scholarly journals Generalized Versus Classical Maximum Entropy for Imaging

1994 ◽  
Vol 158 ◽  
pp. 215-217
Author(s):  
A.T. Bajkova
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Fourier Spectrum ◽  
Careful Analysis ◽  
Entropy Method ◽  
Reconstruction Method ◽  
Generalized Maximum Entropy ◽  
Exact Reconstruction ◽  
Reconstruction Quality ◽  
Complex Functions

The problem of image reconstruction from incomplete and noisy complex Fourier spectrum is considered. The maximum entropy method (MEM) is of great interest as the most effective nonlinear reconstruction method having superresolution effect. Because objects of radio astronomical observations are incoherent radio sources described by real non-negative distributions, application of the classical MEM is quite reasonable. But it is established that the MEM gives acceptable reconstruction quality mostly in the case of point-like sources and in general it does not ensure satisfactory reconstruction of continous, graytone objects, which can considerably restrict applications of the MEM in astronomy. The generalized maximum entropy method (GMEM) was originally proposed for reconstruction of distributions described by complex functions (Bajkova, 1992) and was considered as having the same properties of the classical MEM. More careful analysis of the GMEM and classical MEM for real non-negative objects allowed to establish that the GMEM ensures much more exact reconstruction, especially in the case of continous objects. Explanation and demonstration of this interesting and very important phenomenon is the purpose of the present paper.

scholarly journals Locating Cu in Zeolite SSZ-13 by Synchrotron PXRD Using Maximum Entropy Method

2014 ◽  
Vol 70 (a1) ◽  
pp. C1344-C1344
Author(s):  
Casper Andersen ◽  
Martin Bremholm ◽  
Peter Vennestrøm ◽  
Anders Blichfeld ◽  
Lars Lundegaard ◽  
...  
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Careful Analysis ◽  
Rietveld Analysis ◽  
Entropy Method ◽  
Structural Description ◽  
X Ray Diffraction ◽  
Fundamental Interest ◽  
Catalytically Active ◽  
Framework Species

Efficient elimination of environmentally harmful gaseous NOx compounds from automotive diesel emission remains a challenging task. State-of-the-art zeolites with the chabazite framework containing catalytically active Cu2+ (Cu-SSZ-13) have been commercialized as NOx after-treatment catalysts in diesel-powered vehicles, due to its superior activity, selectivity, and durability.[1] However, to meet current and future legislative demands, continuous improvement is of fundamental interest. Prerequisites for an in depth understanding and further improvements, are detailed complete structural models of the Cu-loaded catalyst. This may be achieved by the use of high resolution synchrotron powder X-ray diffraction (PXRD) and iterative Rietveld analysis and Maximum Entropy Method (MEM). Since the content of Cu2+ is low, a protonated system (H-SSZ-13) and model system with monovalent Ag+ ions (Ag-SSZ-13) are also examined. The protonated and dehydrated H-SSZ-13 shows perfectly empty voids, i.e. no water residue or other non-framework species. The H-SSZ-13 structure is used as the initial model for the MEM calculations. For Ag-SSZ-13 MEM analysis clearly pinpoints the Ag+ ion as being located in the 6-ring shifted into the chabazite cage (Figure 1), consistent with the generally accepted site for Ag+ ions in chabazite and reveals the strength of the iterative Rietveld/MEM analysis. For the more challenging case of Cu-SSZ-13 it was still possible through careful analysis and reasoning to locate two separate positions for the Cu2+ in Cu-SSZ-13 (Figure 1). The B site has been suggested by several other studies, but never confirmed experimentally.[2] This is the most complete structural description of zeolite SSZ-13 with stabilizing and catalytically active Cu2+ ions.[3]

Enhanced Information Recovery in 2D On-and Off-Resonance Nutation NQR using the Maximum Entropy Method

1996 ◽  
Vol 51 (5-6) ◽  
pp. 337-347 ◽  
Author(s):  
Mariusz Maćkowiak ◽  
Piotr Kątowski
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Theoretical Description ◽  
Entropy Method ◽  
Zero Field ◽  
Resonance Effects ◽  
Information Recovery ◽  
Truncation Errors ◽  
Enhanced Resolution ◽  
2D Data

Abstract Two-dimensional zero-field nutation NQR spectroscopy has been used to determine the full quadrupolar tensor of spin - 3/2 nuclei in serveral molecular crystals containing the 3 5 Cl and 7 5 As nuclei. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. It is shown that the replacement of conventional Fourier transform by an alternative data processing by MEM in 2D NQR spectroscopy leads to sensitivity improvement, reduction of instrumental artefacts and truncation errors, shortened data acquisition times and suppression of noise, while at the same time increasing the resolution. The effects of off-resonance irradiation in nutation experiments are demonstrated both experimentally and theoretically. It is shown that off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments, thus facilitating the determination of asymmetry parameters in multiple spectrum. The theoretical description of the off-resonance effects in 2D nutation NQR spectroscopy is given, and general exact formulas for the asymmetry parameter are obtained. In off-resonance conditions, the resolution of the nutation NQR spectrum decreases with the spectrometer offset. However, an enhanced resolution can be achieved by using the maximum entropy method in 2D-data reconstruction.

Estimating the distribution of primary reflection coefficients

Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1417-1422 ◽  
Author(s):  
Danilo R. Velis
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Reflection Coefficients ◽  
Log Data ◽  
Neuquen Basin ◽  
Neuquén Basin ◽  
Skewness And Kurtosis

The distribution of primary reflection coefficients can be estimated by means of the maximum entropy method, giving rise to smooth nonparametric functions which are consistent with the data. Instead of using classical moments (e.g. skewness and kurtosis) to constraint the maximization, nonconventional sample statistics help to improve the quality of the estimates. Results using real log data from various wells located in the Neuquen Basin (Argentina) show the effectiveness of the method to estimate both robust and consistent distributions that may be used to simulate realistic sequences.

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