During measurement of the multi-sphere spectrometer, solutions of the current unfolding methods depend on the prior information. However, during some special circumstances, i.e. experimental validation of the deep penetration problem calculation method, the unfolding process needs to be independent of the prior information, which is essential to validate the computational method for deep-penetration.

This study aims to propose an unfolding method that is independent of the prior information and adaptive to the uncertainties and illness of the unfolding problems.

The iterative regularization unfolding method is based on Krylov subspace method. The Lanczos bidiagnolization was employed to calculate orthogonal basis of the Krylov subspaces, and the Tikhonov regularization was applied to suppressing the uncertainties contained in the measured data. Then, the regularization parameter was determined by the Generalized Cross Validation (GCV) principle to constrain the uncertainties and illness of the unfolding problem. Finally, multi-sphere spectrometer measurement of ²⁴¹Am-Be neutron spectrum was used to verify this established method, and the unfolded spectrums were compared with that of the ISO standard solution.

The unfolded results with the proposed method agree well with the reference spectrum. Relative error of the unfolded results using the proposed method is 16%, while relative errors of the unfolded results using the GRAVEL and ML-EM methods are 103% and 107%, respectively.

Comparing with the current unfolding methods, the proposed method can effectively avoid the "semi-convergence" behavior and achieve better accuracies while large fluctuations contained in the measured counting are suppressed of the ill-conditioned problem.