Gamma spectrum analysis is an important part of gamma-ray spectroscopy which has been widely used in nuclear engineering, environmental science and astrophysics. As the first step of gamma spectrum analysis, smoothing procedure is critical, since it determines the accuracy of afterwards procedures. Ideally, the smoothing procedure should reduce the statistical fluctuation while preserving characteristic peak information simultaneously. However, current widely-used linear smoothing methods are intrinsically non-adaptive and tend to remove weak peak, which may lose characteristic peak of important radionuclides. To solve the problem, an adaptive smoothing method was proposed to improve the accuracy of gamma spectrum analysis in this study. The proposed method assumes that gamma spectrum is a sparse signal that has meaningful peaks only at limited positions. Based on this assumption, the smoothing procedure is formulated as a nonlinear total variation based optimization problem. Solving this problem promotes the sparsity of gamma spectrum, and therefore reduces meaningless fluctuation, so that the spectrum is adaptively smoothed. The proposed method was applied to gamma spectrum obtained by a Monte Carlo experiment that simulated the ORTEC GEM3070 detector, and compared with traditional linear method. The results demonstrate that the proposed method can effectively reduce the statistical fluctuation of measured gamma spectrum while preserving weak peak much better than standard linear methods. With the proposed method, the accuracy of peak identification and peak calculation is significantly improved.

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