Wavelet transform theory: The mathematical principles of wavelet transform in gamma spectroscopy

The objective of the proposed work was focused in presenting a novel algorithm for processing gamma-ray spectra based on theory of wavelet. We discuss the mathematical principles of applying wavelet transform (WT) method in processing γ-ray spectra and removing fluctuations and background from spectrum. The wavelet algorithm can apply accurately to detect most of peaks and determine net area under peaks. The proposed approach is able to detect most weak peaks in the searching processes. Wavelet method with some kind of discretization known as discrete wavelet transform (DWT) has been applied to filter noise and background detected with the spectrum. The effectiveness of the proposed algorithm is demonstrated via simulated spectra with different peaks containing backgrounds and with some measured gamma ray spectra. These analyzed results prove that the proposed DWT routine gives precise results for filtering and removing noise and background. • We discuss wavelet transform principle. • We discuss the wavelet transform principle in gamma spectroscopy. • We use wavelet transform in filtering gamma spectrum.