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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.
This menu item opens a previously saved "state" file into a new window.
This menu item saves the current state of the Denoise Tool into a file.
This menu item closes the Denoise Tool viewer.
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.
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.
The filtered coefficients are displayed as a two-dimensional image using a logarithmic energy scaling. The method is as follows:
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.
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.
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.
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.
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You can specify the exact number of coefficients that you wish to retain. The cumulative power slider bar will be adjusted accordingly.
The hard threshold removes all discarded wavelet coefficients by setting them to zero and computing the inverse wavelet transform. For details see Denoise.
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.
This text window contains the following output results:
The threshold is the actual wavelet power (in the variable's units squared) that is used for the cutoff value.
This is the percent number of coefficients used in the reconstruction. The smaller the percent coefficients the more efficient the filter.
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.
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.
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.