={https://reference.wolfram.com/language/ref/ListDeconvolve.html}, note=[Accessed: 25-December-2024 ]}