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Interactive 1-D Stationary Wavelet Transform Denoising

Now we explore a strategy to denoise signals, based on the 1-D stationary wavelet analysis using the Wavelet Analyzer app. The basic idea is to average many slightly different discrete wavelet analyses.

  1. Start the Stationary Wavelet Transform Denoising 1-D Tool.

    From the MATLAB® prompt, type waveletAnalyzer.

    The Wavelet Analyzer appears.

    Click the SWT Denoising 1-D menu item. The discrete stationary wavelet transform denoising tool for 1-D signals appears.

  2. Load data.

    At the MATLAB command prompt, type

    load noisbloc;
    In the SWT Denoising 1-D tool, select File > Import Signal from Workspace. When the Import from Workspace dialog box appears, select the noisbloc variable. Click OK to import the noisy blocks signal.

  3. 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 Fast Wavelet Transform (FWT) Algorithm in the Wavelet Toolbox User's Guide).

  4. denoise the signal using the Stationary Wavelet Transform.

    While a number of options are available for fine-tuning the denoising 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 denoise 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 denoise 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.