One-Dimensional Analysis for De-Noising Using the Graphical Interface

Wavelet Toolbox

One-Dimensional Analysis for De-Noising Using the Graphical Interface

In this section, we explore a strategy to de-noise signals, based on the one-dimensional stationary wavelet analysis using the graphical interface tools. The basic idea is to average many slightly different discrete wavelet analyses.

Start the Stationary Wavelet Transform De-Noising 1-D Tool.

From the MATLAB prompt, type
- ```
wavemenu
```
The Wavelet Toolbox Main Menu appears

.

Click the SWT De-noising 1-D menu item. The discrete stationary wavelet transform de-noising tool for one-dimensional signals appears.

Load data.

From the File menu, choose the Load Signal option.

When the Load Signal dialog box appears, select the MAT-file noisbloc.mat, which should reside in the Matlab directory toolbox/wavelet/wavedemo.

Click the OK button. The noisy blocks signal is loaded into the SWT De-noising 1-D tool.

Perform a Stationary Wavelet Decomposition.

Select the db1 wavelet from the Wavelet menu and select 5 from the Level menu, and then click the Decompose Signal button. After a pause for computation, the tool displays the stationary wavelet approximation and detail coefficients of the decomposition. These are also called nondecimated coefficients since they are obtained using the same scheme as for the DWT, but omitting the decimation step (see The Fast Wavelet Transform (FWT) Algorithm).

De-Noise the signal using the Stationary Wavelet Transform.

While a number of options are available for fine-tuning the de-noising algorithm, we'll accept the defaults of fixed form soft thresholding and unscaled white noise. The sliders located on the right part of the window control the level-dependent thresholds, indicated by yellow dotted lines running horizontally through the graphs of the detail coefficients to the left of the window. The yellow dotted lines can also be dragged directly using the left mouse button over the graphs.

Note that the approximation coefficients are not thresholded.

Click the De-noise button.

The result is quite satisfactory, but seems to be oversmoothed around the discontinuities of the signal. This can be seen by looking at the residuals, and zooming on a breakdown point, for example around position 800.

Selecting a Thresholding Method..

Select hard for the thresholding mode instead of soft, and then click the De-noise button.

The result is of good quality and the residuals look like a white noise sample. To investigate this last point, you can get more information on residuals by clicking the Residuals button.

One-Dimensional Analysis Using the Command Line Importing and Exporting Information from the Graphical Interface