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Interval-dependent denoising

`sigden = cmddenoise(sig,wname,level)`

`sigden = cmddenoise(sig,wname,level,sorh)`

`sigden = cmddenoise(sig,wname,level,sorh,nb_inter)`

`sigden = cmddenoise(sig,wname,level,sorh,nb_inter,thrParamsIn)`

```
[sigden,coefs]
= cmddenoise(___)
```

```
[sigden,coefs,thrParamsOut]
= cmddenoise(___)
```

```
[sigden,coefs,thrParamsOut,int_DepThr_Cell]
= cmddenoise(sig,wname,level,sorh,nb_inter)
```

```
[sigden,coefs,thrParamsOut,int_DepThr_Cell,BestNbofInt]
= cmddenoise(sig,wname,level,sorh,nb_inter)
```

returns
the denoised signal, `sigden`

= cmddenoise(`sig`

,`wname`

,`level`

)`sigden`

, obtained from an
interval-dependent denoising of the signal, `sig`

,
using the orthogonal or biorthogonal wavelet and scaling filters, `wname`

. `cmddenoise`

thresholds
the wavelet (detail) coefficients down to level, `level`

,
and reconstructs a signal approximation using the modified detail
coefficients. `cmddenoise`

partitions the signal
into intervals based on variance change points in the first level
detail coefficients and thresholds each interval separately. The location
and number of variance change points are automatically selected using
a penalized contrast function [2].
The minimum delay between change points is 10 samples. Thresholds
are obtained using a minimax threshold rule and soft thresholding
is used to modify the wavelet coefficients [1] .

returns
the denoised signal, `sigden`

= cmddenoise(`sig`

,`wname`

,`level`

,`sorh`

,`nb_inter`

,`thrParamsIn`

)`sigden`

, with the denoising
intervals and corresponding thresholds specified as a cell array of
matrices with length equal to `level`

. Each element
of the cell array contains the interval and threshold information
for the corresponding level of the wavelet transform. The elements
of `thrParamsIn`

are N-by-3 matrices with N equal
to the number of intervals. The 1st and 2nd columns contain the beginning
and ending indices of the intervals and the 3rd column contains the
corresponding threshold value. If you specify `thrParamsIn`

, `cmddenoise`

ignores
the value of `nb_inter`

.

`[`

returns a cell array, `sigden`

,`coefs`

,`thrParamsOut`

]
= cmddenoise(___)`thrParamsOut`

,
with length equal to `level`

. Each element of `thrParamsOut`

is
an N-by-3 matrix. The row dimension of the matrix elements is the
number of intervals and is determined by the value of the input arguments.
Each row of the matrix contains the beginning and end points (indices)
of the thresholded interval and the corresponding threshold value.

`[`

returns
a cell array, `sigden`

,`coefs`

,`thrParamsOut`

,`int_DepThr_Cell`

]
= cmddenoise(`sig`

,`wname`

,`level`

,`sorh`

,`nb_inter`

)`int_DepThr_Cell`

, with length equal
to 6. `int_DepThr_Cell`

contains interval and threshold
information assuming the number of change points ranges from 0 to
5. The N-th element of `int_DepThr_Cell`

is a N-by-3
matrix containing the interval information assuming N-1 change points.
Each row of the matrix contains the beginning and end points (indices)
of the thresholded interval and the corresponding threshold value.
Attempting to output `int_DepThr_Cell`

if you use
the input argument, `thrParamsIn`

, results in an
error.

`[`

returns
the optimal number of signal intervals based on the estimated variance
change points in the level-1 detail coefficients. To estimate the
number of change points, `sigden`

,`coefs`

,`thrParamsOut`

,`int_DepThr_Cell`

,`BestNbofInt`

]
= cmddenoise(`sig`

,`wname`

,`level`

,`sorh`

,`nb_inter`

)`cmddenoise`

assumes the
total number is less than or equal to 6 and uses a penalized contrast [2].
Attempting to output `BestNbofInt`

if you use the
input argument, `thrParamsIn`

, results in an error.

[1] Donoho, D. and Johnstone, I. “Ideal
spatial adaptation by wavelet shrinkage”, *Biometrika*,
1994, 81,3, 425–455.

[2] Lavielle, M. “Detection of multiple
changes in a sequence of dependent variables”, *Stochastic
Processes and their Applications*, 1999, 83, 79–102.

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