An iterative regularization method combining the Lanczos bidiagonalization with Tikhonov regularization is proposed and applied to neutron spectrum unfolding of a newly-developed compact multi-sphere spectrometer. The unfolding is processed as a determined problem without any prior information, which is different from the traditional way. Comparison study of the two commonly-used unfolding methods, GRAVEL and MLEM with the iterative regularization method is carried out. The “semi-convergence” behavior appears for readings containing large uncertainties with the GRAVEL and MLEM methods, making the unfolded spectrums deviate from the true solutions. However, there is no semi-convergence behavior appearing with the iterative regularization method. The unfolded spectrums get close to the true solution as the number of iterations grows. Experimental measurement is carried out for measuring neutron spectrum of ²⁴¹ Am–Be neutron source using the compact multi-sphere spectrometer. The measured data are also unfolded. Compared with the ISO reference spectrum, the unfolded results with GRAVEL and MLEM methods deviate from the reference spectrum due to the semi-convergence behavior, while the unfolded spectrum with the iterative regularization method agrees well with the reference spectrum, indicating that the iterative regularization method is adaptable to unfolding problems with both accurate measured readings and measured readings with large uncertainties.

提出了一种将Lanczos双对角化与Tikhonov正则化相结合的迭代正则化方法，并将其应用于新开发的紧凑型多球谱仪的中子谱展开。与传统方法不同，将展开作为没有任何先验信息的确定问题进行处理。进行了两种常用的展开方法GRAVEL和MLEM与迭代正则化方法的比较研究。对于使用GRAVEL和MLEM方法具有较大不确定性的读数，将出现“半收敛”行为，从而使展开的光谱偏离了真实的解。但是，迭代正则化方法没有出现半收敛行为。随着迭代次数的增加，展开的光谱接近于真实的解。²⁴¹ Am –使用紧凑型多球光谱仪作为中子源。测量数据也将展开。与ISO参考光谱相比，GRAVEL和MLEM方法的展开结果由于半收敛行为而偏离了参考光谱，而迭代正则化方法的展开光谱与参考光谱非常吻合，这表明迭代正则化方法具有精确的测量读数和不确定性较大的测量读数，可适应出现的问题。