mswthresh

Perform multisignal 1-D thresholding

Syntax

Y = mswthresh(X,sorh,T)

Y = mswthresh(X,sorh,T,'c')

Description

Y = mswthresh(X,sorh,T) returns the soft or hard T-thresholding of the matrix X. T can be a single value, a matrix the same size as X, or a vector. If T is a vector, thresholding is performed row-wise, and LT = length(T) must be such that size(X,1) ≤ LT. Only the first size(X,1) values of T are used.

Y = mswthresh(X,sorh,T,'c') performs thresholding column-wise, and LT = length(T) must be such that size(X,2) ≤ LT. Only the first size(X,2) values of T are used.

Examples

Multisignal Thresholding

Create a 3-by-3 matrix and a 1-by-3 vector of threshold values.

mat = [1 1 3; 1 1 3; 2 2 3]

mat = 3×3

     1     1     3
     1     1     3
     2     2     3

thr = [1 2 3]

thr = 1×3

     1     2     3

Apply soft thresholding to the matrix row-wise. The kth threshold in thr is applied to the kth row of mat.

mswthresh(mat,'s',thr)

ans = 3×3

     0     0     2
     0     0     1
     0     0     0

Apply soft thresholding to the matrix column-wise. The kth threshold in thr is applied to the kth column of mat.

mswthresh(mat,'s',thr,'c')

ans = 3×3

     0     0     0
     0     0     0
     1     0     0

Apply hard thresholding to the matrix row-wise.

mswthresh(mat,'h',thr)

ans = 3×3

     0     0     3
     0     0     3
     0     0     0

Apply hard thresholding to the matrix column-wise.

mswthresh(mat,'h',thr,'c')

ans = 3×3

     0     0     0
     0     0     0
     2     0     0

Input Arguments

X — Input data

real-valued matrix

Input data to threshold, specified as a real-valued matrix.

Data Types: double

sorh — Type of thresholding

's' | 'h'

Type of thresholding to perform, specified as:

• 's' — Soft thresholding

• 'h' — Hard thresholding

T — Threshold value

real-valued scalar or vector

Threshold value, specified as a real-valued scalar or vector.

Data Types: double

Output Arguments

Y — Thresholded data

real-valued matrix

Thresholded data, returned as a real-valued 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.

Version History

Introduced in R2007a