Wavelet Toolkit Denoise Tool

You can use the Denoise Tool to explore different techniques for removing noise and compressing data using the wavelet transform.

The Denoise Tool is shown in the following figure. The plots and options are described below.

Figure 2-5: The Denoise Tool

waveuse5.gif

File Menu

Open State...

This menu item opens a previously saved "state" file into a new window.

Save State...

This menu item saves the current state of the Denoise Tool into a file.

Close

This menu item closes the Denoise Tool viewer.

Original Data

This window displays a graph of the original one-dimensional vector or two-dimensional image. For images, all values are converted to an intensity (0–255) and a grayscale color palette is used.

Filtered Data

This window displays the data after filtering using the wavelet function and options given on the right. For images, all values are converted to an intensity (0–255) and a grayscale color palette is used.

Wavelet Coefficients

The filtered coefficients are displayed as a two-dimensional image using a logarithmic energy scaling. The method is as follows:

  1. Find the maximum value "Pm" of the original, unfiltered, wavelet power (absolute-value squared of the wavelet coefficients);
  2. Square the filtered wavelet coefficients to get wavelet power, then take the base-10 logarithm of each;
  3. Scale this logarithmic power from the range [–10 Log10(Pm), Log10(Pm)] into the range [32, 255]. Values greater than zero but less than –10 Log10(Pm) are set equal to 32.
  4. Set all values removed by the filter to zero (0).
  5. Display the image using a grayscale color palette.

Using the above method, all retained coefficients will appear in the image, shaded from dark gray (32) to white (255). Coefficients that have been removed will be black.

Coefficient Power

This graph shows the wavelet power for each coefficient, sorted into decreasing order, and scaled so that the total power is 100%. The wavelet power is also shown as a cumulative plot, where each point represents the sum of all of the previous points. Both curves are plotted on a logarithmic x-axis, so that the largest coefficients are easily visible.

The dashed line shows the current cutoff value that you have selected.

Wavelet Options

You can change the current wavelet family or the order. Since all of the denoise options remain constant, you can compare the effects of different wavelet orders and families.

Denoise Options

Cumulative Power

The slider bar allows you to set the cutoff threshold for cumulative power. Coefficients to the right of the dotted line in the Coefficient Power graph will be excluded. The # Coeffs box is adjusted accordingly.

Note
At low cumulative power you may notice that the slider adjusts itself in uneven increments. This is designed so that at least one additional coefficient is either discarded (as the slider moves left) or retained (as the slider moves right). These jumps in power correspond to the discrete steps in the coefficient power graph.

Number of Coefficients

You can specify the exact number of coefficients that you wish to retain. The cumulative power slider bar will be adjusted accordingly.

Hard Threshold

The hard threshold removes all discarded wavelet coefficients by setting them to zero and computing the inverse wavelet transform. For details see Denoise.

Soft Threshold

The soft threshold also sets all discarded wavelet coefficients to zero. However, it also linearly reduces the magnitude of the each retained wavelet coefficient by an amount equal to the largest discarded coefficient. For details see Denoise.

Results Window

This text window contains the following output results:

Threshold

The threshold is the actual wavelet power (in the variable's units squared) that is used for the cutoff value.

Percent of Coefficients

This is the percent number of coefficients used in the reconstruction. The smaller the percent coefficients the more efficient the filter.

RMS Difference

This is the root-mean-square difference between the original data (upper-left plot) and the filtered data (upper-right plot) in the variable units. A smaller number implies a more accurate reconstruction.

Percent Difference

This is the percent difference between the original and filtered data, and is equal to 100% x (RMS difference/StdDev) where StdDev is the standard deviation of the original data. The smaller the percent difference, the more accurate the reconstruction.

Function Call

The text under Function Call contains the actual IDL code used to call the WV_DENOISE function. See WV_DENOISE to copy this code into your own programs to call the denoise function directly.