Wavelet Toolbox

Two-Dimensional Selection of Wavelet Coefficients Using the Graphical Interface

This section takes you through the features of two-dimensional selection of wavelet coefficients using one of the MATLAB Wavelet Toolbox specialized tools. The MATLAB Wavelet Toolbox provides a graphical interface tool to explore some reconstruction schemes based on various wavelet coefficient selection strategies:

• Global selection of biggest coefficients (in absolute value)
• By level selection of biggest coefficients
• Automatic selection of biggest coefficients.

This section will be short since the functionality are similar to the one-dimensional ones examined in the previous section.

For this section, switch the extension mode to symmetric padding using the command

• dwtmode('sym')
  

1. Start the Wavelet Coefficients Selection 2-D Tool.

1. From the MATLAB prompt, type

   • wavemenu
     

   The Wavelet Toolbox Main Menu appears.

   

   Click the Wavelet Coefficients Selection 2-D menu item. The discrete wavelet coefficients selection tool for images appears.

   

2. Load fata.

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

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

3. Perform a Wavelet Decomposition.

1. Select the sym4 wavelet from the Wavelet menu and select 4 from the Level menu, and then click the Analyze button.

   

   The tool displays its wavelet decomposition below the original image (on the left). The selected coefficients are displayed in the middle of the window, below the synthesized image (which, at this step, is the same since all the wavelet coefficients are kept). There are 11874 coefficients, a little bit more than the original image number of pixels, which is 96x96 = 9216.

Note    The difference between 9216 and 11874 comes from the extra coefficients generated by the redundant DWT using the current extension mode (symmetric, 'sym'). Let us mention that since 96 is divisible evenly into 24 = 16, using the periodic extension mode ('per') for the DWT, you obtain for each level the minimum number of coefficients. More precisely, if you type dwtmode('per') and repeat steps 2 to 5, you get the figure displayed below.

.

Selecting Biggest Coefficients Globally..   

1. On the right of the window, find a column labeled Kept. The last line shows the total number of coefficients: 11874. This is a little bit more than the original image number of pixels. You can choose the number of selected biggest coefficients by typing a number instead of 11874, or by using the slider. Type 1100 and press Enter. The numbers of selected biggest coefficients level by level are updated (but cannot be modified, since Global is the current selection method).

   Then click the Apply button.

   

   In the previous trial, the approximation coefficients were all kept. It is possible to relax this constraint by selecting another option from the App. cfs menu (see One-Dimensional Selection of Wavelet Coefficients Using the Graphical Interface).

Selecting Biggest Coefficients by Level..   

1. From the Define Selection method menu, select the By Level option. You can choose the number of selected biggest coefficients by level, or select it using the sliders. Type 100 for each detail, and then click the Apply button.

   

Selecting Coefficients Automatically..   

1. From the Define Selection method menu, select the Stepwise movie option. The tool displays its wavelet decomposition on the left, below the original image. At the beginning, no coefficients are kept so the synthesized image is null. Perform the stepwise movie using the k biggest coefficients, from k = 144 to k = 1500, in steps of 20. Click the Start button. As soon as the result is satisfactory, click the Stop button.

   

   We've stopped the movie at 864 coefficients (including the number of approximation coefficients).

4. Save the synthesized image.

1. This tool lets you save the synthesized image to disk. The toolbox creates a MAT-file in the current directory with a name you choose.

   To save the synthesized image from the present selection, use the menu option FileSave Synthesized Image. A dialog box appears that lets you specify a directory and filename for storing the image and, in addition, the colormap and the wavelet name.

   At the end of this section, turn back the extension mode to zero padding using the command

   • dwtmode('zpd')
     

One-Dimensional Selection of Wavelet Coefficients Using the Graphical Interface

One-Dimensional Extension