Igor Aizenberg | Texas A&M University - Texarkana (original) (raw)

Papers by Igor Aizenberg

Research paper thumbnail of Image processing using cellular neural networks based on multi-valued and universal binary neurons

Multi-valued neurons (MVNs) and universal binary neurons (UBNs) are neural processing elements wi... more Multi-valued neurons (MVNs) and universal binary neurons (UBNs) are neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by a partially-defined multiple-valued function on a single MVN, and an arbitrary mapping described by a partially-defined or fully-defined Boolean function (which does not have to be a threshold function) on a single UBN. Rapidly-converging learning algorithms exist for both types of neurons. Such features of MVNs and UBNs may be used to solve different kinds of problems. One of the most successful applications of MVNs and UBNs is their use as basic neurons in cellular neural networks (CNNs) to solve image processing and image analysis problems

Research paper thumbnail of Method for impulsive noise detection and its applications to the improvement of impulsive noise-filtering algorithms

A new approach to impulsive noise filtering is considered in the paper. It is known that the medi... more A new approach to impulsive noise filtering is considered in the paper. It is known that the median filter is a sliding window filter, with a window N X N. As it is known, the impulsive noise is a 'big' and unusual jump of brightness. So if the central pixel in the window is noisy, its value belongs to one of the ends of the variation representation of the local histogram. We analyze, where the value of central pixel of the window is positioned in the variation series. If it is positioned close to the boarders, we can assume that it is an impulsive corruption and it must be filtered. This kind of analysis could be used for the improvement of many filters: median, rank-order, cellular neural, etc. So, implementing such kind of preliminary noise detection, we achieve the good results. Filters became gentler and less destructive for the image, but steel very effective.

Research paper thumbnail of New nonlinear combined spatial-frequency domain filtering for noise reduction and image enhancement

A new approach to nonlinear filtering is considered in the paper. The key point of this approach ... more A new approach to nonlinear filtering is considered in the paper. The key point of this approach is a combination of spatial and frequency domain filtering. The following filtering technique is proposed for noise reduction. On the first stage a noisy image has to be processed using some powerful nonlinear spatial-domain filter. Since the image will be smoothed after this operation, then its spectra has to be corrected. Taking into account that a major part of a noise is concentrated in the spectra amplitude, also as image smoothing involves a significant spectra amplitude distortion, a method for its correction is proposed. The same technique is also used for solving of the frequency correction (extraction of image details) problem.

Research paper thumbnail of Neural network based on multi-valued neurons: Application in image recognition, type of blur and blur parameters identification

Some important ideas of image recognition using neural network based on multi-valued neurons are ... more Some important ideas of image recognition using neural network based on multi-valued neurons are being developed in this paper. We are going to discuss the recognition of color images, distortion (blur) types, distortion parameters and recognition of images with distorted training set.

Research paper thumbnail of Application of the neural networks based on multi-valued neurons to classification of the images of gene expression patterns

Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and hig... more Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partial-defined multiple-valued function on the single MVN. The MVN-based neural networks are applied to temporal classification of images of gene expression patterns, obtained by confocal scanning microscopy. The classification results confirmed the efficiency of this method for image recognition.

Research paper thumbnail of Blurred image restoration using the type of blur and blur parameters identification on the neural network

ABSTRACT As a rule, blur is a form of bandwidth reduction of an ideal image owing to the imperfec... more ABSTRACT As a rule, blur is a form of bandwidth reduction of an ideal image owing to the imperfect image formation process. It can be caused by relative motion between the camera and the original scene, or by an optical system that is out of focus. Today there are different techniques available for solving of the restoration problem including Fourier domain techniques, regularization methods, recursive and iterative filters to name a few. But without knowing at least approximate parameters of the blur, these filters show poor results.

Research paper thumbnail of Image recognition on the neural network based on multi-valued neurons

Abstract Multi-valued neurons are the neural processing elements with complex-valued weights, hug... more Abstract Multi-valued neurons are the neural processing elements with complex-valued weights, huge functionality, quickly converged learning algorithms. Such features of the multi-valued neurons may be used for solution of the different kinds of problems. A neural network with multi-valued neurons for image recognition is considered in the paper. Such a network with original architecture analyzes the phases of the Fourier spectral coefficients corresponding to the low frequencies.

Research paper thumbnail of Image processing using cellular neural networks based on multi-valued and universal binary neurons

Multi-valued and universal binary neurons (MVN and UBN) are the neural processing elements with t... more Multi-valued and universal binary neurons (MVN and UBN) are the neural processing elements with the complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partially defined multiple-valued function on the single MVN. An arbitrary mapping described by partially defined or fully defined Boolean function, which can be non-threshold, may be implemented on the single UBN. The quickly converging learning algorithms exist for both types of neurons.

Research paper thumbnail of Effective detection and elimination of impulsive noise with a minimal image smoothing

Abstract Impulsive noise filtering is an important problem of image processing. The problem of no... more Abstract Impulsive noise filtering is an important problem of image processing. The problem of noise elimination is closely connected with the problem of maximal preservation of image edges. The requirement of maximal preservation of edges is especially important for images corrupted by impulsive noise with a low corruption rate. To avoid smoothing of the image during filtering, all noisy pixels must be detected. Then only these detected pixels must be corrected. We present in this paper two solutions to the edge preservation problem.

Research paper thumbnail of Digital restoration of watermark images

Abstract Can traditional methods of image restoration be applied for restoration of watermark ima... more Abstract Can traditional methods of image restoration be applied for restoration of watermark images? This paper deals with beta-radiographic hardcopies of watermark images taken from the old books and documents. The fast Fourier transform techniques used for restoration of watermark images. Software tools were implemented in the frame of an integrated system for digital processing, identification of watermark images and database management.

Research paper thumbnail of New applications of the nonlinear cellular neural filters in image processing

abstract Nonlinear cellular neural filters (NCNF) were introduced recently. They are based on the... more abstract Nonlinear cellular neural filters (NCNF) were introduced recently. They are based on the complex non-linearity of multi-valued and universal binary neurons. NCNF include multi-valued filters and cellular neural Boolean filters. Applications of the NCNF to noise reduction, extraction of image details and precise edge detection have been considered recently. This paper develops the previous ideas and presents the new results.

Research paper thumbnail of Type of blur and blur parameters identification using neural network and its application to image restoration

The original solution of the blur and blur parameters identification problem is presented in this... more The original solution of the blur and blur parameters identification problem is presented in this paper. A neural network based on multi-valued neurons is used for the blur and blur parameters identification. It is shown that using simple single-layered neural network it is possible to identify the type of the distorting operator. Four types of blur are considered: defocus, rectangular, motion and Gaussian ones. The parameters of the corresponding operator are identified using a similar neural network.

Research paper thumbnail of A feedforward neural network based on multi-valued neurons

A feedforward neural network based on multi-valued neurons is considered in the paper. It is show... more A feedforward neural network based on multi-valued neurons is considered in the paper. It is shown that using a traditional feedforward architecture and a high functionality multi-valued neuron, it is possible to obtain a new powerful neural network. Its learning does not require a derivative of the activation function and its functionality is higher than the functionality of traditional feedforward networks containing the same number of layers and neurons.

Research paper thumbnail of Neural network based on multi-valued neurons and its application to image recognition and blur recognition

ABSTRACT Some important ideas of image recognition using neural network based on multi-valued neu... more ABSTRACT Some important ideas of image recognition using neural network based on multi-valued neurons are being developed in this paper. We are going to discuss the recognition of color images, which is reduced to recognition of gray-scale images. An approach, which has been developed, is illustrated by simulation results. Recognition of distortion (blur) types, distortion parameters and recognition of images with distorted training set using the same neural network is also considered.

Research paper thumbnail of UNIVERSITY OF DORTMUND

Abstract A multi-layered neural network based on multi-valued neurons is considered in the paper.... more Abstract A multi-layered neural network based on multi-valued neurons is considered in the paper. It is shown that using a traditional architecture of multi-layered feedforward neural network (MLF) and the high functionality of the multi-valued neuron, it is possible to obtain a new powerful neural network. Its training does not require a derivative of the activation function and its functionality is higher than the functionality of MLF containing the same number of layers and neurons.

Research paper thumbnail of Solving the parity n problem and other nonlinearly separable problems using a single universal binary neuron

Summary. A universal binary neuron (UBN) operates with the complex-valued weights and the complex... more Summary. A universal binary neuron (UBN) operates with the complex-valued weights and the complex-valued activation function, which is the function of the argument of the weighted sum. This makes possible the implementation of the nonlinearly separable (nonthreshold) Boolean functions on the single neuron. Hence the functionality of the UBN is incompatibly higher than the functionality of the traditional perceptron, because this neuron can implement the nonthreshold Boolean functions.

Research paper thumbnail of Frequency domain medianlike filter for periodic and quasi-periodic noise removal

ABSTRACT Removal of periodic and quasi-periodic patterns from photographs is an important problem... more ABSTRACT Removal of periodic and quasi-periodic patterns from photographs is an important problem. There are a lot of sources of this periodic noise, eg the resolution of the scanner used to scan the image affects the high frequency noise pattern in the acquired image and can produce moiré patterns. It is also characteristic of gray scale images obtained from single-chip video cameras. Usually periodic and quasi-periodic noise results peaks in image spectrum amplitude.

Research paper thumbnail of Cellular neural networks and computational intelligence in medical image processing

The principal constituents of computational intelligence are fuzzy logic, neural networks and evo... more The principal constituents of computational intelligence are fuzzy logic, neural networks and evolutionary algorithms, with emphasis in their mutual enhancement.

Research paper thumbnail of Multi-Valued Neuron with a Periodic Activation Function

In this Chapter, we consider MVN with a periodic activation function. As we have already seen, MV... more In this Chapter, we consider MVN with a periodic activation function. As we have already seen, MVN's functionality is higher than the one of, for example, sigmoidal neurons. In this Chapter, we will consider how a single MVN may learn nonlinearly separable input/output mappings in that initial n-dimensional space where they are defined. In Section 5.1, we consider a universal binary neuron (UBN), which in fact is the discrete MVN with a periodic activation function for k= 2.

Research paper thumbnail of The genetic code as a function of multiple-valued logic over the field of complex numbers and its learning using multilayer neural network based on multi-valued neurons

Abstract. It is shown in this paper that a model of multiplevalued logic over the field of comple... more Abstract. It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid code from proteins (each of 20 amino acids is coded by the triplet of four nucleic acids).

Research paper thumbnail of Image processing using cellular neural networks based on multi-valued and universal binary neurons

Multi-valued neurons (MVNs) and universal binary neurons (UBNs) are neural processing elements wi... more Multi-valued neurons (MVNs) and universal binary neurons (UBNs) are neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by a partially-defined multiple-valued function on a single MVN, and an arbitrary mapping described by a partially-defined or fully-defined Boolean function (which does not have to be a threshold function) on a single UBN. Rapidly-converging learning algorithms exist for both types of neurons. Such features of MVNs and UBNs may be used to solve different kinds of problems. One of the most successful applications of MVNs and UBNs is their use as basic neurons in cellular neural networks (CNNs) to solve image processing and image analysis problems

Research paper thumbnail of Method for impulsive noise detection and its applications to the improvement of impulsive noise-filtering algorithms

A new approach to impulsive noise filtering is considered in the paper. It is known that the medi... more A new approach to impulsive noise filtering is considered in the paper. It is known that the median filter is a sliding window filter, with a window N X N. As it is known, the impulsive noise is a 'big' and unusual jump of brightness. So if the central pixel in the window is noisy, its value belongs to one of the ends of the variation representation of the local histogram. We analyze, where the value of central pixel of the window is positioned in the variation series. If it is positioned close to the boarders, we can assume that it is an impulsive corruption and it must be filtered. This kind of analysis could be used for the improvement of many filters: median, rank-order, cellular neural, etc. So, implementing such kind of preliminary noise detection, we achieve the good results. Filters became gentler and less destructive for the image, but steel very effective.

Research paper thumbnail of New nonlinear combined spatial-frequency domain filtering for noise reduction and image enhancement

A new approach to nonlinear filtering is considered in the paper. The key point of this approach ... more A new approach to nonlinear filtering is considered in the paper. The key point of this approach is a combination of spatial and frequency domain filtering. The following filtering technique is proposed for noise reduction. On the first stage a noisy image has to be processed using some powerful nonlinear spatial-domain filter. Since the image will be smoothed after this operation, then its spectra has to be corrected. Taking into account that a major part of a noise is concentrated in the spectra amplitude, also as image smoothing involves a significant spectra amplitude distortion, a method for its correction is proposed. The same technique is also used for solving of the frequency correction (extraction of image details) problem.

Research paper thumbnail of Neural network based on multi-valued neurons: Application in image recognition, type of blur and blur parameters identification

Some important ideas of image recognition using neural network based on multi-valued neurons are ... more Some important ideas of image recognition using neural network based on multi-valued neurons are being developed in this paper. We are going to discuss the recognition of color images, distortion (blur) types, distortion parameters and recognition of images with distorted training set.

Research paper thumbnail of Application of the neural networks based on multi-valued neurons to classification of the images of gene expression patterns

Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and hig... more Multi-valued neurons (MVN) are the neural processing elements with complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partial-defined multiple-valued function on the single MVN. The MVN-based neural networks are applied to temporal classification of images of gene expression patterns, obtained by confocal scanning microscopy. The classification results confirmed the efficiency of this method for image recognition.

Research paper thumbnail of Blurred image restoration using the type of blur and blur parameters identification on the neural network

ABSTRACT As a rule, blur is a form of bandwidth reduction of an ideal image owing to the imperfec... more ABSTRACT As a rule, blur is a form of bandwidth reduction of an ideal image owing to the imperfect image formation process. It can be caused by relative motion between the camera and the original scene, or by an optical system that is out of focus. Today there are different techniques available for solving of the restoration problem including Fourier domain techniques, regularization methods, recursive and iterative filters to name a few. But without knowing at least approximate parameters of the blur, these filters show poor results.

Research paper thumbnail of Image recognition on the neural network based on multi-valued neurons

Abstract Multi-valued neurons are the neural processing elements with complex-valued weights, hug... more Abstract Multi-valued neurons are the neural processing elements with complex-valued weights, huge functionality, quickly converged learning algorithms. Such features of the multi-valued neurons may be used for solution of the different kinds of problems. A neural network with multi-valued neurons for image recognition is considered in the paper. Such a network with original architecture analyzes the phases of the Fourier spectral coefficients corresponding to the low frequencies.

Research paper thumbnail of Image processing using cellular neural networks based on multi-valued and universal binary neurons

Multi-valued and universal binary neurons (MVN and UBN) are the neural processing elements with t... more Multi-valued and universal binary neurons (MVN and UBN) are the neural processing elements with the complex-valued weights and high functionality. It is possible to implement an arbitrary mapping described by partially defined multiple-valued function on the single MVN. An arbitrary mapping described by partially defined or fully defined Boolean function, which can be non-threshold, may be implemented on the single UBN. The quickly converging learning algorithms exist for both types of neurons.

Research paper thumbnail of Effective detection and elimination of impulsive noise with a minimal image smoothing

Abstract Impulsive noise filtering is an important problem of image processing. The problem of no... more Abstract Impulsive noise filtering is an important problem of image processing. The problem of noise elimination is closely connected with the problem of maximal preservation of image edges. The requirement of maximal preservation of edges is especially important for images corrupted by impulsive noise with a low corruption rate. To avoid smoothing of the image during filtering, all noisy pixels must be detected. Then only these detected pixels must be corrected. We present in this paper two solutions to the edge preservation problem.

Research paper thumbnail of Digital restoration of watermark images

Abstract Can traditional methods of image restoration be applied for restoration of watermark ima... more Abstract Can traditional methods of image restoration be applied for restoration of watermark images? This paper deals with beta-radiographic hardcopies of watermark images taken from the old books and documents. The fast Fourier transform techniques used for restoration of watermark images. Software tools were implemented in the frame of an integrated system for digital processing, identification of watermark images and database management.

Research paper thumbnail of New applications of the nonlinear cellular neural filters in image processing

abstract Nonlinear cellular neural filters (NCNF) were introduced recently. They are based on the... more abstract Nonlinear cellular neural filters (NCNF) were introduced recently. They are based on the complex non-linearity of multi-valued and universal binary neurons. NCNF include multi-valued filters and cellular neural Boolean filters. Applications of the NCNF to noise reduction, extraction of image details and precise edge detection have been considered recently. This paper develops the previous ideas and presents the new results.

Research paper thumbnail of Type of blur and blur parameters identification using neural network and its application to image restoration

The original solution of the blur and blur parameters identification problem is presented in this... more The original solution of the blur and blur parameters identification problem is presented in this paper. A neural network based on multi-valued neurons is used for the blur and blur parameters identification. It is shown that using simple single-layered neural network it is possible to identify the type of the distorting operator. Four types of blur are considered: defocus, rectangular, motion and Gaussian ones. The parameters of the corresponding operator are identified using a similar neural network.

Research paper thumbnail of A feedforward neural network based on multi-valued neurons

A feedforward neural network based on multi-valued neurons is considered in the paper. It is show... more A feedforward neural network based on multi-valued neurons is considered in the paper. It is shown that using a traditional feedforward architecture and a high functionality multi-valued neuron, it is possible to obtain a new powerful neural network. Its learning does not require a derivative of the activation function and its functionality is higher than the functionality of traditional feedforward networks containing the same number of layers and neurons.

Research paper thumbnail of Neural network based on multi-valued neurons and its application to image recognition and blur recognition

ABSTRACT Some important ideas of image recognition using neural network based on multi-valued neu... more ABSTRACT Some important ideas of image recognition using neural network based on multi-valued neurons are being developed in this paper. We are going to discuss the recognition of color images, which is reduced to recognition of gray-scale images. An approach, which has been developed, is illustrated by simulation results. Recognition of distortion (blur) types, distortion parameters and recognition of images with distorted training set using the same neural network is also considered.

Research paper thumbnail of UNIVERSITY OF DORTMUND

Abstract A multi-layered neural network based on multi-valued neurons is considered in the paper.... more Abstract A multi-layered neural network based on multi-valued neurons is considered in the paper. It is shown that using a traditional architecture of multi-layered feedforward neural network (MLF) and the high functionality of the multi-valued neuron, it is possible to obtain a new powerful neural network. Its training does not require a derivative of the activation function and its functionality is higher than the functionality of MLF containing the same number of layers and neurons.

Research paper thumbnail of Solving the parity n problem and other nonlinearly separable problems using a single universal binary neuron

Summary. A universal binary neuron (UBN) operates with the complex-valued weights and the complex... more Summary. A universal binary neuron (UBN) operates with the complex-valued weights and the complex-valued activation function, which is the function of the argument of the weighted sum. This makes possible the implementation of the nonlinearly separable (nonthreshold) Boolean functions on the single neuron. Hence the functionality of the UBN is incompatibly higher than the functionality of the traditional perceptron, because this neuron can implement the nonthreshold Boolean functions.

Research paper thumbnail of Frequency domain medianlike filter for periodic and quasi-periodic noise removal

ABSTRACT Removal of periodic and quasi-periodic patterns from photographs is an important problem... more ABSTRACT Removal of periodic and quasi-periodic patterns from photographs is an important problem. There are a lot of sources of this periodic noise, eg the resolution of the scanner used to scan the image affects the high frequency noise pattern in the acquired image and can produce moiré patterns. It is also characteristic of gray scale images obtained from single-chip video cameras. Usually periodic and quasi-periodic noise results peaks in image spectrum amplitude.

Research paper thumbnail of Cellular neural networks and computational intelligence in medical image processing

The principal constituents of computational intelligence are fuzzy logic, neural networks and evo... more The principal constituents of computational intelligence are fuzzy logic, neural networks and evolutionary algorithms, with emphasis in their mutual enhancement.

Research paper thumbnail of Multi-Valued Neuron with a Periodic Activation Function

In this Chapter, we consider MVN with a periodic activation function. As we have already seen, MV... more In this Chapter, we consider MVN with a periodic activation function. As we have already seen, MVN's functionality is higher than the one of, for example, sigmoidal neurons. In this Chapter, we will consider how a single MVN may learn nonlinearly separable input/output mappings in that initial n-dimensional space where they are defined. In Section 5.1, we consider a universal binary neuron (UBN), which in fact is the discrete MVN with a periodic activation function for k= 2.

Research paper thumbnail of The genetic code as a function of multiple-valued logic over the field of complex numbers and its learning using multilayer neural network based on multi-valued neurons

Abstract. It is shown in this paper that a model of multiplevalued logic over the field of comple... more Abstract. It is shown in this paper that a model of multiplevalued logic over the field of complex numbers is the most appropriate for the representation of the genetic code as a multiple-valued function. The genetic code is considered as a partially defined multiple-valued function of three variables. The genetic code is the four-letter nucleic acid code, and it is translated into a 20-letter amino acid code from proteins (each of 20 amino acids is coded by the triplet of four nucleic acids).