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Multisignal 1-D denoising using wavelets

`[XD,DECDEN,THRESH] = mswden('den',...)[XD,THRESH] = mswden('densig',...)[DECDEN,THRESH]
= mswden('dendec',...)THRESH = mswden('thr',...)[...] = mswden(OPTION,DIRDEC,X,WNAME,LEV,METH,PARAM)[...] = mswden(...,S_OR_H)[...]
= mswden(...,S_OR_H,KEEPAPP)[...]
= mswden(...,S_OR_H,KEEPAPP,IDXSIG)`

`mswden` computes thresholds
and, depending on the selected option, performs denoising of 1-D signals
using wavelets.

`[XD,DECDEN,THRESH] = mswden('den',...)` returns
a denoised version `XD` of the original multisignal
matrix `X`, whose wavelet decomposition structure
is `DEC`. The output `XD` is obtained
by thresholding the wavelet coefficients, `DECDEN` is
the wavelet decomposition associated to `XD` (see `mdwtdec`), and `THRESH`
is the matrix of threshold values. The input `METH` is
the name of the denoising method and `PARAM` is the
associated parameter, if required.

Valid denoising methods `METH` and associated
parameters `PARAM` are:

'rigrsure' | Principle of Stein's Unbiased Risk |

'heursure' | Heuristic variant of the first option |

'sqtwolog' | Universal threshold |

'minimaxi' | Minimax thresholding (see |

For these methods `PARAM` defines the multiplicative
threshold rescaling:

'one' | No rescaling |

'sln' | Rescaling using a single estimation of level noise based on first level coefficients |

'mln' | Rescaling using a level dependent estimation of level noise |

'penal' | Penal |

'penalhi' | Penal high, |

'penalme' | Penal medium, |

'penallo' | Penal low, |

`PARAM` is a sparsity parameter, and it should
be such that: `1` ≤ `PARAM` ≤
`10`. For `penal` method, no control
is done.

'man_thr' | Manual method |

`PARAM` is an `NbSIG`-by-`NbLEV` matrix
or `NbSIG`-by-(`NbLEV+1`) matrix
such that:

`PARAM(i,j)`is the threshold for the detail coefficients of level`j`for the ith signal (`1`≤`j`≤`NbLEV`).`PARAM(i,NbLEV+1)`is the threshold for the approximation coefficients for the`i`th signal (if`KEEPAPP`is`0`).

where `NbSIG` is the number of signals and `NbLEV` the
number of levels of decomposition.

Instead of the `'den'` input `OPTION`,
you can use `'densig'`, `'dendec'` or `'thr'` `OPTION` to
select output arguments:

`[XD,THRESH] = mswden('densig',...)` or `[DECDEN,THRESH]
= mswden('dendec',...)`

`THRESH = mswden('thr',...)` returns the
computed thresholds, but denoising is not performed.

The decomposition structure input argument `DEC` can
be replaced by four arguments: `DIRDEC`, `X`, `WNAME` and `LEV`.

`[...] = mswden(OPTION,DIRDEC,X,WNAME,LEV,METH,PARAM)` before
performing a denoising or computing thresholds, the multisignal matrix `X` is
decomposed at level `LEV` using the wavelet `WNAME`,
in the direction `DIRDEC`.

You can use three more optional inputs:

`[...] = mswden(...,S_OR_H)` or `[...]
= mswden(...,S_OR_H,KEEPAPP)` or `[...]
= mswden(...,S_OR_H,KEEPAPP,IDXSIG)`

`S_OR_H ('s' or 'h')`stands for soft or hard thresholding (see`mswthresh`for more details).`KEEPAPP (true or false)`indicates whether to keep approximation coefficients (`true`) or not (`false`).`IDXSIG`is a vector that contains the indices of the initial signals, or the string`'all'`.

The defaults are, respectively, `'h'`, `false` and `'all'`.

% Load original 1D-multisignal. load thinker % Perform a decomposition at level 2 using the wavelet db2. dec = mdwtdec('r',X,2,'db2'); % Denoise signals using the universal method % of thresholding (sqtwolog) and the 'sln' % threshold rescaling (with a single estimation % of level noise, based on first level coefficients). [XD,decDEN,THRESH] = mswden('den',dec,'sqtwolog','sln'); % Plot the original signals 1 and 31, and the % corresponding denoised signals. figure; plot(X([1 31],:)','r--','linewidth',2); hold on plot(XD([1 31],:)','b','linewidth',2); grid; set(gca,'Xlim',[1,96]) title('X dashed line and XD solid line')

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