Wavelet Toolbox |

Estimate noise of 1-D wavelet coefficients

**Syntax **

**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**

% The current extension mode is zero-padding (see

`dwtmode`

). % 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.

**See Also**

```
thselect, wavedec, wden
```

**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.

wnoise | wp2wtree |