The Impact of Wavelets on Inverse Spectral Decomposition

In this paper, the impact of wavelets on inverse spectral decomposition is investigated. We introduce the Basis Pursuit optimization algorithm with L1-L2 norm constraint condition to inverse spectral decomposition. Inverse spectral decomposition can produce much higher resolution spectrums than conventional spectral decomposition methods. We will show, however, the wavelets used to establish the wavelet library impact the result of inversion. Unsuitable wavelet library would produce inaccurate spectrum. So, we add the process of wavelet extraction into inversion spectral decomposition. A real 1D trace example and a real 2D data example are provided to test the performance of inversion spectrum by the extracted wavelet library.