Maximum Entropy Method Algorithm Research Articles

HIGH-RESOLUTION LINEAR POLARIMETRIC IMAGING FOR THE EVENT HORIZON TELESCOPE

ABSTRACT Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highly adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT.

Dysnomia, a computer program for maximum-entropy method (MEM) analysis and its performance in the MEM-based pattern fitting

A computer program, Dysnomia, for the maximum-entropy method (MEM) has been tested for the evaluation and advancement of MEM-based pattern fitting (MPF). Dysnomia is a successor to PRIMA, which was the only program integrated with RIETAN-FP for MPF. Two types of MEM algorithms, i.e., 0th-order single-pixel approximation and a variant of the Cambridge algorithm, were implemented in Dysnomia in combination with a linear combination of the “generalizedFconstraints” and arbitrary weighting factors for them. Dysnomia excels PRIMA in computation speed, memory efficiency, and scalability owing to parallel processing and automatic switching of discrete Fourier transform and fast Fourier transform depending on sizes of grids and observed reflections. These features of Dysnomia were evaluated for MPF analyses from X-ray powder diffraction data of three different types of compounds: taurine, Cu2CO3(OH)2(malachite), and Sr9In(PO4)7. Reliability indices in MPF analyses proved to have been improved by using multipleFconstraints and weighting factors based on lattice-plane spacings,d, in comparison with those obtained with PRIMA.

Analysis of simulated fluorescence intensities decays by a new maximum entropy method algorithm.

A new algorithm for the Maximum Entropy Method (MEM) is proposed for recovering the lifetime distribution in time-resolved fluorescence decays. The procedure is based on seeking the distribution that maximizes the Skilling entropy function subjected to the chi-squared constraint χ 2 ~ 1 through iterative linear approximations, LU decomposition of the Hessian matrix of the lagrangian problem and the Golden Section Search for backtracking. The accuracy of this algorithm has been investigated through comparisons with simulated fluorescence decays both of narrow and broad lifetime distributions. The proposed approach is capable to analyse datasets of up to 4,096 points with a discretization ranging from 100 to 1,000 lifetimes. A good agreement with non linear fitting estimates has been observed when the method has been applied to multi-exponential decays. Remarkable results have been also obtained for the broad lifetime distributions where the position is recovered with high accuracy and the distribution width is estimated within 3 %. These results indicate that the procedure proposed generates MEM lifetime distributions that can be used to quantify the real heterogeneity of lifetimes in a sample.

Solution of Radiative Boundary Design Problems Using a Combined Optimization Technique

In this work, a novel combined strategy has been developed and verified for radiative boundary design problems. It is highly efficient and simple to implement and appears promising for obtaining appropriate results in practical applications. In the proposed approach, the determination of the unknown profile of heat flux through active constraints includes utilizing a new search optimization technique that is merged with the maximum entropy method (MEM). It is shown that use of the merged MEM algorithm minimizes both the occurrence of negative values for physically non-negative components, and the oscillatory profile of heat flux. A generalized computational grid based on finite-volume scheme is devised to solve the radiative transfer equation and sensitivity equations. Numerical simulations are conducted to evaluate the performance and accuracy of the present approach with regard to the classical methods involved in its derivation.

Comparison of maximum entropy and filtered back-projection methods to reconstruct rapid-scan EPR images

Reconstruction of two-dimensional images by filtered back-projection (FBP) and by the maximum entropy method (MEM) was compared for spectral-spatial EPR images with differing signal-to-noise ratios. Experimental projections were recorded using direct-detected rapid scans in the presence of a series of magnetic field gradients. The slow-scan absorption lineshapes were calculated by Fourier deconvolution. A Hamming filter was used in conjunction with FBP, but not for MEM. Imperfections in real experimental data, as well as random noise, contribute to discrepancies between the reconstructed image and experimental projections, which may make it impossible to achieve the customary MEM criterion for convergence. The Cambridge MEM algorithm, with allowance for imperfections in experimental data, produced images with more linear intensity scales and more accurate linewidths for weak signals than was obtained with another MEM method. The more effective elimination of noise in baseline regions by MEM made it possible to detect weak trityl 13C trityl hyperfine lines that could not be distinguished from noise in images reconstructed by FBP. Another advantage of MEM is that projections do not need to be equally spaced. FBP has the advantages that computational time is less, the amplitude scale is linear, and there is less noise superimposed on peaks in images. It is useful to reconstruct images by both methods and compare results. Our observations indicate that FBP works well when the number of projections is large enough that the star effect is negligible. When there is a smaller number of projections, projections are unequally spaced, and/or signal-to-noise is lower MEM is advantageous.

Nondestructive in‐depth composition profile of oxy‐hydroxide nanolayers on iron surfaces from ARXPS measurement

AbstractIn this work the maximum entropy method (MEM) is applied, for the first time, to angle‐resolved X‐ray photoelectron spectroscopy (ARXPS) data from oxy‐hydroxide films on iron surfaces. This nondestructively derives information on the in‐depth distribution of the composition and chemical state. An MEM algorithm was created and first tested on the simulated data. The reconstructed composition depth profiles agreed very well with the theoretical ones up to 5% Gaussian noise added to the data. The same algorithm was then applied to ARXPS data from iron samples to investigate the in‐depth variations in the composition and chemical state of the nanosized oxy‐hydroxide film naturally grown on the iron surface. The resulting surface film presents a complex multilayer structure with concentration gradients. The effect of air exposure on the structure was also investigated. Copyright © 2006 John Wiley & Sons, Ltd.

A spatial and spectral maximum entropy method as applied to OVRO solar data

We present rst results of applying a Maximum Entropy Method (MEM) algorithm that acts in both the spatial and spectral domains to data obtained with the frequency-agile solar interferometer at Owens Valley Radio Observatory (OVRO) taken at 45 frequencies in the range 1 18 GHz. The traditional MEM algorithm does not exploit the spatial information available at ad- jacent frequencies in the OVRO data, but rather applies separately to each frequency. We seek an algorithm that obtains a global solution to the visibilities in both the spa- tial and spectral domains. To simplify the development process, the algorithm is at present limited to the one- dimensional spatial case. We apply our 1-d algorithm to observations taken with the OVRO frequency-agile inter- ferometer of active region AR 5417 near the solar limb on March 20, 1989 (vernal equinox). The interferometer's two 27 m antennas and 40 m antenna were arranged in a linear east-west array, which at the vernal equinox gives a good match to the 1-d algorithm. Our results show that includ- ing the spectral MEM term greatly improves the dynamic range of the reconstructed image compared with a re- construction without using this information. The derived brightness temperature spectra show that for AR 5417 the dominant radio emission mechanism is thermal gyrores- onance and we use this information to deduce the spa- tial variation of electron temperature and magnetic eld strength in the corona above the active region.

Application of complex MEM processing for measuring reflective architecture in acoustical archaeology

A measurement of reflective characteristics of architecture is one of the fundamental studies in acoustical archaeology. In this paper an application of maximum entropy method (MEM) processing is discussed for measuring the characteristics of reflective architecture in acoustic archaeology by computer simulation. Chirp signals are supposed to be transmitted from a speaker and reflected acoustical signals of amplitude and phase are recorded using several receivers. Since the received signals are complex, MEM algorithms for processing complex signals are developed and the relative distances between reflective targets and receivers are calculated, resulting in the identification of the location of the targets in 2-D space. In a different view, the proposed mesurement technique is a reconstruction of a target from a one-dimensional complex acoustical hologram. Computer simulation is done in which chirp signals are supposed to be reflected from a target and complex acoustical signals are generated by superposing the signals received by several receivers. Pulse compression of signals of different receivers is conducted using the proposed MEM algorithm, resulting in detection of the distances between the target and receivers. Application of the proposed method to the measurement of the reflective characteristics of architecture in acoustic archaeology is discussed.

A fast MEM algorithm for high resolution direction spectrum estimation

From the point of view of reducing computation and improving performance, this paper discusses the Maximum Entropy Method (MEM) in array data processing and proposes a fast modified MEM (MMEM) on account of noise power cancellation. The simulation results show that the MMEM has better directional performance and higher angular resolution than the MEM. The required (SNR) can be reduced by 7–10 dB and the error of the root-mean square of angle estimation is greatly decreased.

Maximum Entropy Inversion of Induction-Log Data

Summary This paper describes the development and application of some new algorithms based on the maximum entropy method (MEM) for inverting (i.e., deconvolving) induction-log data. The MEM has earned a reputation in many physical science fields as a technique that provides robust and accurate reconstructions of instrumentally blurred data. Dyos recently applied a MEM algorithm to the inversion of synthetic deep-induction-log data. This paper develops some new MEM algorithms that are applied to inversion of model data and to field data from the PhasorSM induction tool. The new algorithms overcome some of the limitations of previous inversion methods and inverse-deconvolution-filter techniques. This paper examines two different MEM algorithms. The first algorithm is based on a functional used to study MEM inversions of synthetic data with a Doll approximation forward model. A second, more efficient MEM algorithm, based on a new Lagrangian functional, is used with an exact forward model to study the inversion of a field log and some model formations. Use of an exact forward model is essential in obtaining accurate and high-resolution MEM inversions in the presence of skin and shoulder effects. The MEM inversions of model data and field logs exhibit vertical resolution, accuracy, and stability that exceed those obtainable with state-of-the-art linear inverse filters. An example of the MEM inversion of a field log in a formation with numerous high-contrast thin beds is discussed and compared with the spherically focused log (SFLSM) and the deep enhanced-resolution Phasor- (IDERSM-) processed log. The MEM inversion exhibits resolution comparable to that of the SFL. It is shown that, as a byproduct, the MEM provides synthetic logs that serve as a self-consistency check on both the quality of entered data and the validity of the Rt profile obtained from inversion.