Wavelet Toolbox

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

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

1. Start the Stationary Wavelet Transform De-Noising 2-D Tool.

1. From the MATLAB prompt, type

   • wavemenu
     

   The Wavelet Toolbox Main Menu appears.

   

   Click the SWT De-noising 2-D menu item.

   The discrete stationary wavelet transform de-noising tool for images appears.

   

2. Load data.

1. From the File menu, choose the Load Image option.

   When the Load Image dialog box appears, select the MAT-file noiswom.mat, which should reside in the MATLAB directory toolbox/wavelet/wavedemo. Click the OK button. The noisy woman image is loaded into the SWT De-noising 2-D tool.

   

3. Perform a Stationary Wavelet Decomposition.

1. Select the haar wavelet from the Wavelet menu, select 4 from the Level menu, and then click the Decompose Image button.

   

   The tool displays the histograms of the stationary wavelet detail coefficients of the image on the left of the window. These histograms are organized as follows:

   • From the bottom for level 1 to the top for level 4
   • On the left horizontal coefficients, in the middle diagonal coefficients, and on the right vertical coefficients

4. De-noise the image using the Stationary Wavelet Transform.

1. 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 to the right of the window control the level dependent thresholds indicated by yellow dotted lines running vertically through the histograms of the coefficients on the left of the window. Click the De-noise button.

   

   The result seems to be oversmoothed and the selected thresholds too aggressive. Nevertheless, the histogram of the residuals is quite good since it is close to a Gaussian distribution, which is the noise introduced to produce the analyzed image noiswom.mat from a piece of the original image woman.mat.

5. Selecting a thresholding method.

1. From the Select thresholding method menu, choose the Penalize low item. The associated default for the thresholding mode is automatically set to hard; accept it. Use the Sparsity slider to adjust the threshold value close to 44.5, and then click the De-noise button.

   

   The result is quite satisfactory, although it is possible to improve it slightly.

   Select the sym6 wavelet and click the Decompose Image button. Use the Sparsity slider to adjust the threshold value close to 40.44, and then click the De-noise button.

   

Two-Dimensional Analysis Using the Command Line

Importing and Exporting Information from the Graphical Interface