# Alexander V PavlovITMO University | SPbNRU ITMO · Department of Photonics and Optical Information Technology

Alexander V Pavlov

Dr.Sc. in Physics and Mathematics

## About

76

Publications

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114

Citations

Introduction

## Publications

Publications (76)

A model of cognitive disorders on the algebra of Fourier-dual operations is proposed. The model meets the criterion of biological motivation and describes main stages of the new information perceiving, that contradicts to the existing subjective knowledge: cognitive dissonance and its reducing. It’s demonstrated, the weakening of low frequencies in...

A Fourier-holography scheme with superimposed holograms and phase conjugation is considered. It is shown that the sub-holograms, arising from the recording of superimposed holograms due to quadratic nonlinearity of the exposure characteristics of holographic recording media, form the connections necessary for the realisation of the quantum-logic me...

The paper adresses the problem of detecting common fragments in a sequence of images recorded in volume recording medium by the method of superimposed Fourier holograms in the joint-Transform scheme. As applied to the description of images as realisations of a homogeneous random field, the dependence of the detection efficiency on the number of sup...

The problem of recognition of the common fragments in a series of images in the absence of a priori criteria relating any one fragment to the common fragments, apart from the frequency of its appearance, is considered with application to recording of superimposed Fourier holograms with spatially modulated reference images. An analysis of the depend...

A Fourier holography scheme in a ring cavity with two Fourier holograms (a matched hologram and a hologram in the correlation plane) has been considered. The dissipation factor of the scheme is determined, and the influence of the hologram recording conditions and the additional filtering caused by the nonlinearity of the exposure characteristics o...

We consider two phenomena that are typical of the volume superimposed holograms, namely, the formation of the dielectric-permittivity structures corresponding to interference of the reference waves, which did not interfere in reality, due to the nonlinearity of the medium, and double diffraction of the waves in the hologram volume. It is shown that...

In the development of an approach to the implementation of fuzzy logics on neural networks with interconnections via the scheme of Fourier holography, a model of logic with exception is proposed, which is associated with the basic Generalized Modus Ponens rule. The exception is recalled from the associative memory by an inference formed by the basi...

In terms of an approach that uses Fourier holography to construct exclusionary logics, an implementation of a cognitive mechanism is proposed for bringing new information into accordance with an internal pictorial world. It is shown that there is a phenomenon of oscillations between stereotypes recorded on the hologram and new information, caused b...

The interaction of two competing mechanisms that participate in the formation of a concept is considered in developing an approach to the implementation of inductive generalization in a Fourier-holography setup as a method of generating abstract concepts on the basis of sensory-pattern processing. These mechanisms are nonlinear iterative mapping in...

As applied to the description of a Fourier-holography layout with phase conjugation in the correlation plane as the implementation of a two-layer neural network, this paper discusses two models of the advancement of hypotheses: linear regression of the conditions of a problem from knowledge, and inductive inference. The factors that influence the a...

The influence of filtration in the Fourier holography scheme, which is caused by nonlinearity of the exposure characteristics of recording media on the homogeneity of processed images in the first two statistical moments, has been investigated. Formulas approximating the dependences of the estimates on the generalized rate (ratio of image size to c...

This paper discusses how spatial-frequency filtering in the 4f scheme of Fourier holography, determined by limiting the dynamic range of the recording medium, affects the homogeneity of the processed image with respect to the first two statistical moments. When numerical modelling is carried out, models of the filters are used that are adequate to...

An approach for fuzzy-valued nonmonotonic logics, based on the algebra
of Fourier-dual operators, to be implemented by Fourier-holography
technique is proposed. Results of computer simulation based on
experimentally implemented logics are presented.

The effect of filtering that arises in the scheme of 4f Fourier holography due to the boundedness of the dynamic range of holographic recording medium on the statistical characteristics
of a random process, as applied to the realization of the linear predictor model, has been investigated. The numerical simulation
has been performed using filter mo...

In working out a method developed earlier for implementing fuzzy logics, it is proposed to use an approach to the implementation of plausible reasoning (abductive and inductive inferences) on a two-layer optical neural network with an array of bidirectional connections, implemented by means of Fourier holography. The requirements on the characteris...

This paper discusses how the filtering that results from the limited dynamic range of a holographic recording medium affects the characteristics of a random process as applied to the implementation of the linear-predictor model by the method Fourier of holography. With numerical modelling, models of the filters are used that are adequate for the ac...

As applied to the problem of fuzzy-valued logics implementation by the Fourier holography method, it is demonstrated that,
if the dependence of the local diffraction efficiency of the Fourier hologram on the spatial frequency is characterized by
the inverse dependence in the region of zero spatial frequency, the transfer function of the 4f scheme o...

This paper shows that Feigenbaum's scenario of transition to chaos can be implemented in a Fourier-holography layout with wave-front reversal in the correlation plane. Based on this, it is proposed to use the Fourier-holography layout with wave-front reversal as an approach to the task of implementing creative thought. The requirements on the trans...

In developing the biologically motivated approach proposed earlier to the implementation of logico-linguistic modeling by the method of Fourier holography, it was shown to be possible to implement logic with exclusions as a particular case of nonmonotonic logic. It was proposed to use one implication operator for both the premise and the exclusion...

The possibility of integrating the principles of imaginative and logical thinking by means of Fourier holography is demonstrated.
The proposed approach develops the concept of logical-linguistic modeling based on fuzzy-valued logics with allowance for
some recent results in brain neurophysiology. The possible implementation of nonmonotonic reasonin...

In developing a biologically motivated approach to the implementation of logico-linguistic modeling proposed earlier, using the method of Fourier holography, it is shown to be possible to integrate the principles of imaging and logical thought, including the implementation of nonmonotonic reasoning. An experimental illustration is given.

The linear regression model is shown to describe adequately the 4-f scheme of Fourier holography with wave front reversal in the correlation plane and with the use of the hologram with the
inverse transfer characteristic at the stage of passage of light in the reverse direction. If an image as a realization of
a random field possesses the property...

This paper shows that a 4f-scheme of Fourier holography with wave-front reversal in the correlation plane can be used to implement a multiple linear regression model that constructs the best prediction for random processes that are steady-state in the broad sense. An experimental illustration is given.

This paper proposes a biologically motivated approach to the implementation by the method of Fourier holography of a logical conclusion on linguistic scales. A linguistic output of the "generalized modus ponens" type is experimentally implemented, similar to ordinary human reasoning. It is shown that it is possible to implement the principle of sub...

In this paper we consider linguistic model as an algebraic model and restrict our consideration to the semantics only. The concept allows "natural-like" language to be used by human-teacher to describe for machine the way of the problem solving, which is based on human"s knowledge and experience. Such imprecision words as "big", "very big", "not ve...

An approach to implement the idea of linguistic modelling by Fourier-holography technique is proposed. The approach is based on deep analogies between Optics as a physical reality and Fuzzy Sets Theory as an abstract construction. We use the concept of linguistic variable, proposed by L.Zadeh and restrict our consideration to the semantics only. We...

Linguistic modeling is the way, which allows human-like language to be used to teach machine. The task is to match metric scale of the machine with linguistic scale of the teacher. We discuss application of Fourier-holography technique to this task. We formulate logical description of 4-f Fourier-holography setup. Restrictions on the model, determi...

In this paper we discuss our approach to based on holographic techniques implementation of neuro-fuzzy predictor for processes, described by Fractal Brownian Motion (FBM) model. We use the model of the predictor as a Riemann Stieltjes integral over the observed traffic of specific weight function. We discuss two-layered bi-directional optical neura...

This paper gives a review of optical information technologies as applied to problems of artificial intelligence.

The approximations of the geometric and Fourier optics are considered from the standpoint of constructing a logic as an algebraic model. Methods of geometric optics allow one to implement a many-valued logic. The constraints imposed by the actual properties of registering media are discussed. By introducing in the model the operations that determin...

The approximations of geometrical and Fourier optics are considered from the viewpoint of constructing logic as an algebraic model. It is shown that the methods of geometrical optics make it possible to implement multivalued logic, while Fourier optics provides both multivalued and fuzzy-valued logics. A physically based implication operator is def...

We discuss a way to implement predictor for stochastic process with stationary increments by using optical neural network.

We consider algebraic foundations of geometrical optics approximation. The consideration is aimed at optical implementation of computational intelligence models. Theory of triangular norms and measure means are used to formulate the description. The process of negative photo-registration is considered as the implementation of the negation, which ge...

Optics has a number of deep analogies with main principles of Computational Intelligence. We can see strong analogies between basic optical phenomena, used in Fourier-holography, and mathematical foundations of Fuzzy Set Theory. Also, analogies between optical holography technique and principles of Neural Networks Paradigm can be seen. Progress in...

Recent developments in architectures, devices, and protocols have dramatically increased the traffic capacity of telecommunication
networks. New control and management techniques are needed for the potential, by this progress promising, to be achieved.
Soft computing (SC) is the approach that gives an attractive way to this goal. From the hardware...

The technique of Fourier holography is considered from the point of view of the construction of an algebraic model. It is shown that the technique yields a construction of a semigroup of fuzzy subsets with convolution as addition and correlation as subtraction. It is proved that in an approximation to linearity of the Fourier transformation, the Su...

Fourier holography is considered as the physical basis of an algebraic model. A constructive interpretation of the formal
axiomatics is presented. It is shown that the scheme of Fourier holography corresponds to an additive semigroup with convolution
serving as abstract summation. The correlation operation plays the role of subtraction, and a diffr...

Progress in telecommunication networks needs new control and management techniques for the potential, by new protocols and architectures promising, to be achieved. Computational Intelligence (CI) gives an attractive way to this goal. From the hardware point of view, the main problem is CI based methods are computationally expensive. Optics gives a...

The choice of a function approximating the exposure dependence of the amplitude transmission of negative recording media is
considered from the standpoint of the theory of measure within the framework of the algebraic model of the system in the geometrical
optics approximation. Two processes are taken into account: photodetection in the quasi-linea...

Our main interest is to formulate algebraic description of both Geometrical and Fourier-approximations of Optics. We use triangular- norms based approach to formulate algebraic descriptions for both geometrical and Fourier-approximations of optics. To take into consideration real nonlinearity of recording media the measure theory is used. Unlimited...

Our main interest is to formulate algebraic description of both Geometrical and Fourier-approximations of Optics. We use triangular- norms based approach to formulate algebraic descriptions for both geometrical and Fourier-approximations of optics. To take into consideration real nonlinearity of recording media the measure theory is used. Unlimited...

Approximations of geometrical and Fourier optics are considered in the framework of the triangular norms technique. For each of the approximations, operators of subsets relations are defined. It is shown that the approximation of the geometrical optics generates a probabilistic many-valued logic and the approximation of the Fourier optics generates...

Our main interest is to establish connections between Optics and Fuzzy Set Theory. We formulate the t-norms based algebraic description of both geometrical and Fourier- approximations of optics. Geometrical optics implements probabilistic operators under the linear approximation of negative recording process. For real recording media not Zadeh's, b...

Our main interest is to establish connections between Optics and Fuzzy Set Theory. We formulate the t-norms based algebraic description of both geometrical and Fourier- approximations of optics. Geometrical optics implements probabilistic operators under the linear approximation of negative recording process. For real recording media not Zadeh's, b...

Optical Fourier holography is interpreted as a method of creating and recording fuzzy relations between sets represented in
the form of images. The properties of the fuzzy relations created by means of a holographic correlator and images implemented
in neural network algorithms are considered.

Construction of algebra of fuzzy numbers by Fourier holography techniques is presented. Implementation of arithmetic operations on both conventional and VSOP fuzzy numbers by both with plane reference wave and joint- transform setups is discussed. Realization of both addition and subtraction operations is presented.

Model of Artificial Vision is discussed. The task is to find the part of reference pattern that presents in the object image. Condition is the task has to be solved in the framework of the Classifical Approach to the image understanding, i.e. without formal description of patterns. In two-layered bidirectional optical neural network image layer as...

Hologram as a fuzzy relation of two subsets is treated. Fuzzy number as a Fourier-transform of the distribution in the plane of hologram is determined. To generate monoid of fuzzy numbers, convolution as an inner composition law is used. Realization of extended ariphmetic operations by holography is discussed.

This paper shows that it is possible to construct an algebra of fuzzy numbers (FNs) by the methods of optical holography. A hologram is regarded as a recorded ratio of subsets of the set of real numbers. An FN is defined as the Fourier transform of an amplitude distribution in the plane of the hologram. The convolution operation is used as the law...

This paper proposes a model of artificial vision that takes into account the general principles for constructing and operating biological prototypes for solving problems of pattern analysis. The model is based on associative-processing methods, implemented by a two-layer optical neural network (NN) with a correlation matrix of connections. The requ...

Two holographic correlator systems - a Vanderlugt correlator and a combined transformation correlator - are considered as devices for implementing the fuzzy ratio of two sets. The properties of the fuzzy ratio are defined as a function of the coupling of the object and reference images, and the properties of the ratio reconstructed during phase con...

The formation of retarding connections in an optical two-layer bidirectional neural network on the basis of a van der Lügt correlator for the achievement of a solution of the "reconstruction of a common fragment of images compared" type is considered theoretically. The efficiency is estimated for the case when the matrix of retarding connections is...

This paper discusses the structure of the interneuronal connections implemented by a Vanderlugt correlator in a two-layer bidirectional optical neural network. The paper describes the modification of the structure and the position of the attractor when the network is reconstructed from an associative-memory type of solution to a type involving rest...

The idea of the Plural Partial Associations is proposed to designate the case of associatability having the prototypes in ordinary life, but not described by the Associative Memory principle. The method based on computation of the correlation functions of the input vector with the back of the reference vectors is discussed as a one of the possible...

A review is given of the use of information-processing methods and resources based on coherent optical correlation to analyze scenes for artificial-vision systems.

This paper discusses an approach to the study of the phase relief of neural networks in which the correlation matrix of the connections between the layers is implemented by a holographic correlator. It is proposed to study the phase relief in terms of its cross sections by hypersurfaces formed by image transformations. The numerical modeling of the...

A method of the numerical investigation of the energy relief of the neural networks (NN) with the correlation interconnections realized by holographic correlator is discussed. The analytical and numerical modeling of the energy relief sectioned by hypersurfaces formed by the transformations of the object image to reference is used.

It is shown that at the numerical simulation of the effect of the geometrical distortions belonging to the group of projective transformation on the correlation of images one should take into account the entire operation band of the filter spatial-frequency spectrum and filter function. The results of numerical simulation are compared with those ex...

Optical neural network formed by placing the holographic correlator into the linear resonator is discussed. Variation of the attractor position by means of inhibitory optical interconnections to achieve new solution types is proposed. The experimental results are presented.

An optical neural network formed by a Van der Lugt correlator placed in a linear cavity is discussed as a realization of a model of a two-layer two-directional network. The structure of the system of interconnections is considered. The possibility is discussed of varying the position of the global minimum in the space of network states adaptively w...

The neural network concept of the complex system for pattern recognition on the complex background is proposed. The main components of this concept are the complex space of the features and the mode of information complexing. The concept about neurophysiological mechanisms of the vision search on the complex background is used as the neural network...

The adaptive neural network model for pattern classification on the complex background is proposed. The method of the detection and extraction of the unknown changing patterns, based on the optical correlation, is proposed. The optical implementation of that NN model, formed by placing the optical correlator in a linear resonator to realize the vec...

The possibilities of the optical neural network formed by placing the optical correlator in a linear resonator to realize the vectors comparison and image preparation are discussed. The adaptive neural network model to pattern recognize on the complex background is proposed. The optical implementation of that NN model is discussed.

The method of the numerical evaluation of the influence of the geometrical distortions on the image correlation without the limitation on the type of the distortions is discussed. The main types of the distortions are described. The results of the theoretical modeling and experiments on the holography correlator are presented.

Types of solutions are shown to which the process can converge in an optical neural network made of a Van der Lught correlator inside a linear resonator. Conditions for obtaining the desired type of solution are specified. For this architecture associative memory is a particular case of a more general form of solutions. The results of experimental...

Linguistic Modeling is the approach that allows human- computer interaction to be established by using natural-like language. We use Fourier-holography technique to implement Linguistic Modeling in the framework of Neuro-Fuzzy approach. We pay attention to implementation of non- monotonic semantics by this technique. We develop theoretical model an...

## Projects

Project (1)