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wnoisest

Estimate noise of 1-D wavelet coefficients

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    Syntax

    stdc = wnoisest(c,l,s)
    stdc = wnoisest(c)

    Description

    stdc = wnoisest(c,l,s) returns estimates of the detail coefficients' standard deviation for levels specified in s. [c,l] is a multilevel wavelet decomposition structure and is the output of wavedec.

    The estimator used is Median Absolute Deviation / 0.6745, well suited for zero-mean Gaussian white noise in the denoising one-dimensional model (see thselect for more information).

    example

    stdc = wnoisest(c) returns estimates of the standard deviations of c, where c is a one-dimensional cell array or a numeric array.

    Examples

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    Open Live Script

    Estimate of the noise standard deviation in an N(0,1) white Gaussian noise vector with outliers.

    Create an N(0,1) noise vector with 10 randomly-placed outliers. 

    rng default;
x = randn(1000,1);
P = randperm(length(x));
indices = P(1:10);
x(indices(1:5)) = 10;
x(indices(6:end)) = -10;

    Obtain the discrete wavelet transform down to level 2 using the Daubechies’ extremal phase wavelet with 3 vanishing moments. 

    [c,l] = wavedec(x,2,'db3');
stdc = wnoisest(c,l,1:2)
    stdc = 1×2

    0.9650    1.0279

    In spite of the outliers, wnoisest provides a robust estimate of the standard deviation.

    Input Arguments

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    Input, specified as a vector, matrix, or 1-D cell array.

    • When used in the syntax stdc = wnoisest(c,l,s), c is the wavelet decomposition output of wavedec: [c,l] = wavedec(x,N,wname). The bookkeeping vector l contains the number of coefficients by level.

    • When used in the syntax stdc = wnoisest(c), c is either a numeric matrix or 1-D cell array.

    Data Types: double

    Bookkeeping vector, specified as a vector of positive integers. l is the output of wavedec: [c,l] = wavedec(x,N,wname). The bookkeeping vector is used to parse the coefficients in the wavelet decomposition c by level.

    Data Types: double

    Detail coefficient levels, specified as a vector of positive integers less than or equal to N, where N is the level of the wavelet decomposition used to obtain [c,l]. Specifically, N = length(l)-2.

    Data Types: double

    Output Arguments

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    Standard deviation estimates, returned as a vector or cell array.

    • If c is the output of wavedec, stdc are estimates of the detail coefficients' standard deviation for the levels specified in s.

    • If c is a one-dimensional cell array, stdc{k} is an estimate of the standard deviation of c{k}, where k = 1,…,length(c).

    • If c is a numeric array, stdc(k) is an estimate of the standard deviation of c(k,:), where k = 1,…,size(c,1).

    References

    [1] Donoho, David L, and Iain M Johnstone. “Ideal Spatial Adaptation by Wavelet Shrinkage.” Biometrika 81, no. 3 (September 1, 1994): 425–55. https://doi.org/10.1093/biomet/81.3.425.

    [2] Donoho, David L., and Iain M. Johnstone. “Adapting to Unknown Smoothness via Wavelet Shrinkage.” Journal of the American Statistical Association 90, no. 432 (December 1995): 1200–1224. https://doi.org/10.1080/01621459.1995.10476626.

    Extended Capabilities

    C/C++ Code Generation
    Generate C and C++ code using MATLAB® Coder™.

    Version History

    Introduced before R2006a

    See Also

    Functions

    Apps