A Fast Rational Model Approach to Parametric Spectral Estimation—Part I: The Algorithm

1990 ◽  
Vol 112 (3) ◽  
pp. 321-327 ◽  
Author(s):  
S. D. Fassois
Keyword(s):  
Spectral Estimation ◽  
A Priori ◽  
Inverse Function ◽  
Memory Storage ◽  
Rational Model ◽  
Arma Process ◽  
Sufficient Statistic ◽  
Guaranteed Stability ◽  
Local Extrema ◽  
Priori Information

A novel, fast rational model (ARMA) approach to parametric spectral estimation, based on correlation-type and guaranteed-stability versions of the Suboptimum Maximum Likelihood scheme that utilizes a quadratic approximation of the negative log-likelihood about an initial estimate in the MA parameter subspace, inverse function estimates, and fundamental ARMA process properties, is introduced. The proposed approach is exclusively based on linear operations, uses the autocovariance function as a “sufficient statistic,” and overcomes the main drawbacks/limitations of alternative approaches by offering high accuracy, minimal computational and memory storage requirements, no need for a priori information, mathematically guaranteed stability (and therefore the capability of estimating all types of spectra, including those characterized by sharp valleys), and complete elimination of the local extrema problem by yielding a unique estimate that is shown to asymptotically converge to the true spectrum. The paper is divided into two parts: The basic form of the proposed approach is derived in the first part, whereas in the second (Fassois, 1990), its consistency is proven, two guaranteed-stability versions developed, and its performance evaluated via numerical simulations and comparisons with standard techniques.

Inversion modeling of gravity with prismatic mass bodies

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1365-1376 ◽  
Author(s):  
Tieng‐Chang Lee ◽  
Shawn Biehler
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Depth Resolution ◽  
Memory Storage ◽  
Inversion Algorithm ◽  
Sampling Window ◽  
Prismatic Bodies ◽  
The Fourier Transform ◽  
Priori Information ◽  
Forward And Inverse Modeling

A combined method for forward and inverse modeling of gravity data is presented. Based on the Fourier transform of Poisson’s equation, the forward modeling is suitable for observation points above, within, and below causative masses with any prescribed density distribution. The inversion is linearized in the spatial domain by superimposing numerous prismatic bodies, each having constant but different density, and fixed geometry. Our inversion algorithm adopts a sampling window to reduce memory storage and computations. Testing, with synthetic and field data, demonstrates that a successful inversion can be obtained from crudely estimated a priori density distributions and uncertainties. Lateral variations in density are well resolved but depth resolution often requires better constrained a priori information. Under various a priori conditions, our modeling indicates that sediment density tends to vary exponentially with depth in the San Jacinto basin, southern California.

A Fast Rational Model Approach to Parametric Spectral Estimation—Part II: Properties and Performance Evaluation

1990 ◽  
Vol 112 (3) ◽  
pp. 328-336 ◽  
Author(s):  
S. D. Fassois
Keyword(s):  
Spectral Analysis ◽  
Performance Evaluation ◽  
Spectral Estimation ◽  
Rational Model ◽  
Basic Form ◽  
Guaranteed Stability ◽  
Consistency Property ◽  
Alternative Techniques ◽  
And Performance ◽  
Model Approach

In the first part of this paper (Fassois, 1990), the basic form of a novel, fast rational model approach to parametric spectral estimation was introduced. In this second part the consistency property of the approach is proven, and two modified versions, characterized by mathematically guaranteed stability, developed. Unlike most alternative techniques, the proposed approach is then capable of effectively estimating all types of spectra, including those characterized by sharp valleys. Its performance is finally evaluated via numerical simulations and comparisons with the Blackman-Tukey and the AR spectral analysis methods.

Innovative Approach to Information Search by Example of a Patent Analysis of an Important Substitution Plan

2020 ◽  
pp. 143-157
Author(s):  
Maria A. Milkova
Keyword(s):  
Information Search ◽  
Topic Modeling ◽  
Cognitive Biases ◽  
A Priori ◽  
Import Substitution ◽  
Innovative Approach ◽  
Iterative Search ◽  
Comprehensive Picture ◽  
Priori Information ◽  
Selection Of

Nowadays the process of information accumulation is so rapid that the concept of the usual iterative search requires revision. Being in the world of oversaturated information in order to comprehensively cover and analyze the problem under study, it is necessary to make high demands on the search methods. An innovative approach to search should flexibly take into account the large amount of already accumulated knowledge and a priori requirements for results. The results, in turn, should immediately provide a roadmap of the direction being studied with the possibility of as much detail as possible. The approach to search based on topic modeling, the so-called topic search, allows you to take into account all these requirements and thereby streamline the nature of working with information, increase the efficiency of knowledge production, avoid cognitive biases in the perception of information, which is important both on micro and macro level. In order to demonstrate an example of applying topic search, the article considers the task of analyzing an import substitution program based on patent data. The program includes plans for 22 industries and contains more than 1,500 products and technologies for the proposed import substitution. The use of patent search based on topic modeling allows to search immediately by the blocks of a priori information – terms of industrial plans for import substitution and at the output get a selection of relevant documents for each of the industries. This approach allows not only to provide a comprehensive picture of the effectiveness of the program as a whole, but also to visually obtain more detailed information about which groups of products and technologies have been patented.

scholarly journals Computational Method for Wavefront Sensing Based on Transport-Of-Intensity Equation

Photonics ◽  
2021 ◽  
Vol 8 (6) ◽  
pp. 177
Author(s):  
Iliya Gritsenko ◽  
Michael Kovalev ◽  
George Krasin ◽  
Matvey Konoplyov ◽  
Nikita Stsepuro
Keyword(s):  
A Priori ◽  
Spherical Wave ◽  
Computational Method ◽  
Optical Systems ◽  
Radius Of Curvature ◽  
Imaging Method ◽  
Wavefront Sensing ◽  
Phase Imaging ◽  
Transport Of Intensity Equation ◽  
Priori Information

Recently the transport-of-intensity equation as a phase imaging method turned out as an effective microscopy method that does not require the use of high-resolution optical systems and a priori information about the object. In this paper we propose a mathematical model that adapts the transport-of-intensity equation for the purpose of wavefront sensing of the given light wave. The analysis of the influence of the longitudinal displacement z and the step between intensity distributions measurements on the error in determining the wavefront radius of curvature of a spherical wave is carried out. The proposed method is compared with the traditional Shack–Hartmann method and the method based on computer-generated Fourier holograms. Numerical simulation showed that the proposed method allows measurement of the wavefront radius of curvature with radius of 40 mm and with accuracy of ~200 μm.

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