  We demonstrate a new approach to efficiently detect weak {\gamma}-ray peak of
the radioactive waste in tomographic {\gamma} scanning (TGS). In the TGS
measurement, {\gamma}-ray peak identification is usually difficult due to the
short measurement time that results in a lower {\gamma}-ray energy produced by
the decay. Consequently, the resulting significant scattering in the low-energy
side leads to strong statistical fluctuations and low detection efficiency that
overwhelm the {\gamma}-ray peak. Here, we propose the use of shift invariance
wavelet algorithm for low-energy part of the spectrum for weak {\gamma}-ray
peak smoothing. The proposed algorithm not only overcomes the pseudo-Gibbs in
the high-resolution {\gamma}-ray spectrum de-noising by the traditional wavelet
transform, but also keeps quality of the weak {\gamma}-ray characteristic peak
as well. Our new approach shows a significantly improved performance of the
figure of merit (FOM) together with lower limit of quantitation (LLOQ) compared
with the traditional wavelet transform. These results indicate the significant
potential of our approach that could effectively increase the accuracy of weak
{\gamma}-ray detecting activation analysis in TGS.
