| Wavelet Toolbox | |
The purpose of this example is to show how to de-noise an image using both a two-dimensional wavelet analysis and a two-dimensional stationary wavelet analysis. De-noising is one of the most important applications of wavelets.
The image to be de-noised is a noisy version of a piece of the following image.
For this example, switch the extension mode to symmetric padding using the command
Open the Wavelet 2-D tool, select from the File menu the Load Image option, and select the MAT-file noiswom.mat, which should reside in the MATLAB directory toolbox/wavelet/wavedemo.
The image is loaded into the Wavelet 2-D tool. Select the haar wavelet and select 4 from the level menu, and then click the Analyze button.
The analysis appears in the Wavelet 2-D window.
Click the De-noise button (located at the middle right) to bring up the Wavelet 2-D -- De-noising window.
Discussion
The graphical tool provides automatically generated thresholds. From the Select thresholding method menu, select the item Penalize low and click the De-noise button.
The de-noised image exhibits some blocking effects. Let's try another wavelet. Click the Close button to go back to the Wavelet 2-D window. Select the sym6 wavelet, and then click the Analyze button. Click the De-noise button to bring up the Wavelet 2-D -- De-noising window again.
From the Select thresholding method menu, select the item Penalize low, and click the De-noise button.
The de-noised image exhibits some ringing effects. Let's try another strategy based on the two-dimensional stationary wavelet analysis to de-noise images. The basic idea is to average many slightly different discrete wavelet analyses. For more information, see the section Discrete Stationary Wavelet Transform (SWT).
Click the Close button to go back to the Wavelet 2-D window and click the Close button again. Open the SWT De-noising 2-D tool, select from the File menu the Load Image option and select the MAT-file noiswom.mat. Select the haar wavelet and select 4 from the level menu, and then click the Decompose Image button.
The selected thresholding method is Penalize low. Use the Sparsity slider to adjust the threshold value close to 44.5 (the same as before to facilitate the comparison with the first trial), and then click the De-noise button.
The result is more satisfactory. It's 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 (the same as before to facilitate the comparison with the second trial), and then click the De-noise button.
At the end of this example, turn back the extension mode to zero-padding using the command
| | De-Noising Signals | Compressing Images | |
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