Neutron Spectrum Unfolding Method Based on Compressed Sensing Theory

Accurate information of neutron spectrum is very important for design and operation of nuclear facilities. The current unfolding methods commonly use the prior information as the initial values of the iteration process, which limits implementation of multiple prior information during the unfolding process and accuracies of the unfolding results are difficult to be enhanced. In this paper, a neutron spectrum unfolding method based on compressed sensing theory was proposed. Multiple prior information can be implemented into the unfolding process due to the basic principle of the compressed sensing theory. The proposed method includes two processes, such as the sparse representation process and the sparse reconstruction process. Two kinds of algorithms, the K-SVD algorithm and the online dictionary learning algorithm, were applied for sparse representation. The K-SVD algorithm is efficient and easy to be implemented. However, computation always fail while the singularity of the training matrix increases. The online dictionary learning algorithm uses the stochastic approximation. It assumes the training set as a distribution and processes one sample from the distribution during each iteration. Hence, the online dictionary learning algorithm can effectively avoid the computation failure caused by matrix singularity. Algorithms based on \ell _0 -norm and \ell _1 -norm were applied for sparse reconstruction. The \ell _0 -norm based algorithm has the closet meaning to sparsity but lacks the ability of suppressing noises containing in the measured data. The \ell _1 -norm based algorithm equivalents the sparse reconstruction to the LASSO equation, which has better performance on suppressing noises. The proposed unfolding method was applied to unfolding problems of multi-sphere spectrometer of measuring several typical neutron spectra. The K-SVD algorithm was applied for sparse representation and the \ell _0 -norm based algorithm was applied for sparse reconstruction. The unfolded spectra agree well with the standard solutions. High accuracies can be obtained with implementation of multiple prior information. Moreover, measured data of multiple activation foils at the irradiation surveillance capsule was also unfolded with the proposed method. To avoid computational failure caused by singularity of the training matrix, the online dictionary learning algorithm was applied for sparse representation. And the \ell _1 -norm based algorithm was applied for sparse reconstruction to suppress noises contained in the measured data. The unfolded spectra agree well with the standard solutions. Besides, dependence of the unfolding process on the number of equations is reduced as a result of implementation of multiple prior information, allowing successful unfolding with acceptable accuracies while removing fission detectors such as ²³⁸U and ²³⁷Np, which lays theoretical foundation for removal of fission detectors in radiation surveillance project.