wnoisest

Estimate noise of 1-D wavelet coefficients

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Syntax

STDC = wnoisest(C,L,S)
STDC = wnoisest(C)
STDC = wnoisest(C)

Description

STDC = wnoisest(C,L,S) returns estimates of the detail coefficients' standard deviation for levels contained in the input vector S. [C,L] is the input wavelet decomposition structure (see wavedec for more information).

If C is a one dimensional cell array, STDC = wnoisest(C) returns a vector such that STDC(k) is an estimate of the standard deviation of C{k}.

If C is a numeric array, STDC = wnoisest(C) returns a vector such that STDC(k) is an estimate of the standard deviation of C(k,:).

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

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.

References

Donoho, D.L.; I.M. Johnstone (1994), “Ideal spatial adaptation by wavelet shrinkage,” Biometrika, vol 81, pp. 425–455.

Donoho, D.L.; I.M. Johnstone (1995), “Adapting to unknown smoothness via wavelet shrinkage via wavelet shrinkage,” JASA, vol 90, 432, pp. 1200–1224.

Extended Capabilities

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

See Also

Functions

Apps

Introduced before R2006a

Wavelet Toolbox Documentation

Support