Algebraic analysis of the Van Cittert iterative method of deconvolution with a general relaxation factor

Xu, Chuan; Aissaoui, Idriss; Jacquey, Serge

doi:10.1364/josaa.11.002804

Cited by 38 publications

(19 citation statements)

References 11 publications

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“…25 Note that, in addition to the dependence on the value of ô (k) in the Jansson method, this relaxation function also depends on the iteration number k. Another interesting and efficient multiplicative correction has been developed inspired by the Bayesian method of probability…”

Section: Deconvolution Methodsmentioning

confidence: 99%

Model-Free Deconvolution of Femtosecond Kinetic Data

Bányász

Keszei

2006

J. Phys. Chem. A

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Though shorter laser pulses can also be produced, pulses of the 100 fs range are typically used in femtosecond kinetic measurements, which are comparable to characteristic times of the studied processes, making detection of the kinetic response functions inevitably distorted by convolution with the pulses applied. A description of this convolution in terms of experiments and measurable signals is given, followed by a detailed discussion of a large number of available methods to solve the convolution equation to get the undistorted kinetic signal, without any presupposed kinetic or photophysical model of the underlying processes. A thorough numerical test of several deconvolution methods is described, and two iterative time-domain methods (Bayesian and Jansson deconvolution) along with two inverse filtering frequency-domain methods (adaptive Wiener filtering and regularization) are suggested to use for the deconvolution of experimental femtosecond kinetic data sets. Adaptation of these methods to typical kinetic curve shapes is described in detail. We find that the modelfree deconvolution gives satisfactory results compared to the classical "reconvolution" method where the knowledge of the kinetic and photophysical mechanism is necessary to perform the deconvolution. In addition, a model-free deconvolution followed by a statistical inference of the parameters of a model function gives less biased results for the relevant parameters of the model than simple reconvolution. We have also analyzed real-life experimental data and found that the model-free deconvolution methods can be successfully used to get undistorted kinetic curves in that case as well. A graphical computer program to perform deconvolution via inverse filtering and additional noise filters is also provided as Supporting Information. Though deconvolution methods described here were optimized for femtosecond kinetic measurements, they can be used for any kind of convolved data where measured experimental shapes are similar.

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Section: Deconvolution Methodsmentioning

confidence: 99%

Model-Free Deconvolution of Femtosecond Kinetic Data

Bányász

Keszei

2006

J. Phys. Chem. A

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“…The standard algorithm is based on the van Cittert decomposition algorithm [19][20][21][22]. Equation (7) is multiplied by R T on both sides to obtain a Toeplitz linear system of equations:…”

Section: Gold Decomposition Algorithmmentioning

confidence: 99%

An inversion decomposition method for better energy resolution of NaI(Tl) scintillation detectors based on a Gaussian response matrix

Yang

et al. 2016

NUCL SCI TECH

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NaI(Tl) scintillation detectors have been widely applied for gamma-ray spectrum measurements owing to advantages such as high detection efficiency and low price. However, the mitigation of the limited energy resolution of these detectors, which detracts from an accurate analysis of the instrument spectra obtained, remains a crucial need. Based on the physical properties and spectrum formation processes of NaI(Tl) scintillation detectors, the detector response to gamma photons with different energies is represented by photopeaks that are approximately Gaussian in shape with unique full-width-at-half-maximum (FWHM) values. The FWHM is established as a detector parameter based on resolution calibrations and is used in the construction of a general Gaussian response matrix, which is employed for the inverse decomposition of gamma spectra obtained from the detector. The Gold and Boosted Gold iterative algorithms are employed to accelerate the decomposition of the measured spectrum. Tests of the inverse decomposition method on multiple simulated overlapping peaks and on experimentally obtained U and Th radionuclide series spectra verify the practicability of the method, particularly in the low-energy region of the spectrum, providing for the accurate qualitative and quantitative analysis of radionuclides.

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“…Through the positive constraint, artificial oscillations particularly around sharp peaks could be avoided. Gold's method was later shown by Xu et al [29] to be a special form of linear deconvolution as by van Cittert in 1931 [30] and uses a variable relaxation function that varies both with channel number and with iteration index [24]. Gold deconvolution is easy to use and unlike many other iterative deconvolution methods, no constants need to be apriori specified.…”

Section: Gold Deconvolutionmentioning

confidence: 99%

“…This ensures that R 0 is non-negative. Van Cittert's linear iterative algorithm of deconvolution, expressed in matrix notation, can now be written as [29][30][31] …”

Section: The Gold Algorithmmentioning

confidence: 99%