How to threshold wavelet coefficients of an image using higher order statastics (skewness, kurtosis)

Iam able to decompose wavelets into required level with different wavelets but thresholding of detailed coefficients by using skewness , kurtosis are unable to perform can you please help me how to threshold coefficients using higher order statistics using Matlab

Answer 1

[Sai Pavan]

Hello Santhosh,

I understand that you want to know the procedure to threshold detailed coefficients after performing wavelet decomposition using higher order statistics.

Please refer to the below workflow to perform the task:

• Decompose the image into its wavelet coefficients based on the chosen level.
• Calculate the skewness and kurtosis of the wavelet coefficients.
• The thresholds can be defined in various ways depending on the skewness and kurtosis values. A simple approach is to set the threshold as a function of the standard deviation of the coefficients, modulated by the skewness and kurtosis as they are used identify how the coefficients' distribution deviates from a normal distribution.
• Use the thresholds to zero out coefficients that are considered insignificant.
• Additionally, after modifying the coefficients, we can reconstruct the image using the inverse wavelet transform.

Please refer to the below code snippet that illustrates the above workflow:

% Read the image
I = double(imread('examp.png'));
% Perform a 2-level wavelet decomposition
[c,s] = wavedec2(I, 2, 'db1');
% For example, extract the detail coefficients at level 2
[H1,V1,D1] = detcoef2('all', c, s, 1);
[H2,V2,D2] = detcoef2('all', c, s, 2);
% Calculate skewness and kurtosis for each set of detail coefficients
skewnessH2 = skewness(H2(:));
kurtosisH2 = kurtosis(H2(:));
skewnessV2 = skewness(V2(:));
kurtosisV2 = kurtosis(V2(:));
skewnessD2 = skewness(D2(:));
kurtosisD2 = kurtosis(D2(:));
% Example threshold calculation
thresholdH2 = std(H2(:)) * (1 + skewnessH2) * (1 + kurtosisH2 - 3);
thresholdV2 = std(V2(:)) * (1 + skewnessV2) * (1 + kurtosisV2 - 3);
thresholdD2 = std(D2(:)) * (1 + skewnessD2) * (1 + kurtosisD2 - 3);
% Apply thresholds
H2(abs(H2) < thresholdH2) = 0;
V2(abs(V2) < thresholdV2) = 0;
D2(abs(D2) < thresholdD2) = 0;

Please refer to the below documentation to learn more about:

• "wavedec2" function: https://www.mathworks.com/help/wavelet/ref/wavedec2.html
• "detcoef2" function; https://www.mathworks.com/help/wavelet/ref/detcoef2.html
• "skewness" function: https://www.mathworks.com/help/stats/skewness.html
• "kurtosis" function: https://www.mathworks.com/help/stats/kurtosis.html

Hope it helps!

[santhosh kumar buddepu]

The rsponse is very much useful, but we cannot expect this much delay, three years back i have posted this question, literally i also forgot the instance. we are expecting fast responses from Mathworks. Thank you