The generalization of maximum entropy method for reconstruction of complex functions

1992 ◽  
Vol 1 (4) ◽  
pp. 313-320 ◽  
Author(s):  
Anisa T. Bajkova
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Complex Functions

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.

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.

Maximum entropy method in phase-encoding NMR imaging

1987 ◽  
Vol 4 (1) ◽  
pp. 78-82 ◽  
Author(s):  
B. C. De Simone ◽  
F. De Luca ◽  
B. Maraviglia
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method ◽  
Nmr Imaging ◽  
Phase Encoding

scholarly journals Correction to “Statistics of multifractal processes using the maximum entropy method”

2011 ◽  
Vol 38 (19) ◽  
pp. n/a-n/a
Author(s):  
V. Nieves ◽  
J. Wang ◽  
R. L. Bras
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method

Maximum entropy method applied to deblurring images on a MasPar MP-1 computer

1991 ◽  
Author(s):  
N. L. Bonavito ◽  
John E. Dorband ◽  
Tim Busse
Keyword(s):  
Maximum Entropy ◽  
Maximum Entropy Method ◽  
Entropy Method
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