Bayesian Multiscale Deconvolution Applied to Gamma-ray Spectroscopy (original) (raw)
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Gamma-ray energy-imaging integrated spectral deconvolution
Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2007
In conventional Compton camera systems, the image reconstruction is performed only in two-dimensional or three-dimensional spatial coordinates for a specific gamma-ray energy. By doing so, a priori knowledge of the incident gamma-ray energy is required, and usually an energy window is applied to select full energy deposition events. In some other applications, spectral-deconvolution algorithms were developed to estimate the incident gamma-ray spectrum by deconvolving the observed energy-loss spectrum. However, usually the spectral system response function of a non-spherical detector depends on the incident gamma-ray's direction, which cannot be modeled by those spectral-deconvolution algorithms. In this paper, we propose a new energy-imaging integrated spectral-deconvolution method, which utilizes both the Compton imaging and the spectral-deconvolution techniques. In the new method, the deconvolution takes place in a integrated spatial and energy space. This technique eliminates the requirement of knowing the gamma-ray energy in the imaging part, and removes the directional dependence in the spectral-deconvolution part. The deconvolved result provides the image at any specific energy, as well as the spectrum at any specific direction. The deconvolution method is based on the maximum likelihood expectation maximization (MLEM) algorithm, which is popular in reconstructing photon-emission images. Since the ML solution estimates the true incident gamma-ray intensity, the deconvolved energy spectrum at the source location is free of Compton continuum. To truthfully reconstruct the source distribution from the observation data, the accuracy of the system response function t ij , i.e. the probability for a photon from source pixel j to be observed as event i, is the most crucial information. Because of the large number of pixels in the energy-imaging integrated space, and the very large number of possible measurement events, it is impossible to pre-calculate the system response function t ij by simulations. In this paper, an analytical approach is introduced so that the system response function can be calculated during the reconstruction process. In order to perform Compton imaging, gamma-ray detectors are required to have position-sensing capability. The energy-imaging integrated deconvolution algorithm is applied to a three-dimensional position-sensitive CdZnTe gamma-ray imaging spectrometer, which can provide not only the energy-deposition information, but also the position information of individual gamma-ray interactions. The results demonstrate that the technique is capable of deconvolving the energy spectrum and of reconstructing the image simultaneously.
Deconvolution of Gamma Ray Spectra Using Singular Value Decomposition of Matrices
Land Forces Academy Review, 2020
The process of identification of radioactive isotopes using gamma ray spectrum produced by scintillation detectors is a fundamental problem in physics. Military applications also require fast and efficient methods, especially in field conditions, for identifying unknown isotopes. The fundamental problem is the relationship between the observed gamma ray spectrum given by the detector and the real spectrum. This problem can be treated as a mathematical problem. The relationship between the real and the observed spectrum can be described by a linear algebraic equation system. In the previous article Cholesky-decomposition has been applied. In this article one more independent mathematical tool is proposed to solve the linear system efficiently.
An alternative approach to process gamma ray spectral data
Spectrochimica Acta Part B-atomic Spectroscopy, 1994
We describe a general formalism for gamma ray spectral data analysis and the mathematical background of this approach. The method uses a priori information stored in a database. The spectrum is analyzed by applying the median estimate method to the deconvolution of multiplets. The technique developed is particularly advantageous when low-level environmental data or complex spectra are under scrutiny for elemental identification and quantification. The formalism may be applicable in the data processing of a variety of spectrometric methods of analysis.
Joint Bayesian Decomposition of a Spectroscopic Signal Sequence
IEEE Signal Processing Letters, 2000
This letter addresses the problem of decomposing a sequence of spectroscopic signals: data are a series of (energy or electromagnetic) spectra and we aim to estimate the peak parameters (centers, amplitudes, and widths). The key idea is to perform the decomposition of the whole sequence and to impose the parameters to evolve smoothly through the sequence. The problem is set within a Bayesian framework whose posterior distribution is sampled using a Markov chain Monte Carlo simulated annealing algorithm. Simulations conducted on synthetic data illustrate the performance of the method.
Application of the Approximate Bayesian Computation Algorithm to Gamma-Ray Spectroscopy
Algorithms
Radioisotope identification (RIID) algorithms for gamma-ray spectroscopy aim to infer what isotopes are present and in what amounts in test items. RIID algorithms either use all energy channels in the analysis region or only energy channels in and near identified peaks. Because many RIID algorithms rely on locating peaks and estimating each peak’s net area, peak location and peak area estimation algorithms continue to be developed for gamma-ray spectroscopy. This paper shows that approximate Bayesian computation (ABC) can be effective for peak location and area estimation. Algorithms to locate peaks can be applied to raw or smoothed data, and among several smoothing options, the iterative bias reduction algorithm (IBR) is recommended; the use of IBR with ABC is shown to potentially reduce uncertainty in peak location estimation. Extracted peak locations and areas can then be used as summary statistics in a new ABC-based RIID. ABC allows for easy experimentation with candidate summar...
REGULARIZED RECONSTRUCTION OF THE DIFFERENTIAL EMISSION MEASURE FROM SOLAR FLARE HARD X-RAY SPECTRA
We address the problem of how to test whether an observed solar hard X-ray bremsstrahlung spectrum (I ()) is consistent with a purely thermal (locally Maxwellian) distribution of source electrons, and, if so, how to reconstruct the corresponding differential emission measure (ξ (T)). Unlike previous analysis based on the Kramers and Bethe-Heitler approximations to the bremsstrahlung cross-section, here we use an exact (solid-angle-averaged) cross-section. We show that the problem of determining ξ (T) from measurements of I () invOlves two successive inverse problems: the first, to recover the mean source-electron flux spectrum (F(E)) from I () and the second, to recover ξ (T) fromF(E). We discuss the highly pathological numerical properties of this second problem within the framework of the regularization theory for linear inverse problems. In particular, we show that an iterative scheme with a positivity constraint is effective in recovering δ-like forms of ξ (T) while first-order Tikhonov regularization with boundary conditions works well in the case of power-lawlike forms. Therefore, we introduce a restoration approach whereby the low-energy part ofF(E), dominated by the thermal component, is inverted by using the iterative algorithm with positivity, while the high-energy part, dominated by the power-law component, is inverted by using first-order regularization. This approach is first tested by using simulatedF(E) derived from a priori known forms of ξ (T) and then applied to hard X-ray spectral data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI).
Tanzania Journal of Engineering and Technology
Performance of a NaI(Tl) scintillation detector based on the gamma-ray spectroscopy system is not satisfactory in retaining its original peak (which is delta like function) of various gamma ray spectrum. The method of achieving precise peak for the various gamma ray was conducted by converting the observed pulse-height distribution of the NaI(Tl) detector to a true photon spectrum. This method is obtained experimentally with the help of an inverse matrix deconvolution method. The method is based on response matrix generated by the Monte Carlo simulation based on Geant4 package of mono-energy gamma-ray photon ranging from 0.050 to 2.04 MeV in the interval of 10 keV. The comparison of the measured and simulated response function was also performed in order to authenticate the simulation response function. Good agreement was observed around the photo-peak region of the spectrum, but slight deviation was observed at low energy region especially below 0.2 MeV. The Compton backscattering ...
Principal-Component Analysis of Gamma-Ray Bursts' Spectra
Il Nuovo Cimento C, 2005
Principal component analysis is a statistical method, which lowers the number of important variables in a data set. The use of this method for the bursts' spectra and afterglows is discussed in this paper. The analysis indicates that three principal components are enough among the eight ones to describe the variablity of the data. The correlation between spectral index alpha and the redshift suggests that the thermal emission component becomes more dominant at larger redshifts.
arXiv (Cornell University), 2023
Cosmic Dawn (CD) and Epoch of Reionization (EoR) are epochs of the universe which host invaluable information about the cosmology and astrophysics of X-ray heating and hydrogen reionization. Radio interferometric observations of the 21-cm line at high redshifts have the potential to revolutionize our understanding of the universe during this time. However, modeling the evolution of these epochs is particularly challenging due to the complex interplay of many physical processes. This makes it difficult to perform the conventional statistical analysis using the likelihood-based Markov-Chain Monte Carlo (MCMC) methods, which scales poorly with the dimensionality of the parameter space. In this paper, we show how the Simulation-Based Inference (SBI) through Marginal Neural Ratio Estimation (MNRE) provides a step towards evading these issues. We use 21cmFAST to model the 21-cm power spectrum during CD-EoR with a six-dimensional parameter space. With the expected thermal noise from the Square Kilometre Array (SKA), we are able to accurately recover the posterior distribution for the parameters of our model at a significantly lower computational cost than the conventional likelihood-based methods. We further show how the same training dataset can be utilized to investigate the sensitivity of the model parameters over different redshifts. Our results support that such efficient and scalable inference techniques enable us to significantly extend the modeling complexity beyond what is currently achievable with conventional MCMC methods.