各種の性質を改善した直交DTCWTの設計に関する研究

The Dual tree complex wavelet transforms (DTCWTs) have been found to be successful in many applications of signal and image processing. DTCWTs employ two real wavelet transforms, where one wavelet corresponds to the real part of complex wavelet and the other is the imaginary part. Two wavelet bases are required to be a Hilbert transform pair. Thus, DTCWTs are nearly shift invariant and have a good directional selectivity in two or higher dimensions with limited redundancies. In this dissertation, we propose two new classes of DTCWTs with improved properties. In Chapter 2, we review the Fourier transform at first and then introduce the fundamentals of dual tree complex wavelet transform. The wavelet transform has been proved to be a successful tool to express the signal in time and frequency domain simultaneously. To obtain the wavelet coefficients efficiently, the discrete wavelet transform has been introduced since it can be achieved by a tree of two-channel filter banks. Then, we discuss the design conditions of two-channel filter banks, i.e., the perfect reconstruction and orthonormality. Additionally, some properties of scaling and wavelet functions including orthonormality, symmetry and vanishing moments are also given. Moreover, the structure of DTCWT is introduced, where two wavelet bases are required to form a Hilbert transform pair. Thus, the corresponding scaling lowpass filters must satisfy the half-sample delay condition. Finally, the objective measures of quality are given to evaluate the performance of the complex wavelet. In Chapter 3, we propose a new class of DTCWTs with improved analyticity and frequency selectivity by using general IIR filters with numerator and denominator of different degree. In the common-factor technique proposed by Selesnick, the maximally at allpass filter was used to satisfy the halfsample delay condition, resulting in poor analyticity of complex wavelets. Thus, to improve the analyticity of complex wavelets, we present a method for designing allpass filters with the specified degree of flatness and equiripple phase response in the approximation band. Moreover, to improve the frequency selectivity of scaling lowpass filters, we locate the specified number of zeros at z = -1 and minimize the stopband error. The well-known Remez exchange algorithm has been applied to approximate the equiripple response. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem. Furthermore, we investigate the performance on the proposed DTCWTs and dedicate how to choose the approximation band and stopband properly. It is shown that the conventional DTCWTs proposed by Selesnick are only the special cases of DTCWTs proposed in this dissertation. In Chapter 4, we propose another class of almost symmetric DTCWTs with arbitrary center of symmetry. We specify the degree of flatness of group delay, and the number of vanishing moments, then apply the Remez exchange algorithm to minimize the difference between two scaling lowpass filters in the frequency domain, in order to improve the analyticity of complex wavelets. Therefore, the equiripple behaviour of the error function can be obtained through a few iterations. Moreover, two scaling lowpass filters can be obtained simultaneously. As a result, the complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Since the group delay of scaling lowpass filters can be arbitrarily specified, the scaling functions have the arbitrary center of symmetry. Finally, several experiments of signal denoising are carried out to demonstrate the efficiency of the proposed DTCWTs. It is clear that the proposed DTCWTs can achieve better performance on noise reduction.電気通信大学201

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

Design and Analysis of A New Illumination Invariant Human Face Recognition System

In this dissertation we propose the design and analysis of a new illumination invariant face recognition system. We show that the multiscale analysis of facial structure and features of face images leads to superior recognition rates for images under varying illumination. We assume that an image I ( x,y ) is a black box consisting of a combination of illumination and reflectance. A new approximation is proposed to enhance the illumination removal phase. As illumination resides in the low-frequency part of images, a high-performance multiresolution transformation is employed to accurately separate the frequency contents of input images. The procedure is followed by a fine-tuning process. After extracting a mask, feature vector is formed and the principal component analysis (PCA) is used for dimensionality reduction which is then proceeded by the extreme learning machine (ELM) as a classifier. We then analyze the effect of the frequency selectivity of subbands of the transformation on the performance of the proposed face recognition system. In fact, we first propose a method to tune the characteristics of a multiresolution transformation, and then analyze how these specifications may affect the recognition rate. In addition, we show that the proposed face recognition system can be further improved in terms of the computational time and accuracy. The motivation for this progress is related to the fact that although illumination mostly lies in the low-frequency part of images, these low-frequency components may have low- or high-resonance nature. Therefore, for the first time, we introduce the resonance based analysis of face images rather than the traditional frequency domain approaches. We found that energy selectivity of the subbands of the resonance based decomposition can lead to superior results with less computational complexity. The method is free of any prior information about the face shape. It is systematic and can be applied separately on each image. Several experiments are performed employing the well known databases such as the Yale B, Extended-Yale B, CMU-PIE, FERET, AT&T, and LFW. Illustrative examples are given and the results confirm the effectiveness of the method compared to the current results in the literature

A VISION-BASED QUALITY INSPECTION SYSTEM FOR FABRIC DEFECT DETECTION AND CLASSIFICATION

Published ThesisQuality inspection of textile products is an important issue for fabric manufacturers. It is desirable to produce the highest quality goods in the shortest amount of time possible. Fabric faults or defects are responsible for nearly 85% of the defects found by the garment industry. Manufacturers recover only 45 to 65% of their profits from second or off-quality goods. There is a need for reliable automated woven fabric inspection methods in the textile industry. Numerous methods have been proposed for detecting defects in textile. The methods are generally grouped into three main categories according to the techniques they use for texture feature extraction, namely statistical approaches, spectral approaches and model-based approaches. In this thesis, we study one method from each category and propose their combinations in order to get improved fabric defect detection and classification accuracy. The three chosen methods are the grey level co-occurrence matrix (GLCM) from the statistical category, the wavelet transform from the spectral category and the Markov random field (MRF) from the model-based category. We identify the most effective texture features for each of those methods and for different fabric types in order to combine them. Using GLCM, we identify the optimal number of features, the optimal quantisation level of the original image and the optimal intersample distance to use. We identify the optimal GLCM features for different types of fabrics and for three different classifiers. Using the wavelet transform, we compare the defect detection and classification performance of features derived from the undecimated discrete wavelet and those derived from the dual-tree complex wavelet transform. We identify the best features for different types of fabrics. Using the Markov random field, we study the performance for fabric defect detection and classification of features derived from different models of Gaussian Markov random fields of order from 1 through 9. For each fabric type we identify the best model order. Finally, we propose three combination schemes of the best features identified from the three methods and study their fabric detection and classification performance. They lead generally to improved performance as compared to the individual methods, but two of them need further improvement

Uses of Complex Wavelets in Deep Convolutional Neural Networks

Image understanding has long been a goal for computer vision. It has proved to be an exceptionally difficult task due to the large amounts of variability that are inherent to objects in a scene. Recent advances in supervised learning methods, particularly convolutional neural networks (CNNs), have pushed forth the frontier of what we have been able to train computers to do. Despite their successes, the mechanics of how these networks are able to recognize objects are little understood, and the networks themselves are often very difficult and time-consuming to train. It is very important that we improve our current approaches in every way possible. A CNN is built from connecting many learned convolutional layers in series. These convolutional layers are fairly crude in terms of signal processing - they are arbitrary taps of a finite impulse response filter, learned through stochastic gradient descent from random initial conditions. We believe that if we reformulate the problem, we may achieve many insights and benefits in training CNNs. Noting that modern CNNs are mostly viewed from and analyzed in the spatial domain, this thesis aims to view the convolutional layers in the frequency domain (viewing things in the frequency domain has proved useful in the past for denoising, filter design, compression and many other tasks). In particular, we use complex wavelets (rather than the Fourier transform or the discrete wavelet transform) as basis functions to reformulate image understanding with deep networks. In this thesis, we explore the most popular and well-developed form of using complex wavelets in deep learning, the ScatterNet from Stephane Mallat. We explore its current limitations by building a DeScatterNet and found that while it has many nice properties, it may not be sensitive to the most appropriate shapes for understanding natural images. We then develop a locally invariant convolutional layer, a combination of a complex wavelet transform, a modulus operation, and a learned mixing. To do this, we derive backpropagation equations and allow gradients to flow back through the (previously fixed) ScatterNet front end. Connecting several such locally invariant layers allows us to build learnable ScatterNet, a more flexible and general form of the ScatterNet (while still maintaining its desired properties). We show that the learnable ScatterNet can provide significant improvements over the regular ScatterNet when being used as a front end for a learning system. Additionally, we show that the locally invariant convolutional layer can directly replace convolutional layers in a deep CNN (and not just at the front-end). The locally invariant convolutional layers naturally downsample the input (because of the complex modulus) while increasing the channel dimension (because of the multiple wavelet orientations used). This is an operation that often happens in a CNN by a combination of a pooling and convolutional layer. It was at these locations in a CNN where the learnable ScatterNet performed best, implying it may be useful as learnable pooling layer. Finally, we develop a system to learn complex weights that act directly on the wavelet coefficients of signals, in place of a convolutional layer. We call this layer the wavelet gain layer and show it can be used alongside convolutional layers. The network designer may then choose to learn in the pixel or wavelet domains. This layer shows a lot of promise and affords more control over what regions of the frequency space we want our layer to learn from. Our experiments show that it can improve on learning in the pixel domain for early layers of a CNN

Discrete Wavelet Transforms

The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

A Novel Multimodal Image Fusion Method Using Hybrid Wavelet-based Contourlet Transform

Various image fusion techniques have been studied to meet the requirements of different applications such as concealed weapon detection, remote sensing, urban mapping, surveillance and medical imaging. Combining two or more images of the same scene or object produces a better application-wise visible image. The conventional wavelet transform (WT) has been widely used in the field of image fusion due to its advantages, including multi-scale framework and capability of isolating discontinuities at object edges. However, the contourlet transform (CT) has been recently adopted and applied to the image fusion process to overcome the drawbacks of WT with its own advantages. Based on the experimental studies in this dissertation, it is proven that the contourlet transform is more suitable than the conventional wavelet transform in performing the image fusion. However, it is important to know that the contourlet transform also has major drawbacks. First, the contourlet transform framework does not provide shift-invariance and structural information of the source images that are necessary to enhance the fusion performance. Second, unwanted artifacts are produced during the image decomposition process via contourlet transform framework, which are caused by setting some transform coefficients to zero for nonlinear approximation. In this dissertation, a novel fusion method using hybrid wavelet-based contourlet transform (HWCT) is proposed to overcome the drawbacks of both conventional wavelet and contourlet transforms, and enhance the fusion performance. In the proposed method, Daubechies Complex Wavelet Transform (DCxWT) is employed to provide both shift-invariance and structural information, and Hybrid Directional Filter Bank (HDFB) is used to achieve less artifacts and more directional information. DCxWT provides shift-invariance which is desired during the fusion process to avoid mis-registration problem. Without the shift-invariance, source images are mis-registered and non-aligned to each other; therefore, the fusion results are significantly degraded. DCxWT also provides structural information through its imaginary part of wavelet coefficients; hence, it is possible to preserve more relevant information during the fusion process and this gives better representation of the fused image. Moreover, HDFB is applied to the fusion framework where the source images are decomposed to provide abundant directional information, less complexity, and reduced artifacts. The proposed method is applied to five different categories of the multimodal image fusion, and experimental study is conducted to evaluate the performance of the proposed method in each multimodal fusion category using suitable quality metrics. Various datasets, fusion algorithms, pre-processing techniques and quality metrics are used for each fusion category. From every experimental study and analysis in each fusion category, the proposed method produced better fusion results than the conventional wavelet and contourlet transforms; therefore, its usefulness as a fusion method has been validated and its high performance has been verified

Machine learning: statistical physics based theory and smart industry applications

The increasing computational power and the availability of data have made it possible to train ever-bigger artificial neural networks. These so-called deep neural networks have been used for impressive applications, like advanced driver assistance and support in medical diagnoses. However, various vulnerabilities have been revealed and there are many open questions concerning the workings of neural networks. Theoretical analyses are therefore essential for further progress. One current question is: why is it that networks with Rectified Linear Unit (ReLU) activation seemingly perform better than networks with sigmoidal activation?We contribute to the answer to this question by comparing ReLU networks with sigmoidal networks in diverse theoretical learning scenarios. In contrast to analysing specific datasets, we use a theoretical modelling using methods from statistical physics. They give the typical learning behaviour for chosen model scenarios. We analyse both the learning behaviour on a fixed dataset and on a data stream in the presence of a changing task. The emphasis is on the analysis of the network’s transition to a state wherein specific concepts have been learnt. We find significant benefits of ReLU networks: they exhibit continuous increases of their performance and adapt more quickly to changing tasks.In the second part of the thesis we treat applications of machine learning: we design a quick quality control method for material in a production line and study the relationship with product faults. Furthermore, we introduce a methodology for the interpretable classification of time series data