The deconvolution of lunar brightness temperature based on the maximum entropy method using Chang'e-2 microwave data

A passive and multi-channel microwave sounder onboard the Chang＇e-2 orbiter has successfully acquired microwave observations of the lunar surface and subsurface structure. Compared with the Chang＇e-1 orbiter, the Chang＇e-2 orbiter obtained more accurate and comprehensive microwave brightness temperature data, which are helpful for further research. Since there is a close relationship between mi- crowave brightness temperature data and some related properties of the lunar regolith, such as the thickness, temperature and dielectric constant, precise and high resolution brightness temperature data are necessary for such research. However, through the detection mechanism of the microwave sounder, the brightness temperature data ac- quired from the microwave sounder are weighted by the antenna radiation pattern, so the data are the convolution of the antenna radiation pattern with the lunar brightness temperature. In order to obtain the real lunar brightness temperature, a deconvolution method is needed. The aim of this paper is to solve the problem associated with per- forming deconvolution of the lunar brightness temperature. In this study, we introduce the maximum entropy method （MEM） to process the brightness temperature data and achieve excellent results. The paper mainly includes the following aspects： first, we introduce the principle of the MEM; second, through a series of simulations, the MEM has been verified as an efficient deconvolution method; and third, the MEM is used to process the Chang＇e-2 microwave data and the results are significant.

PHASE EXTENSION AND STRUCTURE ANALYSIS BY THE MAXIMUM ENTROPY METHOD

Excellent results are obtained in structure analysis with jew phases of structure factors by the maximum-entropy method (MEM) for CaGaN PbCO3 and ReBe22 single crystals. The computation time and memory space are minimized by symmetry operations so that structure analysis by the MEM can be carried out with a personal computer.

Reconstructing parton distribution function based on maximum entropy method

A new method based on the maximum entropy principle for reconstructing the parton distribution function(PDF)from moments is proposed.Unlike traditional methods,the new method does not require any artificial assumptions.For the case of moments with errors,we introduce Gaussian functions to soften the constraints of moments.Through a series of tests,the effectiveness and reconstruction efficiency of this new method are evaluated comprehensively,demonstrating that this method is reasonable and can achieve high-quality reconstruction with at least the first six moments as input.Finally,we select a set of lattice quantum chromodynamics(QCD)results regarding moments as input and provide reasonable reconstruction results for the pion.

Numerical and experimental study of twin-fluid two-phase internal-mixing atomizer to develop maximum entropy method

This paper presents an analytical, numerical, and experimental study on atomization characteristics and droplet distribution of a twin-fluid two-phase internal mixing atomizer to develop a Maximum Entropy Method(MEM). A two-phase Eulerian-Lagrangian method is utilized for atomization modeling of the inside and outside atomizer. In order to modify energy and momentum sources in the MEM, parametric studies are performed, and experimental tests are carried out to verify the results by applying the shadowgraph method. An advanced test stand is developed to prepare a wide range of changes in atomization characteristics and mixing ratios. A high degree of consistency is found between numerical results from the developed MEM and experimental tests with different gas-phase pressures and liquid flow rates. The droplet diameter and velocity distribution are reviewed based on various Weber numbers, sources of energy, and momentum. Turbulence modeling assists to estimate the breakup length and time scale precisely in the developed MEM, and distribution ranges with mean values are achieved. With reference to a strong correlation between upstream turbulence flow and the developed MEM verified by experimental tests, an ideal droplet size and velocity distribution prediction is observed.

Estimating proton radius and proportion of other non-perturbative components in the proton by the maximum entropy method

In this paper,we apply the Maximum Entropy Method to estimate the proton radius and determine the valence quark distributions in the proton at extremely low resolution scale Q02.Using the simplest functional form of the valence quark distribution and standard deviations of quark distribution functions in the estimation of the proton radius,we obtain a quadratic polynomial for the relationship between the proton radius and the momentum fraction of other non-perturbative components in the proton.The proton radii are approximately equal to the muonic hydrogen experimental result rp = 0.841 fm and the CODATA analysis rp = 0.877 fm when the other non-perturbative components account for 17.5% and 22.3% respectively.We propose ＂ghost matter＂ to explain the difference in other non-perturbative components（4.8%） that the electron can detect.

Generalized Maximum Fuzzy Entropy Methods with Applications on Wind Speed Data

This study is connected with new Generalized Maximum Fuzzy Entropy Methods （GMax（F）EntM） in the form of MinMax（F）EntM and MaxMax（F）EntM belonging to us. These methods are based on primary maximizing Max（F）Ent measure for fixed moment vector function in order to obtain the special functional with maximum values of Max（F）Ent measure and secondary optimization of mentioned functional with respect to moment vector functions. Distributions, in other words sets of successive values of estimated membership function closest to （furthest from） the given membership function in the sense of Max（F）Ent measure, obtained by mentioned methods are defined as （MinMax（F）Ent）m which is closest to a given membership function and （MaxMax（F）Ent）m which is furthest from a given membership function. The aim of this study consists of applying MinMax（F）EntM and MaxMax（F）EntM on given wind speed data. Obtained results are realized by using MATLAB programme. The performances of distributions （MinMax（F）En0m and （MaxMax（F）Ent）m generated by using Generalized Maximum Fuzzy Entropy Methods are established by Chi-Square, Root Mean Square Error criterias and Max（F）Ent measure.

MAXIMUM ENTROPY DECONVOLUTION OF XPS PEAK

Necessity of XPS spectrum deconvolution, disadvantages of the traditional Fast Fourier Transform decon-volution method (FFT) , principle, method and advantages of Maximum Entropy Deconvolution Method (MEM) are de-scribed. Criteria for determing the number of data points sam-pled in MEM are the main point disccussed in the paper,some XPS deconvolution applications of our MEM software show that the MEM makes XPS deconvolution much easier than the traditional FFT method.

Risk calculation method for complex engineering system

This paper presents a rapid and simple risk calculation method for large and complex engineering systems, the simulated maximum entropy method （SMEM）, which is based on integration of the advantages of the Monte Carlo and maximum entropy methods, thus avoiding the shortcoming of the slow convergence rate of the Monte Carlo method in risk calculation. Application of SMEM in the calculation of reservoir flood discharge risk shows that this method can make full use of the known information under the same conditions and obtain the corresponding probability distribution and the risk value. It not only greatly improves the speed, compared with the Monte Carlo method, but also provides a new approach for the risk calculation in large and complex engineering systems.

COMPARISONS AMONG THE SOLUTIONS OF FIBER TEXTURE VECTOR

The texture vectors, as the fundatnental elements of the vector method (VM), are usually determined by the Durand's iterative method. In present paper, the texture vector is derived by two kinds of the maximum entropy method (MEM), which choose pole figure data (MEM(I)) and the series coefficients of pole figures (MEM(II)), respectively, as a constrained condition. The detailed comparisons, including the texture vector and residual vector in the pole figure and ODF, among the results obtained by different methods are given through the ideal fiber texture simulation with Gaussian distribution. It is demonstrated that, although both methods the good results in the ideal texture simulation, the solution on assumption of maximum entropy displays more attractive results. In order to compare the sensitivity of the different methods to the experimental errors, the stochastical errors in pole figures are introduced by the computer random processes (Monte-Carlo simulation). The Monte-Carlo simulation shows that the MEM with the series coefficients as a constrained condition is rather sensitive to the 'experimental' errors, however, inversely the conventional VM and MEM with pole figure data as a constrained condition.

Detection of fabric defects based on bilateral filter and frangi filter

Aimed at low contrast effect on fabric detection,a method based on bilateral filter and frangi filter is proposed. Firstly,in order to reduce the influence of fabric background texture information on the detection results,bilateral filter is used to deal with the fabric image. Then frangi filter is used to filter the fabric image after bilateral filtering to enhance the fabric defect area information. Finally,a maximum entropy method is implemented on the fabric image after frangi filtering to separate the defected area. Experimental results show that the proposed method can effectively detect defects.

The MEM in Measuring Data Processing

A kind of new method in measuring data processing called maximum entropy method(MEM) is introduced. The probability-density function (pdf) is deduced by MEM under the restraint of the square of the data. A group of experiment data is processed using the method and the result closed to the real distribution is got. The different pdf got under different order of square and by different content of samples is discussed. It draws conclusions that the pdf in the square restrain with more order than three using MEM can give the distribution of the data basically, and it is not suitable to use the square restraint of data when the samples are less.

Charge distribution around Ba-O and Ti-O bonds in BaTi_(1-x)Zr_(x)O_(3)through powder X-ray diffraction

Ferroelectric lead-free BaTi_(1-x)Zr_(x)O_(3)ceramic powder samples with various compositions(x=0,0.04,0.06)have been synthesized by conventional high-temperature solid-state reaction method at 1450℃for 10 h.Influences of Zr doping on the inter-atomic bonding and charge density distributions inside the lattice structure of BaTiO_(3)were analyzed through powder X-ray diffraction(XRD)and maximum entropy method.Lattice parameter and cell volume values are found to be increasing with the incorporation of Zr content.Calculated average grain sizes are found to be in the range of 23-28 nm.Maximum entropy mapping of electron density analysis reveals the reduction in ionic nature along Ba-O bond and the enhancement of covalent nature along Ti-O bond.Energy band gap values were determined from ultraviolet-visible(UV-Vis)spectra.Surface morphology and microstructures of the samples were analyzed from scanning electron microscopy(SEM)micrographs.Particles with irregular sizes were observed in all the prepared ceramics.Stoichiometry of the samples was further confirmed by energydispersive X-ray spectroscopy(EDAX).

Electronic structure and bonding interactions in Ba1-xSrxZr0.1Ti0.9O3 ceramics

An investigation on the precise electronic structure and bonding interactions has been carried out on Ba1-xSrxZr0.1Ti0.9O3 （short for BSZT, x = 0, 0.05, 0.07 and 0.14） ceramic systems prepared via high-temperature solid state reaction technique. The influence of Sr doping on the BSZT structure has been examined by characterizing the prepared samples using PXRD, UV-visible spectrophotometry, SEM and EDS. Powder profile refinement of X-ray data confirms that all the synthesized samples have been crystallized in cubic perovskite structure with single phase. Charge density distribution of the BSZT systems has been completely analyzed by the maximum entropy method （MEM）. Co-substitution of Sr at the Ba site and Zr at the Ti site into the BaTiOz structure presents the ionic nature between Ba and O ions and the covalent nature between Ti and O ions, revealed from MEM calculations. Optical band gap values have been evaluated from UV-visible absorption spectra. Particles with irregular shapes and well defined grain boundaries are clearly visualized from SEM images. The phase purity of the prepared samples is further confirmed by EDS qualitative spectral analysis.

Imaging source with Gaussian proper time distribution

Making use of the maximum entropy method, we study the most probable source function in heavy ion collisions. An anisotropic Gaussian source is deduced by simply assuming that the particles are emitted within a finite proper-time. The general relations between the most probable source function and the minimal assumptions are discussed, which are instructive in constructing a self-consistent source function from observed Hanbury-Brown/Twiss（HBT） correlations.

APPLICATION OF MEM SPECTRAL ESTIMATION TO MU RADAR OBSERVATION

Preliminary results of the wind velocity estimation using the Maximum Entropy Method (MEM) to MU radar observation data sets are presented. The comparison of the results from the periodogram method and the MEM shows that the MEM estimation is reliable, and has higher accuracy, resolution and detectability than the estimation from periodogram method. The high accuracy power spectrum obtained by the MEM is very useful to studying the atmospheric turbulence structure. However. the MEM needs the longer computing time for obtaining the high accuracy spectrum. Particularly, the estimation of MEM will bring serious devia- tion at lower signal-to-noise ratio.