Monday, June 13, 2016

Wavelet denoising

I found this interesting post about wavelet thresholding on Banco Silva's blog. Unfortunately the code does not run under PyWavelets 0.4.0/Scipy 0.17.1 , but it inspired me to write a demo which does.
One pic says more than thousand words, so here it is:
As one can see, we add so much noise that the images practically disappear, but wavelet reconstruction (db8 in this case) is smart enough to recover the main features. The key point in the code is
threshold = noiseSigma * np.sqrt(2 * np.log2(noisy_img.size))
rec_coeffs = coeffs
rec_coeffs[1:] = (pywt.threshold(i, value=threshold, mode="soft") for i in rec_coeffs[1:])
Here soft thresholding  is used, where the wavelet coeffiicients whose absolute value is less than the threshold are assumed to be noise and hence set to zero, so as to denoise the signal. The other coefficients are shifted by sign*theshold so as to mantain the main patterns. Here a standard Donoho-Johnstone universal threshold is used. A look at the code may tell you more. 

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