Calculating the power spectrum of digital X-ray images in the wavelet domain

Abstract

The multiresolution approximation decomposes an image in scales or frequency bands. The knowledge of the image power distribution in these bands is therefore important for understanding the performance of image processing algorithms. However the spectra calculated in the wavelet domain depend on the characteristics of the wavelet selected and the method used to extend the image. This extension must be done before convolving the image with the wavelet decomposition filters. On the other hand, the calculated spectrum depends on the number of vanishing moments of the wavelet and the symmetry of the wavelet filters. In this work the Fourier power spectrum and the power spectrum in the wavelet domain are compared for one ensemble of images. Highly non-symmetric Daubechies and very symmetric symlet wavelets of different vanishing moments Nv are used in combination with different extension methods. The best matching between spectrums is found for symlet wavelets and symmetric padding extension. Also, removing the extended part of the subbands before the power calculation improves the result.