Performance evaluation of the simpli¯ed spherical harmonics approximation for cone-beam X-ray luminescence computed tomography imaging

As an emerging molecular imaging modality,cone-beam X-ray luminescence computed tomog-raphy(CB-XLCT)uses X-ray-excitable probes to produce near-infrared(NIR)luminescence and then reconst ructs three-dimensional(3D)distribution of the probes from surface measurements.A proper photon-transportation model is critical to accuracy of XLCT.Here,we presented a systematic comparison between the common-used Monte Carlo model and simplified spherical harmonics(SPN).The performance of the two methods was evaluated over several main spec-trums using a known XLCT material.We designed both a global measurement based on the cosine similarity and a locally-averaged relative error,to quantitatively assess these methods.The results show that the SP_(3) could reach a good balance between the modeling accuracy and computational efficiency for all of the tested emission spectrums.Besides,the SP_(1)(which is equivalent to the difusion equation(DE))can be a reasonable alternative model for emission wavelength over 692nm.In vivo experiment further demonstrates the reconstruction perfor-mance of the SP:and DE.This study would provide a valuable guidance for modeling the photon-transportation in CB-XLCT.

INTERPOLATION SOLUTION TO A BOUNDARY VALUE PROBLEM OF HARMONIC FIELD

This article is a improvement on author＇s early work （Acta Mathematica Scientia, Vol.30 No.2 Ser.A 2010）. In this article, there are two new contributions： 1） The restrictive conditions on approximation domain boundary is improved essentially. 2） The Fejer points is extended by perturbed Fejer points with stable order of approximation.

Nonlinear system identification framework of folding fins with freeplay using backbone curves

Due to wear and manufacturing tolerance,the freeplay is unavoidable in the hinges of folding fins,which exerts significant effects on the aerodynamic characteristics.This paper proposes a backbone-curve-based framework for the dynamical identification of folding fins containing the freeplay nonlinearity.With no need to measure the input force signal and the response signals of nonlinear related Degrees of Freedom(DOFs),the proposed method is more direct and elegant than most existing nonlinear identification approaches,and it contains three steps:Firstly,the underlying linear model of the folding fin structure is obtained through the modal test on its linear sub-parts,and then,the harmonic approximation solves the analytical expressions of the backbone curves of measurable DOFs.Secondly,response data measured from the sine-sweep test are used to extract the fitting points of backbone curves for these DOFs.Finally,the curve fitting approach is applied to identify the freeplay parameters.A series of numerical experiments verify the effectiveness of the proposed method.A real-life folding fin structure is also employed to illustrate how the method can be applied.These examples demonstrate that the identification framework can give an accurate dynamic model of the folding fin structure.

STABLE BOUNDARY CONDITIONS AND DISCRETIZATION FOR P_(N) EQUATIONS

A solution to the linear Boltzmann equation satisfies an energy bound,which reflects a natural fact:The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the energy transported into the volume by particles entering the volume over time.In this paper,we present boundary conditions(BCs)for the spherical harmonic(P_(N))approximation,which ensure that this fundamental energy bound is satisfied by the P_(N) approximation.Our BCs are compatible with the characteristic waves of P_(N) equations and determine the incoming waves uniquely.Both,energy bound and compatibility,are shown on abstract formulations of P_(N) equations and BCs to isolate the necessary structures and properties.The BCs are derived from a Marshak type formulation of BC and base on a non-classical even/odd-classification of spherical harmonic functions and a stabilization step,which is similar to the truncation of the series expansion in the P_(N) method.We show that summation by parts(SBP)finite differences on staggered grids in space and the method of simultaneous approximation terms(SAT)allows to maintain the energy bound also on the semi-discrete level.