Two-dimensional Signal Processing Research Articles

Bidimensional uncertainty product associated with two specific Gyrator domains

The uncertainty principle for a two-dimensional signal, giving us a lower bound for the product of the spreads (uncertainty product) of the signal representations in two specific Gyrator domains (GDs), is developed and presented. The GDs are defined by the Gyrator transform (GT), which is a new mathematical tool for analysis and processing of two-dimensional signals belonging to the linear canonical transforms. The obtained lower bound for the uncertainty principle depends on the two rotation angles that define the two GDs of the two-dimensional signal. The resulting uncertainty principle could be used in image processing and applications based on the GT. Finally, we show that the uncertainty principle for the antisymmetric Fourier transform with a rotation of the coordinates at π/2 is a special case of the bidimensional uncertainty product associated with two specific GDs.

Dispersion-Diversity Multicore Fiber Signal Processing.

Beyond playing a primary role in high-capacity communication networks, multicore optical fibers can bring many advantages to optical and microwave signal processing, as not only space but also chromatic dispersion are introduced as new degrees of freedom. The key lies in developing radically new multicore fibers where the refractive index profile of each individual core is tailored properly to provide parallel dispersion-diversity signal processing with application in a variety of scenarios such as parallel channel equalization, analogue-to-digital conversion, optical computing, pulse generation and shaping, multiparameter fiber sensing, medical imaging, optical coherence tomography, broadband measurement instrumentation, and next-generation fiber-wireless communications. Here, we experimentally prove, for the first time to our knowledge, reconfigurable two-dimensional dispersion-managed signal processing performed by a novel dispersion-diversity heterogeneous multicore fiber. The fiber comprises seven different trench-assisted cores featuring a different refractive index profile in terms of both radial geometry and core dopant concentration. As a representative application case, we demonstrate reconfigurable microwave signal filtering with increased compactness as well as performance flexibility and versatility as compared to previous technologies.

Theoretical foundations of digital vector Fourier analysis of two-dimensional signals padded with zero samples

Introduction: The practice of using Fourier-processing of finite two-dimensional signals (including images), having confirmed its effectiveness, revealed a number of negative effects inherent in it. A well-known method of dealing with negative effects of Fourier-processing is padding signals with zeros. However, the use of this operation leads to the need to provide information control systems with additional memory and perform unproductive calculations. Purpose: To develop new discrete Fourier transforms for efficient and effective processing of two-dimensional signals padded with zero samples. Method: We have proposed a new method for splitting a rectangular discrete Fourier transform matrix into square matrices. The method is based on the application of the modulus comparability relation to order the rows (columns) of the Fourier matrix. Results: New discrete Fourier transforms with variable parameters were developed, being a generalization of the classical discrete Fourier transform. The article investigates the properties of Fourier transform bases with variable parameters. In respect to these transforms, the validity has been proved for the theorems of linearity, shift, correlation and Parseval's equality. In the digital spectral Fourier analysis, the concepts of a parametric shift of a two-dimensional signal, and a parametric periodicity of a two-dimensional signal have been introduced. We have estimated the reduction of the required memory size and the number of calculations when applying the proposed transforms, and compared them with the discrete Fourier transform. Practical relevance: The developed discrete Fourier transforms with variable parameters can significantly reduce the cost of Fourier processing of two-dimensional signals (including images) padded with zeros.

Sliding Space-Frequency Processing of Finite Two-Dimensional Real Discrete Signals Based on the Fourier Transform with Variable Parameters

In the field of Fourier processing of finite signals, three main directions of scientific research have been identified: Fourier processing of one-dimensional finite signals - processing of scalar functions of a scalar argument, Fourier processing of two-dimensional finite signals - processing of scalar functions of a vector argument, multichannel Fourier processing - processing of vector functions of a scalar argument. As part of the creation of a generalized theory of Fourier processing of finite signals, the authors proposed: the theory of spectral analysis of discrete signals at finite intervals in the bases of parametric exponential functions and the theory of two-dimensional digital signal processing in Fourier bases with variable parameters. The developed theories, generalizing the theory of Fourier processing of one-dimensional and two-dimensional signals, are based: on the introduction of new concepts of the shift of finite discrete signals in one-dimensional and two-dimensional cases and the introduction of new basic Fourier processing systems of discrete signals, which have the properties of multiplicativity, functions in the system. The mathematical apparatus of two-dimensional discrete Fourier transform with variable parameters in matrix and algebraic form is considered. A new method for processing finite two-dimensional real discrete signals in the spatial-frequency domain based on the discrete Fourier transform with variable parameters, the method of sliding spatial-frequency processing, has been introduced. An efficient method and algorithm for fast diagonal sliding spatial-frequency processing of finite two-dimensional real discrete signals based on the discrete Fourier transform with variable parameters has been developed. The estimation of the efficiency and effectiveness of the algorithm of the diagonal sliding two-dimensional discrete Fourier transform with variable parameters from the point of view of computational costs is carried out. As a result of experimental studies on model two-dimensional discrete finite signals, the validity, efficiency and reliability of the proposed method of sliding spatial-frequency processing of finite two-dimensional real discrete signals based on the discrete Fourier transform with variable parameters have been proved. A comparison (from the point of view of computational costs) of the developed method of sliding spatial-frequency processing of finite two-dimensional real discrete signals based on the discrete Fourier transform with variable parameters with the standard method of sliding processing of this type of signals is carried out.

ОПТИМИЗАЦИЯ СТРУКТУРЫ МНОГОЧАСТОТНОГО МОДЕМА

The paper considers the solution to the problem of increasing the spectral efficiency of a digital transmission system with multifrequency modulation and optimal finite signals that do not cause intersymbol interference in various channels of a multifrequency modem. Applying the method of multi-frequency data transmission based on two-dimensional signal processing, high-speed data transmission is organized over frequency-limited communication channels based on wired technologies of the xDSL standard. The well-known and new modem, which is superior in efficiency to similar modems, are presented. In this paper, the modernization of a multifrequency modem with optimal finite signals based on quadrature amplitude modulation (QAM) is considered. The peculiarity of this structure is as follows: the use of new, synthesized optimal finite OFS-2 signals with increased noise immunity; in the application of the new structure of the multi-frequency modem MFM3; in the use of a frequency-limited GCS in the UEP DCS at the reception in order to compensate for the amplitude and phase distortions introduced by it. Comparative results of calculations of the spectral-energy efficiency of the considered multi-frequency modulated modem MFM3 with OFS-2 and narrow-band subcarriers are illustrated by the graphs in Fig. and presented in Table . Implementation of the new modem in digital telecommunications systems will significantly increase their spectral efficiency. The proposed approach can be used to organize high-speed data transmission over frequency-limited communication channels based on wired technologies of the xDSL standard. For the first time, an adaptive multi-channel digital transmission system with a new multi-frequency modem and new optimal second-type finite signals with increased spectral and energy efficiency has been developed, taking into account optimal estimates of the parameters of the direct communication channel transmitted via the feedback channel and used both in transmission (in the modulator) and reception (in the demodulator).

Applying Haar Wavelets in Tasks of Digital Processing of Two-Dimensional Signals

In this article, a system application of local basis functions discussed, defined on compact media. formulas for estimating the accuracy of calculating the spectral energy by the method of two-dimensional Haar wavelets and main concepts of Haar fast transformation, spectral energy of Haar coefficients will be discussed in this article. effectiveness will be shown in order to solve problems of sampling of compact signals. Signals cannot only be functions of time, defined at finite intervals, but also functions of arguments of a different physical nature, for example, distances along surfaces.

Classification of power quality disturbances by 2D-Riesz Transform, multi-objective grey wolf optimizer and machine learning methods

In this study, a new method combined with two-dimensional Riesz Transform (RT) in feature extraction stage and Multi-Objective Grey Wolf Optimizer (MOGWO) with k-Nearest Neighbor (KNN) algorithm in the feature selection stage is introduced to classify Power Quality (PQ) disturbances. After determining the most suitable feature group, classification models are created by using machine learning approaches. Although one-dimensional (1D) signal processing methods by nature are used in the classification stage of PQ disturbances, it is observed that studies have developed in the literature including two-dimensional (2D) signal processing. 2D signal processing approach is used because it gives good feature diversity and leads to creation a good model. In this study, firstly PQ disturbances events data is collected synthetically and experimentally. 1D signals are converted to 2D signals to apply 2D-RT. In 2D-RT, it is obtained 12 sub bands matrices to find better features for one 2D matrix. 15 statistical and image-based features are calculated for each band. Totally 180 features are obtained for one sub bands matrix. At this point, with the MOGWO-KNN method, it is aimed to create a simple classification model with high performance by selecting the most suitable features obtained by 2D-RT. The models based on KNN, SVM, MLP and ensemble learner methods are created to investigate if there is a better classification accuracy or not. The simulation study is also done for data consists of noisy (40 dB, 30 dB, 20 dB noise levels) and multiple events. The model can classify 9 types of multiple disturbances in 18 PQ disturbances. At the same time, a robust model that classify even noisy situations is created. It is showed that the proposed PQ disturbances classification method gives high performance compared to the methods in the literature for both simulations and real data.

Image enhancement in a miniature self-imaging degenerate optical cavity

Image-amplifying optical cavities offer an intriguing platform for nonlinear optical processing of two-dimensional signals, with potential applications in optical information processing and optically implemented artificial neural networks. Here, we analyze the performance of a self-imaging degenerate cavity via numerical simulations and show the existence of a cavity size-dependent minimum spread in the transverse mode resonances. This non-degeneracy, in turn, leads to an inherent trade-off between the amplification and the fidelity of the intracavity image as the cavity finesse changes. Our results point to a promising path to nonlinear image processing in a low-power, small-form-factor optical cavity.

Based on Compressed Sensing of Orthogonal Matching Pursuit Algorithm Image Recovery

Compressive sensing theory mainly includes the sparsely of signal processing, the structure of the measurement matrix and reconstruction algorithm. Reconstruction algorithm is the core content of CS theory, that is, through the low dimensional sparse signal recovers the original signal accurately. This thesis based on the theory of CS to study further on seismic data reconstruction algorithm. We select orthogonal matching pursuit algorithm as a base reconstruction algorithm. Then do the specific research for the implementation principle, the structure of the algorithm of AOMP and make the signal simulation at the same time. In view of the OMP algorithm reconstruction speed is slow and the problems need to be a given number of iterations, which developed an improved scheme. We combine the optimized OMP algorithm of constraint the optimal matching of item selection strategy, the backwards gradient projection ideas of adaptive variance step gradient projection method and the original algorithm to improve it. Simulation experiments show that improved OMP algorithm is superior to traditional OMP algorithm of improvement in the reconstruction time and effect under the same condition. This paper introduces CS and most mature compressive sensing algorithm at present orthogonal matching pursuit algorithm. Through the program design realize basic orthogonal matching pursuit algorithms, and design realize basic orthogonal matching pursuit algorithm of one-dimensional, two-dimensional signal processing simulation.

TWO-DIMENSIONAL SIGNAL PROCESSING IN THE DISCRETE FOURIER BASIS

Исследуются проблемы обработки двумерных сигналов в пространственно-частотной области на базе двумерного дискретного преобразования Фурье. Рассмотрено общее определение и математическое описание двумерного дискретного сигнала в пространственной области. Дана алгебраическая форма двумерного дискретного преобразования Фурье, кратко рассмотрены основные свойства двумерного дискретного преобразования Фурье. Проведен (по отечественным и зарубежным информационным источникам) системный анализ дискретных двумерных сигналов (природы их происхождения, источников формирования), а также методов их обработки, основанных на двумерном дискретном преобразовании Фурье. Рассмотрены приложения дискретных двумерных сигналов в различных предметных областях. Рассмотрены достоинства и недостатки цифровых методов дискретной двумерной обработки на основе двумерного дискретного преобразования Фурье. Выдвинута рабочая гипотеза решения проблематики дискретной двумерной обработки сигналов в пространственно-частотной области путем разработки новых двумерных базисных систем, сочетающих преимущества двумерного дискретного базиса Фурье и снижающих (устраняющих) влияние его негативных эффектов. Показано, что двумерный вариант дискретного канонического разложения случайных сигналов, разработанный В. С. Пугачевым, предполагает (по умолчанию) видоизменение стандартной циклической двумерной корреляционной функции исходного сигнала. Предложены пути решения указанной проблемы.

SCATTERING TARGET IDENTIFICATION BASED ON RADIAL BASIS FUNCTION ARTIFICIAL NEURAL NETWORKS IN THE PRESENCE OF NON-STATIONARY NOISE

The paper deals with the radar target discrimination problem performed on complex radar images. The approach based on radial basis function (RBF) artificial neural network (ANN) is proposed for the identification of point scatterers placed within a radar image. The renewed concept of simple adaptive units as the foundation for network assembling allows one to design an ANN-based feature extraction scheme for the two-dimensional signal processing. It was shown that ANN implementing RBF neural processing units could be applied for the identification of radar targets described by the set of separated scatterers, even in cases where the relative distance between the scatterers is comparable to or less than the effective width of each scatterer. The obtained results indicate a high accuracy estimation of separate scatterer centers in the presence of noise which is not limited to the stationary case but supposed to be cyclostationary. It was also shown that the parameters describing the coordinates of scattering centers could be successfully extracted from the trained ANN after about one hundred epochs spent on ANN training process, which is carried out by means of modified gradient descent method. The main result is to demonstrate the possibility of using neural networks to automatically analyze radar images, which is an integral part of a set of tasks that form the target recognition problem. The proposed algorithm implements an approach of identification systems made using a neural network training procedures.

Sliding signal processing in telecommunication networks based on two-dimensional discrete Fourier transform

A method of vertical sliding processing of two-dimensional discrete signals in the spatial frequency domain is proposed — a method of fast vertically sliding two-dimensional discrete Fourier transform. The mathematical representation of the two-dimensional discrete Fourier transform in algebraic and matrix form is considered. An effective method of vertically sliding two-dimensional discrete Fourier transform is proposed. The algorithm developed in the framework of the proposed method allows calculating the coefficients (bins) of this transformation in real time.

Investigation of power quality disturbances by using 2D discrete orthonormal S-transform, machine learning and multi-objective evolutionary algorithms

Abstract The aim of this paper is to investigate the power quality analysis by using 2D discrete orthonormal S-transform, machine learning and multi-objective evolutionary algorithms. The fact that PQ signals are one-dimensional (1D) signals due to their nature leads to the search for feature extraction approaches based on 1D signal processing methods. Due to the electric network is getting more and more complicated day by day, it is necessary to determine effectively the disturbances events. In the proposed method, extraction of a new feature based on two-dimensional (2D) signal processing by 2D Fast Discrete Orthonormal Stockwell Transform (2D-FDOST) method and determination of the most suitable feature group by Non-dominated Sorting Genetic Algorithm II (NSGA-II) method are performed. Eleven different PQ events are synthetically produced based on mathematical modelling. 1D signals are transformed into 2D signals with equal row and column numbers. Statistical and image-based features are created on the amplitude and phase matrices obtained by 2D-FDOST method from 2D signals. The NSGA-II method, which is one of the multi-objective evolutionary optimization methods, is used to convert a large number of feature vectors into a small number of useful feature groups. NSGA-II produces the optimal solution for two different fitness functions that calculate the number of features and classifier performance. By using different machine learning classifiers for selected features, a model classifying PQ disturbances with high performance and robust structure against noisy situations is created.

Missing Surface Estimation Based on Modified Tikhonov Regularization: Application for Destructed Dental Tissue.

Estimation of missing digital information is mostly addressed by one or two-dimensional signal processing methods; however, this problem can emerge in multi-dimensional data including 3D images. Examples of 3D images dealing with missing edge information are often found using dental micro-CT, where the natural contours of dental enamel and dentine are partially dissolved or lost by caries. In this paper, we present a novel sequential approach to estimate the missing surface of an object. First, an initial correct contour is determined interactively or automatically, for the starting slice. This contour information defines the local search area and provides the overall estimation pattern for the edge candidates in the next slice. The search for edge candidates in the next slice is performed in the perpendicular direction to the obtained initial edge in order to find and label the corrupted edge candidates. Subsequently, the location information of both initial and nominated edge candidates are transformed and segregated into two independent signals (X-coordinates and Y-coordinates) and the problem is changed into error concealment. In the next step, the missing samples of these signals are estimated using a modified Tikhonov regularization model with two new terms. One term contributes in the denoising of the corrupted signal by defining an estimation model for a group of mildly destructed samples, and the other term contributes in the estimation of the missing samples with the highest similarity to the samples of the obtained signals from the previous slice. Finally, the reconstructed signals are transformed inversely to edge pixel representation. The estimated edges in each slice are considered as initial edge information for the next slice and this procedure is repeated slice by slice until the entire contour of the destructed surface is estimated. The visual results as well as quantitative results (using both contour-based and area-based metrics) for seven image datasets of tooth samples with considerable destruction of the dentin-enamel junction (DEJ) demonstrates that the proposed method can accurately interpolate the shape and the position of the missing surfaces in computed tomography images in both two and three dimensions (e.g. 14.87 ±3.87 μ m of mean distance (MD) error for the proposed method versus 7.33 ±0.27 μm of MD error between human experts and 1.25 ±~0 % error rate (ER) of the proposed method versus 0.64 ±~0 % of ER between human experts (~1% difference)).

Investigation of the basic Haar wavelet-transformations in the problem of decryption of space images on detection of waste disposal fields

In this paper, we study the use of orthogonal transformations, namely, the basic Haar wavelet transforms, for data processing of the Earth remote sensing. The internal structure of orthogonal Haar transforms is considered. The Haar matrix is divided into blocks of the same type, so that parallelization of the computations is possible. The expediency of replacing the spectral components corresponding to the whole block (or several blocks) of the original matrix with zeros is asserted. Theoretical and experimental studies are carried out to improve the results of image classification (on the example of cluster analysis). The Haar wavelet expansion coefficients are used as indicators when decoding space images for the presence of waste disposal sites. The aim of this paper is to describe the approach, on the basis of which an optimal method is established on a class of vectors with real components, application of two-dimensional discrete Haar wavelet transformations in the problem of recognition of space images for the presence of waste disposal sites. General methodology of research. The paper uses elements of mathematical analysis, wavelet analysis, the theory of discrete orthogonal transformations, and methods for decoding cosmic images. Scientific novelty. Encoding by means of conversion is an indirect method, especially effective in processing of two-dimensional signals, in particular, space images used for remote sensing of the Earth. We propose the approach that takes into account the structure of the wavelet-Haar matrix, while recognizing waste disposal fields by means of space images. The article comprises the result of the experimental application of wavelet-Haar transformations for decoding of space images. We consider this case, both with and without the technique of taking into account the structure of the wavelet-Haar matrices.

Radar-based living object protection for inductive charging of electric vehicles using two-dimensional signal processing

As battery capacities become suitable for the mass market, there is an increasing demand on technologies to charge electric vehicles. Wireless charging is regarded as the most promising technique for automatic and convenient charging. Especially in publicly accessible parking spaces, foreign objects are able to enter the large air gap between the charging coils easily. Since the evoked magnetic field does not meet regulations, wireless charging systems are demanded to take further precautions related to the protection of endangered objects. Thus, additional sensors are required to protect primarily living objects by preventing them from being exposed to the magnetic field. In this paper, we propose a new approach for monitoring the air gap under the vehicle underbody using an automotive radar sensor on the vehicle side. The concept feasibility is evaluated with the help of a prototypical implementation. Further, two-dimensional signal processing techniques are applied to meet the requirements of inductive charging systems. Consequently, this paper provides measurement data for relevant use cases frequently discussed in the community of inductive charging.

A comparative study of two-dimensional multifractal detrended fluctuation analysis and two-dimensional multifractal detrended moving average algorithm to estimate the multifractal spectrum

Multifractal detrended fluctuation analysis (MFDFA) and multifractal detrended moving average (MFDMA) algorithm have been established as two important methods to estimate the multifractal spectrum of the one-dimensional random fractal signal. They have been generalized to deal with two-dimensional and higher-dimensional fractal signals. This paper gives a brief introduction of the two-dimensional multifractal detrended fluctuation analysis (2D-MFDFA) and two-dimensional multifractal detrended moving average (2D-MFDMA) algorithm, and a detailed description of the application of the two-dimensional fractal signal processing by using the two methods. By applying the 2D-MFDFA and 2D-MFDMA to the series generated from the two-dimensional multiplicative cascading process, we systematically do the comparative analysis to get the advantages, disadvantages and the applicabilities of the two algorithms for the first time from six aspects such as the similarities and differences of the algorithm models, the statistical accuracy, the sensitivities of the sample size, the selection of scaling range, the choice of the q-orders and the calculation amount. The results provide a valuable reference on how to choose the algorithm from 2D-MFDFA and 2D-MFDMA, and how to make the schemes of the parameter settings of the two algorithms when dealing with specific signals in practical applications.

Two-dimensional analog signal processing and its implications on circuit theory

The main focus of this paper is on two-dimensional (2-D) analog filtering. The development of the bivariate and bifrequency theory for autonomous dynamic systems and circuits are reviewed. The two-...

Bit error rate performance for head skew angle in shingled magnetic recording using dual reader heads

The two-dimensional magnetic recording (TDMR) exploits two-dimensional signal processing using the neighboring read-back waveforms. We allocate dual readers for the intended tracks and evaluate the effects of head skew angle on the bit error rate performance in partial response class-I maximum likelihood system with a two-dimensional finite impulse response filter using two read-back waveforms under TDMR R/W channel specifications of 4 Tbit/in.2. The results show that the effect of positive skew angle is larger than that of negative skew angle, and the center of skew angle should be shifted to minus direction.

The design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms: a review of the literature

Recently, the design of the two-dimensional digital filter has become a subject of interest in the field of two-dimensional signal processing. The two-dimensional digital filter has been applied in many important areas such as image processing, television systems and seismic signal processing. In digital filter design, there are several indispensable aims such as stability, reduced computational complexity and computational time. Thus, researchers and practitioners have investigated various advanced methods based on metaheuristic optimization algorithms for the design of the two-dimensional digital filter. Metaheuristic optimization algorithms have been applied to solve different complicated problems in various fields and they have also been successfully used in digital filter design. This paper presents a review of the design approaches of two-dimensional digital filters based on metaheuristic optimization algorithms such as the genetic algorithm, differential evolution and particle swarm optimization. By comparing the proposed design approaches based on metaheuristic optimization algorithms, it is observed that the genetic algorithm is the most preferred algorithm and emerging novel algorithms using metaheuristic optimization algorithms have better performance in terms of computational complexity and computational time. It is hoped that this review will be helpful for researchers and practitioners studying the design of two-dimensional digital filters.