Constrained regularization in nuclear spectroscopy

Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints

“…23 However, for high spectral content CDBS data NϾ10 5 , in which the regularization parameter ␣р10 Ϫ4 , there is no noticeable difference in the quality of deconvolution, all derivatives essentially yielding the same result. This finding is the same as that of Chambless and Broadway, 21,22 who also used nonnegativity constraints in deconvolution. FIG.…”

“…These are produced on the high energy side by pulse pileup and on the low energy side by incomplete charge collection. In the case of the positron source being 22 Na, events are present on the low and high energy sides due to coincident Compton events from the 1.27 MeV gamma ray associated with this source. However, the cross pieces need not be of undue concern since in the first place their intensity is much less than that of the real annihilation events on the diagonal, and second, under the proviso that we have ''subtracted off'' any Compton background, the remaining counts can in some sense be considered as part of the instrumental resolution function, the features being connected with the main signal in the same way for both the CDBS spectrum and the instrumental ''blurring'' function.…”

“…12͑a͒, where background counts due to Compton events from the 1.27 MeV gamma ray associated with 22 Na have been subtracted off by fitting a Gaussian to the ''cross'' data on the high energy sides of both E 1 and E 2 . ͑This background was not considered to be part of the experimental signal in contrast to the ''tailing'' counts on the low energy side of the ''cross,'' which may be considered as part of the instrumental resolution.…”

“…Many different algorithms have been used such as the Stokes method, 7,9-12 the maximum entropy method, 13,14 iterative methods, [15][16][17][18] optimized linear filtering, 19 and the method of generalized least squares. [20][21][22][23][24] It is the latter method which is presented in detailed form in this article. Although the methods listed above have all given promising results, none of them, excepting Ref.…”

Optimized Coincidence Doppler Broadening Spectroscopy Using Deconvolution Algorithms

“…Despite the advent on CDBS, its energy resolution (typically ~5mrad ACAR equivalent) is still inferior to that of ACAR (~1mrad). For some time it has been recognized that good deconvolution algorithms applied to DBS spectra can give significant improvement in EMD measurement [3,4], but there has been little work done on the 2D "image" type data of CDBS. In our present study, we have employed a CDBS with a non-negativity least squares deconvolution algorithm [5,6] to study the EMDs of six polycrystalline metals ---Al, Cd, Cu, Mg, Pb and Zn.…”