Deconvolution of X-ray diffraction profiles by using series expansion

Sánchez-Bajo, F.; Cumbrera, F.L.

doi:10.1107/s0021889899015575

Cited by 8 publications

(3 citation statements)

References 21 publications

(13 reference statements)

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“…Minimization problems of the form (2) can be found in the signal deconvolution literature and elsewhere: some examples include super-resolution in imaging [6], entropy estimation for discrete distributions [7], X-ray diffraction [8], and neural spike sorting [3]. Here, P θ (w) is a convex penalty function of (θ, w).…”

Section: Model Fitting -Existing Approachesmentioning

confidence: 99%

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Deconvolution of High-Dimensional Mixtures via Boosting, with Application to Diffusion-Weighted MRI of Human Brain

Zheng,

Pestilli,

Rokem

2014

Preprint

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Diffusion-weighted magnetic resonance imaging (DWI) and fiber tractography are the only methods to measure the structure of the white matter in the living human brain. The diffusion signal has been modelled as the combined contribution from many individual fascicles of nerve fibers passing through each location in the white matter. Typically, this is done via basis pursuit, but estimation of the exact directions is limited due to discretization [1,2]. The difficulties inherent in modeling DWI data are shared by many other problems involving fitting non-parametric mixture models. Ekanadaham et al. [3] proposed an approach, continuous basis pursuit, to overcome discretization error in the 1-dimensional case (e.g., spikesorting). Here, we propose a more general algorithm that fits mixture models of any dimensionality without discretization. Our algorithm uses the principles of L2-boost [4], together with refitting of the weights and pruning of the parameters. The addition of these steps to L2-boost both accelerates the algorithm and assures its accuracy. We refer to the resulting algorithm as elastic basis pursuit, or EBP, since it expands and contracts the active set of kernels as needed. We show that in contrast to existing approaches to fitting mixtures, our boosting framework (1) enables the selection of the optimal bias-variance tradeoff along the solution path, and (2) scales with high-dimensional problems. In simulations of DWI, we find that EBP yields better parameter estimates than a non-negative least squares (NNLS) approach, or the standard model used in DWI, the tensor model, which serves as the basis for diffusion tensor imaging (DTI) [5]. We demonstrate the utility of the method in DWI data acquired in parts of the brain containing crossings of multiple fascicles of nerve fibers.

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Section: Model Fitting -Existing Approachesmentioning

confidence: 99%

“…Run main loop 5. Return β, the solution to the least-squares problem(8) Main Loop While max(w) > :2. Letting j be the smallest index such that w j = max(w), set S ← S ∪ {j} 3.…”

mentioning

confidence: 99%

Deconvolution of High-Dimensional Mixtures via Boosting, with Application to Diffusion-Weighted MRI of Human Brain

Zheng,

Pestilli,

Rokem

2014

Preprint

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“…The use of deconvolution techniques of X-ray diffraction (XRD) pattern has been subjected to widespread investigation and is well documented in the literature [1][2][3]. Song et al [4] reported that the deconvoluted sample diffraction intensity improved by exact sampling of diffraction intensity.…”

Section: Introductionmentioning

confidence: 99%

Intrinsic shape analysis of X-ray diffraction using Stokes deconvolution

2014

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A deconvolution algorithm is proposed for X-ray diffraction profile analysis. The stability of the algorithm and the influence of the regularization parameter in the deconvoluted results were investigated with respect to the full width at half maximum (FWHM) and the signal to noise ratio. Reliability of the deconvolution profile was estimated. A simple algorithm is proposed that allows obtaining knowledge of the behaviors of the intrinsic physical profile with different instrumental and measured ones. The experimental powder diffraction of prepared NiO nanoparticles has been analyzed by the proposed technique. The algorithm applied to determine the microstructure characteristics compared to those of Sherrer and Stoke's methods. The method has the advantage that the grain-size or microstrain can be calculated directly without using normal approximation correction and the success of this technique is dependent on the value of the regularization parameter.

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Röntgendiffraktometrie

Rafaja¹

2014

Moderne Methoden Der WerkstoffprüFung

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Deconvolution of X-ray diffraction profiles by using series expansion

Cited by 8 publications

References 21 publications

Deconvolution of High-Dimensional Mixtures via Boosting, with Application to Diffusion-Weighted MRI of Human Brain

Deconvolution of High-Dimensional Mixtures via Boosting, with Application to Diffusion-Weighted MRI of Human Brain

Intrinsic shape analysis of X-ray diffraction using Stokes deconvolution

Röntgendiffraktometrie

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