Savitzky-Golay Filter

Features:

The filter smooths raw noisy signal data from the spectral coordinate using a least-squares digital polynomial filter.

Steps:

1.      Select Filtering and Enhancement → Savitzky-Golay.

2.      The pop-up dialogue window will ask for additional parameters Polynomial Order and Frame size.

Polynomial Order corresponds to the degree of the polynomial fitted to the points in the moving frame. The default value is 2. Polynomial Order value must be smaller than Frame Size if the frame size is a positive integer. The default value is 10.

Frame Size modifies the frame size for the smoothing function. If the Frame Size value is greater than 1, the rolling window is the size of the input number (i.e., 10) and independent of the number of bands/channels. Higher values smooth the signal more with an increase in computation time. If Frame Size is less than 1, the window size is a fraction of the number of points in the total number of channels. For example, if the Frame Size value 0.05, the window size is equal to 5% of the number of points in the total number of channels.

The smoothing of the spectra occurs in a pixel-by-pixel manner. When the process is complete, the new image will replace the original image. A pop-up message box will inform that the process is complete. Click OK to remove the message box.

(Optional) You can estimate the effect of the filter on the resulting image by running Structure Similarity Index. For that, select Filtering and Enhancement → Structure Similarity Index from the menu bar. This index calculates the structural similarity (SSIM) index comparing the original dataset with the filtered one. A value closer to 1 indicates higher similarity and a value closer to 0 indicates low similarity.

(Optional) You can also estimate the result of filtering on the images using image quality measurements. For that select Filtering and Enhancement → Image Quality → Image Quality (BRISQUE). A new window with the image quality index for every channel will be calculated. Lower values correspond to better quality. In this example, Savitzky-Golay smoothing with the default values significantly increases the quality of the images between 1100 nm and 1550 nm.

Additional Information:

IDCubePro® uses a modified version of the Savitzky-Golay algorithm. The original algorithm developed by Savitzky and Golay assumes the input vector corresponding to the band/channel dimension has uniformly spaced separation units, while the current algorithm also allows one that is not uniformly spaced.

When the input bands/channels vector is evenly spaced, the least-squares fitting is performed once so that the signal is filtered with the same coefficients, and the speed of the algorithm increases considerably.

The algorithm specifies the degree of the polynomial fitted to the points in the moving frame. The default order of the polynomial fitted to the points in the moving frame is equal to 2. The default frame size is 10 samples. Both parameters can be modified in the IDCubePro®.