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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:

Wolfram Language code: TotalVariationFilter[[image]]

Filter a 3D image:

Wolfram Language code: TotalVariationFilter[[image], 0.3]

Total variation filtering on noisy data:

Wolfram Language code: data = Table[Sin[i ^ 2 + i] + RandomReal[{-.2, .3}], {i, 0, Pi, 0.01}]; result = TotalVariationFilter[data];
Wolfram Language code: ListLinePlot[#, Axes -> False]& /@ {data, result}

Scope  (9)

Data  (6)

Filter a 2D array:

Wolfram Language code: TotalVariationFilter[(⁠| | | | | | - | - | - | - | | 0 | 0 | 0 | 0 | | 0 | 0 | 1 | 0 | | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 0 |⁠)]//MatrixForm

Filter a TimeSeries:

Wolfram Language code: ts = TemporalData[TimeSeries, {{{0., -0.27267267057145633, -0.6672983789995302, -0.5338541947930846, -0.6117404489279314, -0.6755527076595494, -0.02125421294486496, -0.10792797291843935, -0.6138271235477938, -0.3248568606554575, -0.08843449054 ... 2053424, -0.49980440691873723, -0.5388679788215971, -0.4101602764645551}}, {{0, 1., 0.01}}, 1, {"Continuous", 1}, {"Continuous", 1}, 1, {ValueDimensions -> 1, ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}}}, False, 10.1];
Wolfram Language code: filtered = TotalVariationFilter[ts, 0.5]; ListLinePlot[{ts, filtered}, PlotLegends -> {"original data", "filtered"}]

Filter an audio signal:

Wolfram Language code: a = \!\(\*AudioBox["![Embedded Audio Player](audio://content-tdkn9)"]\); filtered = TotalVariationFilter[a]//AudioNormalize
Wolfram Language code: AudioPlot[{a, filtered}]

Denoise an image:

Wolfram Language code: TotalVariationFilter[[image]]

TotalVariationFilter works with numerical sparse arrays:

Wolfram Language code: TotalVariationFilter[SparseArray[1 -> 3, 3]]

Filtering of video frames:

Wolfram Language code: TotalVariationFilter[Video["ExampleData/fish.mp4"], .5]

Parameters  (3)

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

Wolfram Language code: data = Table[Sin[i ^ 2 + i] + RandomReal[NormalDistribution[0, 0.3]], {i, 0, Pi, 0.01}]; {ListLinePlot[data, Axes -> False], ListLinePlot[TotalVariationFilter[data], Axes -> False]}

Use a custom regularization value:

Wolfram Language code: {ListLinePlot[data, Axes -> False], ListLinePlot[TotalVariationFilter[data, 0.3], Axes -> False]}

The default regularization value for Laplacian noise is 0.8:

Wolfram Language code: TotalVariationFilter[[image], Method -> "Laplacian"]

Use a large custom value:

Wolfram Language code: TotalVariationFilter[[image], 2., Method -> "Laplacian"]

Use different regularization parameters:

Wolfram Language code: TotalVariationFilter[[image], #]& /@ {.02, .2}

Options  (4)

Method  (2)

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

Wolfram Language code: TotalVariationFilter[[image], Method -> "Laplacian"]

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

Wolfram Language code: TotalVariationFilter[[image], Method -> "Poisson"]

MaxIterations  (2)

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

Wolfram Language code: data = Table[Sin[i ^ 2 + i] + RandomReal[NormalDistribution[0, 0.3]], {i, 0, Pi, 0.01}]; ListLinePlot[TotalVariationFilter[data, 0.3, MaxIterations -> #], Axes -> False]& /@ {1, 10, 30}

Denoise a grayscale image:

Wolfram Language code: i = [image]; TotalVariationFilter[i, 0.2, MaxIterations -> 10]

Use a larger number of iterations:

Wolfram Language code: TotalVariationFilter[i, 0.2, MaxIterations -> 100]

Applications  (5)

Denoise a color image:

Wolfram Language code: TotalVariationFilter[[image], 1, Method -> "Laplacian", MaxIterations -> 100]

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

Wolfram Language code: TotalVariationFilter[[image], 0.35, Method -> "Poisson"]

Remove Gaussian color noise from an image:

Wolfram Language code: i = [image]; TotalVariationFilter[i, .06, MaxIterations -> 100]

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

Wolfram Language code: TotalVariationFilter[[image], .1]

Unsharp masking using TotalVariationFilter:

Wolfram Language code: i = [image]; 2i - TotalVariationFilter[i, 1]
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_2026_totalvariationfilter, author="Wolfram Research", title="{TotalVariationFilter}", year="2025", howpublished="\url{https://reference.wolfram.com/language/ref/TotalVariationFilter.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_totalvariationfilter, organization={Wolfram Research}, title={TotalVariationFilter}, year={2025}, url={https://reference.wolfram.com/language/ref/TotalVariationFilter.html}, note=[Accessed: 13-June-2026]}