Hard shrinking

Noise reduction by wavelet hard shrinking

"Hard shrinking" tries to remove noise in the input signal x with the following steps:

compute the discrete wavelet transform of x
replace each value d of each detail signal by

where the threshold t is , r is the noise level and n the length of x.
reconstruct the signal from the replaced detail values and the last approximation.

The parameters are

Octaves n: Number of octaves of the discrete wavelet transform
Noise level (standard deviation) nl: Estimated standard deviation of the noise

y = WaveletHardShrink(x,n,nl); signal x,y; int n; float nl;

Wavelet

Donoho [35]