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TotalVariationFilter[data]

iteratively reduces noise while preserving rapid transitions in data.

TotalVariationFilter[data,param]

assumes a regularization parameter value param.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Data  
Parameters  
Options  
Method  
MaxIterations  
Applications  
See Also
Related Guides
History
Cite this Page

TotalVariationFilter

TotalVariationFilter[data]

iteratively reduces noise while preserving rapid transitions in data.

TotalVariationFilter[data,param]

assumes a regularization parameter value param.

Details and Options

  • TotalVariationFilter, also known as total variation regularization, is an iterative filter commonly used to reduce different types of additive or multiplicative noise while preserving sharp transitions.
  • In TotalVariationFilter[data,param], the value of regularization parameter param is typically in the range 0 to 1.
  • The data can be any of the following:
  • listarbitrary-rank numerical array
    tseriestemporal data such as TimeSeries, TemporalData, …
    imagearbitrary Image or Image3D object
    audioan Audio object
    videoa Video object
  • The following options can be specified:
  • MaxIterations 30maximum number of iterations to be performed
    Method "Gaussian"type of noise to be removed
  • Possible Method settings include: »
  • "Gaussian"additive Gaussian, uniform and other types of noise
    "Laplacian"salt-and-pepper or impulse noise
    "Poisson"multiplicative noise, as in low-light conditions

Examples

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Basic Examples  (3)

Denoise a grayscale image:

Filter a 3D image:

Total variation filtering on noisy data:

Scope  (9)

Data  (6)

Filter a 2D array:

Filter a TimeSeries:

Filter an audio signal:

Denoise an image:

TotalVariationFilter works with numerical sparse arrays:

Filtering of video frames:

Parameters  (3)

The default regularization parameter value, assuming additive Gaussian noise, is 0.1:

Use a custom regularization value:

The default regularization value for Laplacian noise is 0.8:

Use a large custom value:

Use different regularization parameters:

Options  (4)

Method  (2)

Salt-and-pepper noise is best removed using the Laplacian method:

Use the Poisson method to remove noise from an image captured with low light:

MaxIterations  (2)

Filtering of a 1D array using different values of MaxIterations:

Denoise a grayscale image:

Use a larger number of iterations:

Applications  (5)

Denoise a color image:

Use the Poisson method to remove noise from an image captured with low light:

Remove Gaussian color noise from an image:

Use a TotalVariationFilter to remove smaller stars from an astronomical image:

Unsharp masking using TotalVariationFilter:

Wolfram Research (2010), TotalVariationFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/TotalVariationFilter.html (updated 2025).

Text

Wolfram Research (2010), TotalVariationFilter, Wolfram Language function, https://reference.wolfram.com/language/ref/TotalVariationFilter.html (updated 2025).

CMS

Wolfram Language. 2010. "TotalVariationFilter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2025. https://reference.wolfram.com/language/ref/TotalVariationFilter.html.

APA

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

BibTeX

@misc{reference.wolfram_2025_totalvariationfilter, author="Wolfram Research", title="{TotalVariationFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/TotalVariationFilter.html}", note=[Accessed: 13-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_totalvariationfilter, organization={Wolfram Research}, title={TotalVariationFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/TotalVariationFilter.html}, note=[Accessed: 13-August-2025]}