wthresh

Soft or hard thresholding

Syntax

Y = wthresh(X,sorh,T)

Description

Y = wthresh(X,sorh,T) returns the soft or hard thresholding, indicated by sorh, of the vector or matrix X. T is the threshold value.

Examples

Hard and Soft Thresholding

Generate a signal and set a threshold.

y = linspace(-1,1,100);
thr = 0.4;

Perform hard and soft thresholding.

yhard = wthresh(y,"h",thr);
ysoft = wthresh(y,"s",thr);

Plot the results and compare with the original signal.

tiledlayout(1,3)
nexttile
plot(y,y)
ylim([-1 1])
title("Original Signal")
nexttile
plot(y,yhard)
ylim([-1 1])
title("Hard Threshold")
nexttile
plot(y,ysoft)
ylim([-1 1])
title("Soft Threshold")

Denoise Signal Using Thresholding

Load the noisy Doppler signal. Obtain the nondecimated discrete wavelet transform of the signal down to level 4.

load noisdopp
wt = modwt(noisdopp,4);

Determine the Donoho-Johnstone universal threshold based on the finest-scale wavelet coefficients.

thr = median(abs(wt(1,:)-median(wt(1,:))))/0.6745;

Apply soft thresholding to the wavelet transform and invert the result to obtain a denoised signal.

wtthr = wthresh(wt,"s",thr);
xden = imodwt(wtthr);

Plot the original and denoised signals.

plot([noisdopp(:) xden(:)])
axis tight
legend("Original","Thresholded",Location="southeast")

Input Arguments

X — Input data

vector | matrix

Input data to threshold, specified as a vector or matrix.

Data Types: single | double
Complex Number Support: Yes

sorh — Type of thresholding

"s" | "h"

Type of thresholding to perform:

• "s" — Soft thresholding

• "h" — Hard thresholding

T — Threshold value

positive real number

Threshold value, specified as a positive real number.

Data Types: single | double

Output Arguments

Y — Thresholded data

vector | matrix

Thresholded data, returned as a vector or matrix. Y has the same dimensions as X.

Algorithms

If sorh is "s", Y is the soft thresholding of X: $$\text{Y}=\text{sign(X)}·{(|\text{X}|-\text{T})}_{+}$$ where

$${(x)}_{+}=\{\begin{array}{ccc}x& \text{if}& x\ge 0\\ 0& \text{otherwise}& \end{array}$$

Soft thresholding is wavelet shrinkage.

If sorh is "h", Y is the hard thresholding of X: $$\text{Y}=\text{X}·1_{(|\text{X}|>\text{T})}$$ where

$$1_{(|\text{X}|>\text{T})}=\{\begin{array}{ccc}1& \text{if}& \left|\text{X}\right|>\text{T}\\ 0& \text{otherwise}& \end{array}$$

Hard thresholding is cruder than soft thresholding.

Extended Capabilities

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

Version History

Introduced before R2006a

R2023b: Threshold complex-valued and single-precision input

The wthresh function supports complex-valued and single-precision input.