## Hard shrinking

Purpose

Description

Macro Synopsis

Modules

Related Functions

References

### Purpose

Noise reduction by wavelet hard shrinking

### Description

"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

### Macro Synopsis

`y = WaveletHardShrink(x,n,nl);`

signal x,y;

int n;

float nl;

### Modules

Wavelet

### Related Functions

Define wavelet, Load wavelet,
Save wavelet, Decompose,
Reconstruct, Soft shrinking,
Sure shrinking.

### References

Donoho [35]