Boundary Value Problems in Physics and Engineering By Frank Chorlton. Pp. 250. (Van Nostrand: London, July 1969.) 70s

Boundary value problems

1. Introduction.- 1 Fundamentals of the Theory of Digital Signal Processing.- 2. Elements of Signal Theory.- 2.1 Signals as Mathematical Functions.- 2.2 Signal Space.- 2.3 The Most Common Systems of Basis Functions.- 2.3.1 Impulse Basis Functions.- 2.3.2 Harmonic Functions.- 2.3.3 Walsh Functions.- 2.3.4 Haar Functions.- 2.3.5 Sampling Functions.- 2.4 Continuous Representations of Signals.- 2.5 Description of Signal Transformations.- 2.5.1 Linear Transformations.- 2.5.2 Nonlinear Element-by-Element Transforms.- 2.6 Representation of Linear Transformations with Respect to Discrete Bases.- 2.6.1 Representation Using Vector Responses.- 2.6.2 Matrix Representations.- 2.6.3 Representation of Operators by Means of Their Eigenfunctions and Eigenvalues.- 2.7 Representing Operator with Respect to Continuous Bases.- 2.7.1 Operator Kernel.- 2.7.2 Description in Terms of Impulse Responses.- 2.7.3 Description Using Frequency Transfer Functions.- 2.7.4 Description with Input and Output Signals Referred to Different Bases.- 2.7.5 Description Using Eigenfunctions.- 2.8 Examples of Linear Operators.- 2.8.1 Shift-Invariant Filters.- 2.8.2 The Identity Operator.- 2.8.3 Shi ft Operator.- 2.8.4 Sampling Oparator.- 2.8.5 Gating Operator (Multiplier).- 3. Discretization and Quantization of Signals.- 3.1 Generalized Quantization.- 3.2 Concepts of Discretization and Element-by-Element Quantization.- 3.2.1 Discretization.- 3.2.2 Element-by-Element Quantization.- 3.3 The Sampling Theorem.- 3.4 Sampling Theory for Two-Dimensional Signals.- 3.5 Errors of Discretization and Restoration of Signals in Sampling Theory.- 3.6 Other Approaches to Discretization.- 3.7 Optimal Discrete Representation and Dimensionality of Signals.- 3.8 Element-by-Element Quantization.- 3.9 Examples of Optimum Quantization.- 3.9.1 Example: The Threshold Metric.- 3.9.2 Example: Power Criteria for the Absolute Value of the Quantization Error.- 3.9.3 Example: Power Criteria for the Relative Quantization Error.- 3.10 Quantization in the Presence of Noise. Quantization and Representation of Numbers in Digital Processors.- 3.11 Review of Picture-Coding Methods.- 4. Discrete Representations of Linear Transforms.- 4.1 Problem Formulation and General Approach.- 4.2 Discrete Representation of Shift-Invariant Filters for Band-Limited Signals.- 4.3 Digital Filters.- 4.4 Transfer Functions and Impulse Responses of Digital Filters.- 4.5 Boundary Effects in Digital Filtering.- 4.6 The Discrete Fourier Transform (DFT).- 4.7 Shifted, Odd and Even DFTs.- 4.8 Using Discrete Fourier Transforms.- 4.8.1 Calculating Convolutions.- 4.8.2 Signal Interpolation.- 4.9 Walsh and Similar Transforms.- 4.10 The Haar Tansform. Addition Elements of Matrix Calculus.- 4.11 Other Orthogonal Tansforms. General Representations. Review of Applications.- 5. Linear Transform Algorithms.- 5.1 Fast Algorithms of Discrete Orthogonal Transforms.- 5.2 Fast Haar Transform (FHT) Algorithms.- 5.3 Fast Walsh Transform (FWT) Algorithms.- 5.4 Fast Discrete Fourier Transform (FFT) Algorithms.- 5.5 Review of Other Fast Algorithms. Features of Two-Dimensional Transforms.- 5.5.1 Truncated FFT and FWT Algorithms.- 5.5.2 Transition Matrices Between Various Transforms.- 5.5.3 Calculation of Two-Dimensional Transforms.- 5.6 Combined DFT Algorithms.- 5.6.1 Combined DFT Algorithms of Real Sequences.- 5.6.2 Combined SDFT (1/2, 0) Algorithms of Even and Real Even Sequences.- 5.7 Recursive DFT Algorithms.- 5.8 Fast Algorithms for Calculating the DFT and Signal Convolution with Decreased Multiplication.- 6. Digital Statistical Methods.- 6.1 Principles of the Statistical Description of Pictures.- 6.2 Measuring the Grey-Level Distribution.- 6.2.1 Step Smoothing.- 6.2.2 Smoothing by Sliding Summation.- 6.2.3 Smoothing with Orthogonal Transforms.- 6.3 The Estimation of Correlation Functions and Spectra.- 6.3.1 Averaging Local Spectra.- 6.3.2 Masking (Windowing) the Process by Smooth Functions.- 6.3.3 Direct Smoothing of Spectra.- 6.4 Generating Pseudorandom Numbers.- 6.5 Measuring Picture Noise.- 6.5.1 The Prediction Method.- 6.5.2 The Voting Method.- 6.5.3 Measuring the Variance and the Auto-Correlation Function of Additive Wideband Noise.- 6.5.4 Evaluation of the Intensity and Frequency of the Harmonic Components of Periodic Interference and Other Types of Interference with Narrow Spectra.- 6.5.5 Evaluation of the Parameters of Pulse Noise, Quantization Noise and Strip-Like Noise.- 2 Picture Processing.- 7. Correcting Imaging Systems.- 7.1 Problem Formulation.- 7.2 Suppression of Additive Noise by Linear Filtering.- 7.3 Filtering of Pulse Interference.- 7.4 Correction of Linear Distortion.- 7.5 Correction of Amplitude Characteristics.- 8. Picture Enhancement and Preparation.- 8.1 Preparation Problems and Visual Analysis of Pictures.- 8.1.1 Feature Processing.- 8.1.2 Geometric Transformations.- 8.2 Adaptive Quantization of Modes.- 8.3 Preparation by Nonlinear Transformation of the Video Signal Scale.- 8.4 Linear Preparation Methods.- 8.5 Methods of Constructing Graphical Representation: Computer Graphics.- 8.6 Geometric Picture Transformation.- 8.6.1 Bilinear Interpolation.- 8.6.2 Interpolation Using DFT and SDFT.- 9. Measuring the Coordinates of Objects in Pictures.- 9.1 Problem Formulation.- 9.2 Localizing a Precisely Known Object in a Spatially Homogeneous Picture.- 9.3 Uncertainty in the Object and Picture Inhomogeneity. Localization in "Blurred" Pictures.- 9.3.1 "Exhaustive" Estimator.- 9.3.2 Estimator Seeking an Averaged Object.- 9.3.3 Adjustable Estimator with Fragment-by Fraament Optimal Fi1tering.- 9.3.4 Non-Adjustable Estimator.- 9.3.5 Localization in Blurred and Noisy Pictures.- 9.4 Optimal Localization and Picture Contours. Choice of Reference Objects.- 9.5 Algorithm for the Automatic Detection and Extraction of Bench-Marks in Aerial and Space Photographs.- 10-Conclusion.- References.

Digital picture processing : an introduction

Image denoising review: From classical to state-of-the-art approaches

HighlightsFlexible, scalable traffic lights dynamic control system for isolated intersections.Multiple parallel fuzzy controllers dynamically manage both the phase and green time.Outperforms other works in terms of vehicle waiting time and balancing between phases.Very effective under heavy traffic and when phases have unbalanced arrival rates.Lightweight effective implementable on COTS devices: broad practical impact expected. This paper proposes a novel approach to dynamically manage the traffic lights cycles and phases in an isolated intersection. The target of the work is a system that, comparing with previous solutions, offers improved performance, is flexible and can be implemented on off-the-shelf components. The challenge here is to find an effective design that achieves the target while avoiding complex and computationally expensive solutions, which would not be appropriate for the problem at hand and would impair the practical applicability of the approach in real scenarios. The proposed solution is a traffic lights dynamic control system that combines an IEEE 802.15.4 Wireless Sensor Network (WSN) for real-time traffic monitoring with multiple fuzzy logic controllers, one for each phase, that work in parallel. Each fuzzy controller addresses vehicles turning movements and dynamically manages both the phase and the green time of traffic lights. The proposed system combines the advantages of the WSN, such as easy deployment and maintenance, flexibility, low cost, noninvasiveness, and scalability, with the benefits of using four parallel fuzzy controllers, i.e., better performance, fault-tolerance, and support for phase-specific management. Simulation results show that the proposed system outperforms other solutions in the literature, significantly reducing the vehicles waiting times. A proof-of-concept implementation on an off-the-shelf device proves that the proposed controller does not require powerful hardware and can be easily implemented on a low-cost device, thus paving the way for extensive usage in practice.

http://lobello.dieei.unict.it/public_files/publications/1-s2.0-S0957417415001104-main.pdf

A novel approach for dynamic traffic lights management based on Wireless Sensor Networks and multiple fuzzy logic controllers

Parameter identification of PEMFC model based on hybrid adaptive differential evolution algorithm

This paper proposes a multi-agent type-2 fuzzy logic control (FLC) method optimized by differential evolution (DE) for multi-intersection traffic signal control. Type-2 fuzzy sets can deal with models' uncertainties efficiently because of its three-dimensional membership functions, but selecting suitable parameters of membership functions and rule base is not easy. DE is adopted to decide the parameters in the type-2 fuzzy system, as it is easy to understand, simple to implement and possesses low space complexity. In order to avoid the computational complexity, the expert rule base and the parameters of membership functions (MF) are optimized by turns. An eleven-intersection traffic network is studied in which each intersection is governed by the proposed controller. A secondary layer controller is set in every intersection to select the proper phase sequence. Furthermore, the communication among the adjacent intersections is implemented using multi-agent system. Simulation experiments are designed to compare communicative type-2 FLC optimized by DE with type-1 FLC, fixed-time signal control, etc. Experimental results indicate that our proposed method can enhance the vehicular throughput rate and reduce delay, queue length and parking rate efficiently.

Type-2 fuzzy multi-intersection traffic signal control with differential evolution optimization

Singular value decomposition and local near neighbors for face recognition under varying illumination

The non-local means (NLM) provides a useful tool for image denoising and many variations of the NLM method have been proposed. However, few works have tried to tackle the task of adaptively choosing the patch size according to region characteristics. Presented is a region-based NLM method for noise removal. The proposed method first analyses and classifies the image into several region types. According to the region type, a local window is adaptively adjusted to match the local property of a region. Experimental results show the effectiveness of the proposed method and demonstrate its superiority to the state-of-the-art methods.

Region-based non-local means algorithm for noise removal

Driven by the spectacular success of deep learning, several advanced models based on neural networks have recently been proposed for single-image super-resolution, incrementally revealing their superiority over their alternatives. In this paper, we pursue this latest line of research and present an improved network structure by taking advantage of the proposed component learning. The core idea and difference of this learning strategy are to use the residual extracted from the input to predict its counterpart in the corresponding output. To this end, a global decomposition procedure is designed on the basis of convolutional sparse coding and performed on the input for extracting the low-resolution (LR) residual component from it. Owing to the properties of this decomposition, the represented residual component still stays in the LR space so that the subsequent part is capable of operating it economically in terms of computational complexity. Thorough experimental results demonstrate the merit and effectiveness of the proposed component learning strategy, and our trained model outperforms many state-of-the-art methods in terms of both speed and reconstruction quality.

Fast Single-Image Super-Resolution via Deep Network With Component Learning

In this paper, we propose a novel superresolution (SR) reconstruction algorithm to handle license plate texts in real traffic videos. To make license plate numbers more legible, a generalized discontinuity-adaptive Markov random field (DAMRF) model is proposed based on the recently reported bilateral filtering, which not only preserves edges but is robust to noise as well. Moreover, instead of looking for a fixed value for the regularization parameter, a method for automatically estimating it is applied to the proposed model based on the input images. Information needed to determine the regularization parameter is updated at each iteration step, which is based on the available reconstructed image. Finally, we use the graduated nonconvexity optimization procedure to minimize the cost function. Results on synthetic and real traffic sequences are presented, which show the effectiveness of the proposed method and demonstrate its superiority to the conventional DAMRF SR method.

Weili Zeng

Papers

Type-2 fuzzy multi-intersection traffic signal control with differential evolution optimization

Singular value decomposition and local near neighbors for face recognition under varying illumination

Region-based non-local means algorithm for noise removal

Fast Single-Image Super-Resolution via Deep Network With Component Learning

A Generalized DAMRF Image Modeling for Superresolution of License Plates