X‐ray spectrum unfolding using a regularized truncated SVD method

Abstract

New procedures to characterize the x-ray primary beam, obtaining an accurate assessment of the actual photon spectrum, are needed for quality control of x-ray tubes for medical purposes. The Compton scattering technique is very useful for determining x-ray spectra (in the 10-150 kV p range), avoiding the pile-up effect in the detector, since usually there is insufficient space available to apply other techniques. The Compton scattering procedure was simulated using the Monte Carlo method by means of the MCNP code. In order to validate the simulation model, experimental measurements were made at the Centro Nacional de Dosimetría (CND), Valencia, Spain, using a calibrated x-ray tube. Different spectra were measured varying the operational parameters (kV, mA, Al). Furthermore, CND provided the theoretical spectra corresponding to the x-ray measurement conditions. Using the developed model, a response matrix was obtained by simulating the interactions of different monoenergetic beams. During the construction of the primary photon spectrum it is necessary to calculate the inverse of the response matrix. Because this matrix is ill-conditioned, its inversion is not a simple process. This problem was solved using a truncated singular value decomposition (TSVD), method together with variational regularization. The performance of the methodology was tested with experimental and simulated x-ray spectra.

Application of the Tikhonov Unfolding Method for Reconstruction of Primary X-Ray Spectra from X-Ray Equipments

“…The effect of these discrepancies is analyzed from the point of view of spectrum quality parameters in Section III. 4.…”

“…In a previous work, 4) authors described the Modified Truncated Singular Value Decomposition (MTSVD) unfolding method and its application to the Compton scattering.…”

Atomic spectrometry update—X-ray fluorescence spectrometry

“…The use of MC simulation to predict the complete EDXRF spectrum or the X-ray tube spectrum continued during the review period. Although directed at X-ray tubes for X-ray radiography, the MC method described by Gallardo et al 44 could doubtless be applied to lower energies typical of XRF spectrometry. Rather than making direct measurements of the tube output spectrum, which is clearly the optimum approach, the authors used the 901 Compton scattered spectrum from a Perspex scatter block measured by a HPGe detector.…”

Unfolding X-ray spectra using a flat panel detector. Determination of the accuracy of the method with the Monte Carlo method

“…In previous works, authors have applied TSVD and MTSVD methods jointly with regularization tools to unfold X-ray spectra using a Compton spectrometer in the radiodiagnostic energy range (Gallardo et al, 2006) and in the mammography energy range (Querol et al, 2011). However, the Compton spectrometer technique requires the using of detectors of high resolution, such as HPGe detectors (with liquid nitrogen cooling).…”