wnoisest (Wavelet Toolbox)

Estimate noise of 1-D wavelet coefficients.

STDC = wnoisest(C,L,S)

Description

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

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

Examples

% Generate Gaussian white noise. 
    init = 2055415866; randn('seed',init); 
    x = randn(1,1000);

% Decompose x at level 2 using db3 wavelet. 
    [c,l] = wavedec(x,2,'db3');

% Estimate standard deviation of coefficients 
% at each level 1 and 2. 
% Since x is a Gaussian white noise with unit 
% variance, estimates must be close to 1. 
    wnoisest(c,l,1:2)

ans =
    1.0111 1.0763

% Now suppose that x contains 10 outliers. 
    ind = 50:50:500;
    x(ind) = 100 * ones(size(ind));

% Decompose x at level 1 using db3 wavelet. 
    [ca,cd] = dwt(x,'db3');

% Ordinary estimate of cd standard deviation 
% overestimates noise level. 
    std(cd)

ans =
    8.0206

% Robust estimate of cd standard deviation 
% remains close to 1 the noise level. 
    median(abs(cd))/0.6745

ans =
    1.0540

Limitations

This procedure is well suited for Gaussian white noise.