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In this paper, we propose an applicable algorithm of the so-called adaptive Fourier decomposition in H 2 (ℂ +) the Hardy H 2 space on the upper half-plane ℂ + , which provides a new method for decomposing real-valued signals and analytic signals on the real line. As a by-product, a new approach for computing the Hilbert transform on the real line is also given. Numerical experiments are used to demonstrate the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Aquila optimizer (AO) is an efficient meta-heuristic optimization method, which mimics the hunting style of Aquila in nature. However, the AO algorithm may suffer from immature convergence during the exploitation stage. In this paper, two strategies are elegantly employed into conventional AO, such as random opposition-based learning and nonlinear flexible jumping factor, which can efficiently enhance the performance of conventional AO. Experiments on 1 7 benchmark functions and image segmentation demonstrate the effectiveness of the proposed algorithm. Comparison with several state-of-the-art meta-heuristic optimization techniques indicates the efficacy of the developed method. [ABSTRACT FROM AUTHOR]

In Blind Hyperspectral Unmixing, the accuracy of the estimated number of endmembers affects the succeeding steps of extraction of endmember signatures and acquiring their fractional abundances. The characteristics of endmember signature depend on the nature of the material on the ground and share similar characteristics for variants of the same material. In this paper, we introduce a new concept of sub-endmembers to identify similar materials that are variants of a global endmember. Identifying the sub-endmembers will provide a meaningful interpretation of the endmember variability along with increased unmixing accuracy. This paper proposes a new algorithm exploiting both the spatial and spectral information present in hyperspectral data. The hyperspectral data are segmented into homogenous regions (superpixels) based on the Simple Linear Iterative Clustering (SLIC) algorithm, and the mean spectral of each region is accounted for in finding the global endmembers. The difference of eigenvalues-based thresholding method is used to find the number of global and sub-endmembers. The method has been tested on synthetic and real hyperspectral data and has successfully estimated the number of global endmembers as well as sub-endmembers. The method is also compared with other state-of-the-art methods, and better performances are obtained at a reasonably lower computational complexity. [ABSTRACT FROM AUTHOR]

Tremendous efficient optimization methods have been proposed for strongly convex objectives optimization in modern machine learning. For non-strongly convex objectives, a popular approach is to apply a reduction from non-strongly convex to a strongly convex case via regularization techniques. Reduction on objectives with adaptive decrease on regularization tightens the optimal convergence of algorithms to be independent on logarithm factor. However, the initialization of parameter of regularization has a great impact on the performance of the reduction. In this paper, we propose an aggressive reduction to reduce the complexity of optimization for non-strongly convex objectives, and our reduction eliminates the impact of the initialization of parameter on the convergent performances of algorithms. Aggressive reduction not only adaptively decreases the regularization parameter, but also modifies regularization term as the distance between current point and the approximate minimizer. Our aggressive reduction can also shave off the non-optimal logarithm term theoretically, and make the convergent performance of algorithm more compact practically. Experimental results on logistic regression and image deblurring confirm this success in practice. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm is discussed for constructing the two-direction Armlet multiwavelet. First, the definition of two-direction Armlet multiwavelet is presented in this paper. A two-direction multiwavelet can be changed to a special multi-wavelet. By Two-scale Similar Transform (TST), a transform can be taken on the two-scale matrix symbols of a two-direction multi-wavelets. This transform keeps the orthogonality of the two-direction multi-wavelets. However, the condition is discussed which the two-direction multi-wavelet corresponding to a two-direction multi-scaling function is an Armlet with order n. An approach is given for constructing the transform matrix. Finally, an example is given for discussing the two-direction Armlet multi-wavelet with order 2. [ABSTRACT FROM AUTHOR]

Continuous wavelet transform (CWT) is a linear convolution of signal and wavelet function for a fixed scale. This paper studies the algorithm of CWT with Morlet wavelet as mother wavelet by using nonzero-padded linear convolution. The time domain filter, which is a non-causal filter, is the sample of wavelet function. By making generalized discrete Fourier transform (GDFT) and inverse transform for this filter, we can get a geometrically weighted periodic extension of the filter when evaluated outside its original support. From this extension of the time domain filter, we can get a causal filter. In this paper, GDFT-based algorithm for CWT, which has a more concise form than that of linear convolution proposed by Jorge Martinez, is constructed by using this causal filter. The analytic expression of the GDFT of this filter, which is essential for GDFT-based algorithm for CWT, is deduced in this paper. The numerical experiments show that the calculation results of GDFT-based algorithm are stable and reliable; the running speed of GDFT-based algorithm is faster than that of the other two algorithms studied in our previous work. [ABSTRACT FROM AUTHOR]

In linear regression, outliers have a serious effect on the estimation of regression model parameters and the prediction of final results, so outlier detection is one of the key steps in data analysis. In this paper, we use a mean shift model and then we apply the penalty function to penalize the mean shift parameters, which is conducive to get a sparse parameter vector. We choose Sorted L1 regularization (SLOPE), which provides a convex loss function, and shows good statistical properties in parameter selection. We apply an iterative process which using gradient descent method and parameter selection at each step. Our algorithm has higher computational efficiency since the calculation of inverse matrix is avoided. Finally, we use Cross-Validation rules (CV) and Bayesian Information Criterion (BIC) criteria to fine tune the parameters, which helps our program identify outliers and obtain more robust regression coefficients. Compared with other methods, the experimental results show that our program has a fantastic performance in all aspects of outlier detection. [ABSTRACT FROM AUTHOR]

In this paper, image fusion method based on a new class of wavelet — non-separable wavelet with compactly supported, linear phase, orthogonal and dilation matrix [formula] is presented. We first construct a non-separable wavelet filter bank. Using these filters, the images involved are decomposed into wavelet pyramids. Then the following fusion algorithm was proposed: for low-frequency part, the average value is selected for new pixel value, For the three high-frequency parts of each level, the standard deviation of each image patch over 3×3 window in the high-frequency sub-images is computed as activity measurement. If the standard deviation of the area 3×3 window is bigger than the standard deviation of the corresponding 3×3 window in the other high-frequency sub-image. The center pixel values of the area window that the weighted area energy is bigger are selected. Otherwise the weighted value of the pixel is computed. Then a new fused image is reconstructed. The performance of the method is evaluated using the entropy, cross-entropy, fusion symmetry, root mean square error and peak-to-peak signal-to-noise ratio. The experiment results show that the non-separable wavelet fusion method proposed in this paper is very close to the performance of the Haar separable wavelet fusion method. [ABSTRACT FROM AUTHOR]

The Fog computing is rising as a dominant and modern computing model to deliver Internet of Things (IoT) computations, which is an addition to the cloud computing standard to get it probable to perform the IoT requests in the network of edge. In those above independent and dispersed environment, resource allocation is vital. Therefore, scheduling will be a test to enhance potency and allot resources properly to the tasks. This paper offers a distinct task scheduling algorithm in the fog computing environment that tries to depreciate the makespan and maximize resource utilization. This algorithm catalogues the task based on the mean Suffrage value. The suggested algorithm gives much resource utilization and diminishes makespan. Our offered algorithm is compared with different alive scheduling for performance investigation, and test results confirm that our algorithm has a more significant resource utilization rate and low makespan than other familiar algorithms. [ABSTRACT FROM AUTHOR]

In the first 'Wavelets and Statistics' conference proceedings 1, our group published 'Wavelab and Reproducible Research', in which we advocated using the internet for publication of software and data so that research results could be duplicated by others. Much has happened in the last decade that bears on the notion of reproducibility, and we will review our experience. We will also describe a new software package BEAMLAB containing routines for multiscale geometric analysis, and describe some of its capabilities. BEAMLAB makes available, in one package, all the code to reproduce all the figures in our recently published articles on beamlets, curvelets and ridgelets. The interested reader can inspect the source code to see what algorithms were used, and how parameters were set to produce the figures, and will then be able to modify the source codes to produce variations of our results. Some new examples of numerical studies based on BEAMLAB are provided here. [ABSTRACT FROM AUTHOR]

Improved ant colony optimization (ACO) algorithms for continuous-domain optimization have been widely applied in recent years, but these improved methods have a weak perception of environmental information changes and only rely on the residues of the pheromones in the path to guide colony evolution. In this paper, we propose an ant colony algorithm based on the reinforcement learning model (RLACO). RLACO can acquire more environmental information by calculating the diversity of the ant colony, and, uses the diversity and other basic information of the ant colony to establish a reinforcement learning model. At different stages of evolution, the algorithm chooses an optimal strategy that can maximize the reward to improve the global search ability and convergence speed of the colony. The experimental results on CEC 2017 test functions show that the proposed algorithm is superior to other algorithms for continuous-domain optimization in convergence speed, accuracy and global search ability. [ABSTRACT FROM AUTHOR]

This paper presents a novel method for video-based face recognition (VFR) based on M-estimator and image set collaborative representation. Since a video is essentially an image set, the VFR problem can be cast as a special case of the image set-based face recognition (FR) problem. To measure the distance between the query image set and the gallery image set, we develop an M-estimator-based image set collaborative representation (MISCR) model. To implement MISCR, we devise an efficient half-quadratic-based optimization algorithm to tackle the complicated optimization problem. We also establish the convergence property of the devised algorithm. Our other contribution is to propose an MISCR-based classifier for the general image set classification problem, including VFR as a special case. The experiments using real-world benchmark databases demonstrate the efficacy and robustness of the proposed method for VFR. [ABSTRACT FROM AUTHOR]

The recognition rate of SIFT algorithm in single hand vein database has been as high as 99.5%. But with the development of Internet-plus technology, the demand for distributed systems becomes more and more significant. However, the problem of picture quality caused by cross-device makes the intraclass variations larger. For example, when gathering the dorsal hand vein images, subtle changes in relative distance and orientation among the imaging camera, the illumination LED arrays and the different location of users' hand, as well as shielding by the external housing box from ambient light sources and so on, these will make large difference to one person's hand images. So, including the contrast, the lightness, the shifting, the angle of rotation, the size and so on, these differences make it possible to use some traditional methods to recognize dorsal hand vein with a low recognition rate of less than 50%. Therefore, based on the traditional SIFT, this paper optimized the scale factor , extreme searching neighborhood structure and matching threshold . It can be seen that the cross-device hand vein feature is more robust, and the recognition rate reached an average of 88.5%. [ABSTRACT FROM AUTHOR]

The multi-task learning (MTL) methods consider learning a problem together with other related problems simultaneously. The major challenge of MTL is how to selectively screen the shared information. The information of each task must be related to the others, but when sharing information between two unrelated tasks it degenerates the performance of both tasks. To ensure the related problems are related to the main task is the most important point in MTL. In this paper, we will design a novel algorithm to calculate the degrees of relationship among tasks by using a semantical space of features in each task and then build semantical tree to achieve better learning performance. We propose an MTL method under this algorithm which achieves good experimental performance. Our experiments are taken on both image classification and video action recognition, compared with the state-of-the-art MTL methods. Our method proposes good performance in the four public datasets. [ABSTRACT FROM AUTHOR]

Based on wavelet transform and chaos algorithm, this paper presents a Network Traffic Forecasting Combination Model. The model introduces chaos algorithm for training the BP network and optimizing weights so as to avoid gradient descent algorithm that slowly converges and likely obtains local optimum results. Before forecasting, we first perform wavelet decomposition on the pretreated flow. Then, we utilize the FARIMA model and the improved Elman neural network model to forecast according to approximate components and detailed components, respectively. At last, we use the combination model for the network traffic forecasting. Simulation results confirmed the improved accuracy of the model, and comparing to traditional FARIMA model and wavelet neural network (WNN) model, the model can reduce the deviation. [ABSTRACT FROM AUTHOR]

Trajectory representation model has been proposed to describe non-rigid deformation. An optimal trajectory space finding algorithm for 3D non-rigid structure from motion (OTSF-NRSFM) based on this model also has been proposed. However, the influence of the wavelet basis selection on the OTSF-NRSFM algorithm has still not been studied. To help OTSF-NRSFM researchers select wavelet basis properly, we investigated the influences of wavelet basis selection. Two typical wavelet bases, DCT basis and WHT basis, are discussed in this paper. The spectrum properties of wavelet basis and feature point trajectory, trajectory representation results on synthetic shark data, OTSF-NRSFM reconstruction results on synthetic data and real data are analyzed. The results show that the wavelet selection has much influence on OTSF-NRSFM reconstruction results of some non-rigid feature points, which have complicated trajectory. This paper gives researchers some inspiration about wavelet basis selection in OTSF-NRSFM algorithm. [ABSTRACT FROM AUTHOR]

Ramanujan Sums (RS) have been found to be very successful in signal processing recently. However, as far as we know, the RS have not been applied to image analysis. In this paper, we propose two novel algorithms for image analysis, including moment invariants and pattern recognition. Our algorithms are invariant to the translation, rotation and scaling of the 2D shapes. The RS are robust to Gaussian white noise and occlusion as well. Our algorithms compare favourably to the dual-tree complex wavelet (DTCWT) moments and the Zernike's moments in terms of correct classification rates for three well-known shape datasets. [ABSTRACT FROM AUTHOR]

As a powerful unsupervised learning technique, clustering is the fundamental task of big data analysis. However, many traditional clustering algorithms for big data that is a collection of high dimension, sparse and noise data do not perform well both in terms of computational efficiency and clustering accuracy. To alleviate these problems, this paper presents Feature K-means clustering model on the feature space of big data and introduces its fast algorithm based on Alternating Direction Multiplier Method (ADMM). We show the equivalence of the Feature K-means model in the original space and the feature space and prove the convergence of its iterative algorithm. Computationally, we compare the Feature K-means with Spherical K-means and Kernel K-means on several benchmark data sets, including artificial data and four face databases. Experiments show that the proposed approach is comparable to the state-of-the-art algorithm in big data clustering. [ABSTRACT FROM AUTHOR]

In this paper, an efficient novel dual permutation–substitution structure-based color image encryption algorithm is proposed. Initially, the Secure Hash Algorithm-512 (SHA-512) is applied to the input image to generate the initial values for the Lü system dynamically. In the first stage of permutation, inter-color-component pixel shuffling is carried out with a circular pixel-swapping mechanism. In the second stage, intra-color-component pixel shuffling is executed, based on pseudorandom positions generated by the Lü chaotic system. Pixel values are changed in the substitution stage, based on float-valued chaotic sequences generated by the Lü system. The performance of the proposed algorithm is evaluated with metrics such as key space, key sensitivity, histograms, correlation coefficients (vertical, horizontal and diagonal), information entropy, number of pixel changes rate (NPCR), unified average changing intensity (UACI), peak signal-to-noise ratio (PSNR), mean absolute error (MAE), contrast analysis, encryption time and the National Institute of Standards and Technology Special Publication 800-22 (NIST SP 800-22) statistical test. The experimental results obtained and performance assessment show that the proposed scheme has produced good results. [ABSTRACT FROM AUTHOR]

In this paper, wavelet transform on a regression curve is investigated by using length-preserving projection and its application in financial data is also discussed. First, properties of wavelet filters on the regression trend curves are studied and two-scale equation of wavelet function is deduced on the regression trend curves. Second, the decomposition and reconstruction algorithm of discrete wavelet transform on regression trend curves is derived. Finally, two examples in financial data are given for discussion, based on decomposition and reconstruction algorithms on regression trend curves. Some new research interpretations are presented in dealing with financial data such as "volatility on regression growth trend", "error on regression growth trend", and so on. [ABSTRACT FROM AUTHOR]

Differential privacy becomes a standard for evaluating the privacy protection performance for an algorithm these years. However, the definition of differential privacy seems not so easy to understand as the classical k-anonymity and etc. In this paper, we propose a new measure which is more comprehensible. Some properties of such measure are investigated and the relationship between our new definition and differential privacy is studied. [ABSTRACT FROM AUTHOR]

This paper considers the problem of recovering a low-rank matrix from a small number of measurements consisting of linear combinations of the matrix entries. We extend the elastic-net regularization in compressive sensing to a more general setting, the matrix recovery setting, and consider the elastic-net regularization scheme for matrix recovery. To investigate on the statistical properties of this scheme and in particular on its convergence properties, we set up a suitable mathematic framework. We characterize some properties of the estimator and construct a natural iterative procedure to compute it. The convergence analysis shows that the sequence of iterates converges, which then underlies successful applications of the matrix elastic-net regularization algorithm. In addition, the error bounds of the proposed algorithm for low-rank matrix and even for full-rank matrix are presented in this paper. [ABSTRACT FROM AUTHOR]

In this paper, six robust non-blind watermarking schemes based on curvelet transform are proposed. Single band watermarking method was proposed in Ref. 1. This paper develops the single band watermarking method and adds Human Vision System (HVS) to form six different multi-bands watermarking methods. With the increasing redundancy of watermark, the robustness of the algorithm will be investigated and comparative studies with the single band watermarking will be shown. The experimental results demonstrate that the proposed algorithms have great robustness against various imaging attacks. [ABSTRACT FROM AUTHOR]

This paper presents a wavelet-based computationally efficient implementation of the Linear Minimum Mean Square Error (LMMSE) algorithm in image super-resolution. The image super-resolution reconstruction problem is well-known to be an ill-posed inverse problem of large dimensions. The LMMSE estimator to be implemented in the image super-resolution reconstruction problem requires an inversion of a very large dimension matrix, which is practically impossible. Our suggested implementation is based on breaking the problem into four consecutive steps, a registration step, a multi-channel LMMSE restoration step, a wavelet-based image fusion step and an LMMSE image interpolation step. The objective of the wavelet fusion step is to integrate the data obtained from each observation into a single image, which is then interpolated to give a high-resolution image. The paper explains the implementation of each step. The proposed implementation has succeeded in obtaining a high-resolution image from multiple degraded observations with a high PSNR. The computation time of the suggested implementation is small when compared to traditional iterative image super-resolution algorithms. [ABSTRACT FROM AUTHOR]

Most of the content-based image retrieval systems require a distance computation of feature vectors for each candidate image in the image database. This exhaustive search is highly time-consuming and inefficient. This limits the usefulness of such system. Thus there is a growing need for a fast image retrieval system. Multiresolution data-structure algorithm provides a good solution to the above problem. In this paper we propose a wavelet-based multiresolution data-structure algorithm. Wavelet-based multiresolution data-structure further reduce the number of computation by around 50%. In the proposed approach we reuse the information obtained at lower resolution levels to calculate the distance at a higher resolution level. Apart from this, the proposed structure saves memory overheads by about 50% over multiresolution data-structure algorithm. The proposed algorithm can be easily combined with other algorithms for performance enhancement.[sup 4] In this paper we use the proposed technique to match luminance histogram for image retrieval. Fuzzy histograms enhances performance by considering the similarity between neighboring bins. We have extended the proposed approach to fuzzy histograms for better performance. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) is a promising method to represent facial images using nonnegative features under a low-rank nonnegative basis-image matrix. The facial images usually reside on a low-dimensional manifold due to the variations of illumination, pose and facial expression. However, NMF has no ability to uncover the manifold structure of data embedded in a high-dimensional Euclidean space, while the manifold structure contains both local and nonlocal intrinsic features. These two kinds of features are of benefit to class discrimination. To enhance the discriminative power of NMF, this paper proposes a novel NMF algorithm with manifold structure (Mani-NMF). Two quantities related to adjacent graph and non-adjacent graph are incorporated into the objective function, which will be minimized by solving two convex suboptimization problems. Based on the gradient descent method and auxiliary function technique, we acquire the update rules of Mani-NMF and theoretically prove the convergence of the proposed Mani-NMF algorithm. Three publicly available face databases, Yale, pain expression and CMU databases, are selected for evaluations. Experiments results show that our algorithm achieves a better performance than some state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

In order to obtain higher small target detection accuracy, this paper presents an effective algorithm inspired by the local contrast mechanism. The proposed method can enhance target signal and suppress background clutter simultaneously. In the first stage, a enhanced image is obtained using the proposed Weighted Laplacian of Gaussian. In the second stage, an adaptive threshold is adopted to segment the target. Experimental results on two challenging image sequences show that the proposed method can detect the bright and dark targets simultaneously, and is not sensitive to sea-sky line of the infrared (IR) image. So it is fit for small IR target detection. [ABSTRACT FROM AUTHOR]

In this paper, we present an algorithm to automatically detect meaningful modes in a histogram. The proposed method is based on the behavior of local minima in a scale-space representation. We show that the detection of such meaningful modes is equivalent in a two classes clustering problem on the length of minima scale-space curves. The algorithm is easy to implement, fast and does not require any parameter. We present several results on histogram and spectrum segmentation, grayscale image segmentation and color image reduction. [ABSTRACT FROM AUTHOR]

The paper presents a detailed analysis of algorithms used for the forward and the inverse discrete wavelet transform (DTWT) of finite-length signals. The paper provides answers to questions such as "how many wavelet coefficients are computed from the signal at a given depth of the decomposition" or conversely, "how many signal samples are needed to compute a single wavelet coefficient at a given depth of the decomposition" or "how many coefficients at a given depth are influenced by the selected type of boundary treatment" or "how many samples of the input signal simultaneously influence two neighboring wavelet coefficients at a given depth of the decomposition". As a byproduct, the rigorous analysis of the algorithms gives details needed for the implementation. The paper is accompanied by several Matlab functions. [ABSTRACT FROM AUTHOR]

Recently, semi-supervised learning (SSL) has attracted significant attention in machine learning fields. While numerous experimental results have shown the effectiveness of SSL methods, the theoretical analysis in this area is still poorly understood. In this paper, we investigate the generalization performance of the recently proposed sparse graph-based semi-supervised classification algorithm. We use a computationally more simple way to solve the algorithm and present the excess misclassification error bounds. In detail, the Fenchel-Legendre conjugate is first employed to reform the algorithm to an inf-sup problem. Then, the covering number is used to estimate the excess misclassification error. Experiment results are given to demonstrate the effectiveness of the sparse SSL algorithm with new solving strategy. [ABSTRACT FROM AUTHOR]

Having high accuracy results in data clustering and preserving the privacy of data are among the main challenges in privacy preserving clustering (PPC) techniques. High dimensionality of data is another challenge in PPC, which reduces the efficiency of the data mining algorithms. Therefore, PPC algorithms are divided into two categories. The algorithms in the first category protect the data privacy and do not reduce the data dimensionality whereas the algorithms in the second category not only preserve the data privacy but also reduce the data dimensionality. The techniques based on geometric data transformation methods (GTDMs) are related to the first category whereas the techniques based on random projection (RP), discrete cosine transform (DCT) and Haar wavelet transform (HWT) are related to the second category. The GTDMs algorithms do not reduce the data dimensionality. This is the main drawback of this algorithm which causes reduction in the performance of data mining algorithm in large datasets. The technique based on Haar wavelet transform automatically recognizes the dimensionality of the transformed data by using data energy. However, the main problem is the nature of Haar wavelet, which has one vanishing point. In this paper, we show that using Daubechies-2 wavelet, which has two vanishing points, increases the clustering quality. Therefore, to fix the drawback of the PPC algorithm based on ITaar wavelet, we introduce a new algorithm to improve both the clustering quality and the privacy measure of data by using Daubechies-2 wavelet transform (D2WT). The results of experiments using several datasets, comparing the new algorithm with other existing techniques, are also presented in this paper. [ABSTRACT FROM AUTHOR]

The fusion of infrared and visible images of the same scene aims to generate a composite image which can provide a more comprehensive description of the scene. In this paper, we propose an infrared and visible image fusion method based on convolutional neural networks (CNNs). In particular, a siamese convolutional network is applied to obtain a weight map which integrates the pixel activity information from two source images. This CNN-based approach can deal with two vital issues in image fusion as a whole, namely, activity level measurement and weight assignment. Considering the different imaging modalities of infrared and visible images, the merging procedure is conducted in a multi-scale manner via image pyramids and a local similarity-based strategy is adopted to adaptively adjust the fusion mode for the decomposed coefficients. Experimental results demonstrate that the proposed method can achieve state-of-the-art results in terms of both visual quality and objective assessment. [ABSTRACT FROM AUTHOR]

Clustering is a fundamental learning task in a wide range of research fields. The most popular clustering algorithm is arguably the K-means algorithm, it is well known that the performance of K-means algorithm heavily depends on initialization due to its strong non-convexity nature. To overcome the initialization issue, in this paper, we first relax the K-means model as an optimization problem with non-convex constraints, then employ the Proximal Alternating Linearized Minimization (PALM) method to solve the relaxed non-convex optimization model. The convergence analysis of PALM algorithm for the clustering problem is also provided. Experimental results on several benchmark datasets are conducted to evaluate the efficiency of our approach. [ABSTRACT FROM AUTHOR]

A constructive algorithm based on the theory of spectral pairs for constructing nonuniform wavelet basis in was considered by Gabardo and Nashed [Nonuniform multiresolution analysis and spectral pairs, J. Funct. Anal. 158 (1998) 209-241]. In this setting, the associated translation set is a spectrum which is not necessarily a group nor a uniform discrete set, given where (an integer) and is an odd integer with such that and are relatively prime and is the set of all integers. The objective of this paper is to construct nonuniform wavelet frame on local fields. A necessary condition and four sufficient conditions for nonuniform wavelet frame on local fields are given. [ABSTRACT FROM AUTHOR]

This paper, proposes a novel approach for feature extraction based on the segmentation and morphological alteration of handwritten multi-lingual characters. We explored multi-resolution and multi-directional transforms such as wavelet, curvelet and ridgelet transform to extract classifying features of handwritten multi-lingual images. Evaluating the pros and cons of each multi-resolution algorithm has been discussed and resolved that Curvelet-based features extraction is most promising for multi-lingual character recognition. We have also applied some morphological operation such as thinning and thickening then feature level fusion is performed in order to create robust feature vector for classification. The classification is performed with K-nearest neighbor (K-NN) and support vector machine (SVM) classifier with their relative performance. We experiment with our in-house dataset, compiled in our lab by more than 50 personnel. [ABSTRACT FROM AUTHOR]

This paper presents a new approach of face recognition based on wavelet network using 2D fast wavelet transform and multiresolution analysis. This approach is divided in two stages: the training stage and the recognition stage. The first consists to approximate every training face image by a wavelet network. The second consists in recognition of a new test image by comparing it to all the training faces, the distances between this test face and all images from the training set are calculated in order to identify the searched person. The usual training algorithms presents some disadvantages when the weights of the wavelet network are computed by applying the back-propagation algorithm or by direct solution which requires computing an inversion of matrix, this computation may be intensive when the learning data is too large. We present in this paper our solutions to overcome these limitations. We propose a novel learning algorithm based on the 2D Fast Wavelet Transform. Furthermore, we have increased the performances of our algorithm by introducing the Levenberg-Marquardt method to optimize the learning functions and using the Beta wavelet which has at both an analytical expression and wavelet filter bank. Extensive empirical experiments are performed to compare the proposed method with other approaches as PCA, LDA, EBGM and RBF neural network using the ORL and FERET benchmarks. [ABSTRACT FROM AUTHOR]

A main issue in machine learning research is to analyze the generalization performance of a learning machine. Most classical results on the generalization performance of regularization algorithms are derived merely with the complexity of hypothesis space or the stability property of a learning algorithm. However, in practical applications, the performance of a learning algorithm is not actually affected only by an unitary factor just like the complexity of hypothesis space, stability of the algorithm and data quality. Therefore, in this paper, we develop a framework of evaluating the generalization performance of regularization algorithms combinatively in terms of hypothesis space complexity, algorithmic stability and data quality. We establish new bounds on the learning rate of regularization algorithms based on the measure of uniform stability and empirical covering number for general type of loss functions. As applications of the generic results, we evaluate the learning rates of support vector machines and regularization networks, and propose a new strategy for regularization parameter setting. [ABSTRACT FROM AUTHOR]

Detecting outliers in high dimensional datasets is quite a difficult data mining task. Mining outliers in subspaces seems to be a promising solution, because outliers may be embedded in some interesting subspaces. Due to the existence of many irrelevant dimensions in high dimensional datasets, it is of great importance to eliminate the irrelevant or unimportant dimensions and identify outliers in interesting subspaces with strong correlation. Normally, the correlation among dimensions can be determined by traditional feature selection techniques and subspace-based clustering methods. The dimension-growth subspace clustering techniques find interesting subspaces in relatively lower possible dimension space, while dimension-growth approaches intend to find the maximum cliques in high dimensional datasets. This paper presents a novel approach by identifying outliers in correlated subspaces. The degree of correlation among dimensions is measured in terms of the mean squared residue. In doing so, we employ the frequent pattern algorithms to find the correlated subspaces. Based on the correlated subspaces obtained, outliers are distinguished from the projected subspaces by using classical outlier detection techniques. Empirical studies show that the proposed approach can identify outliers effectively in high dimensional datasets. [ABSTRACT FROM AUTHOR]

This paper investigates the scope of wavelets for performance improvement in spread spectrum image watermarking. Performance of a digital image watermarking algorithm, in general, is determined by the visual invisibility of the hidden data (imperceptibility), reliability in the detection of the hidden information after various common and deliberate signal processing operations (robustness) applied on the watermarked signals and the amount of data to be hidden (payload) without affecting the imperceptibility and robustness properties. In this paper, we propose a few spread spectrum (SS) image watermarking schemes using discrete wavelet transform (DWT), biorthogonal DWT and M-band wavelets coupled with various modulation, multiplexing and signaling techniques. The performance of the watermarking methods are also reported along with the relative merits and demerits. [ABSTRACT FROM AUTHOR]

In this paper, we examine the wavelet characterization of Hardy space H1, and show that the H1-norm is a good choice for modelizing the oscillating patterns. Furthermore, we give the discrete representation of H1-norm by using wavelet coefficients, and apply it to the variational image decomposition models. Finally, we give the iterative algorithm, and present various numerical results on images to demonstrate the potential of our methods. [ABSTRACT FROM AUTHOR]

Feature extraction is one of the most challenging problems in pattern recognition fields and has attracted great attention recently. In this paper, we propose a novel feature extraction algorithm named tensor locality sensitive discriminant analysis which accepts tensors as inputs. The algorithm preserves the key structure of data by using the labeled samples and has high performance as well as low time complexity. Experiments on the three standard databases show that the proposed method has better performance and achieves high accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a selective curvelet coefficient digital watermarking algorithm is proposed. Traditionally, curvelet watermarks are embedded into all sample frequency bands. However, the study of individual band behavior and the use of single band for watermarking have not been reported. The selective band will provide an addition security feature against any physical tampering. This paper aims to give an intensive study on the robustness of watermarking using selective curvelet coefficients from a single band and to find out the best band for embedding watermark. Wrapping of specially selected Fourier samples is employed to implement Fast Discrete Curvelet Transforms (FDCT) to transform the digital image to the curvelet domain. [ABSTRACT FROM AUTHOR]

Since its advent, the use of digital camera in mobile phones is getting more popular, where information retrieval based on visual appearance of an object is very useful when specific parameters for the object are not known. Though it is well-liked, it needs energy aware algorithms to carry out the various tasks such as segmentation and feature extraction. In this paper, a new energy aware fuzzy color segmentation algorithm is proposed and which has been applied for face segmentation in criminal identification using mobile devices. The criminals in the application are in three classes. They are New Criminal (NC), Suspected Criminal (SC) and Confirmed Criminal (CC). It is basically a mobile image-based content search engine that takes photographs of criminals as image queries and finds their relevant contents by matching them to the similar contents in the criminal databases. The energy aware fuzzy color segmentation is used to obtain the most significant parts of an image — facial regions of the persons and which are used in building image-based queries to the databases. Content search methodology in the application is also improved through the fuzzy modeling to make the application more flexible and simpler. Through the experiment conducted, it has been found that the proposed color segmentation algorithm is more robust and it reduces the computational time in searching process by minimizing the number of false cases. It could detect the faces in the images where the other known algorithms have failed to detect. [ABSTRACT FROM AUTHOR]

In recent years, image coding based on wavelet transform has made rapid progress. In this paper, quincunx lifting scheme in wavelet transform is introduced and all phase interpolation filter banks which can be used in the lifting scheme for prediction and update are designed. Based on the basic idea of set partitioning in hierarchical trees (SPIHT) algorithm, the binary tree image coding algorithm is proposed. Just like SPIHT, the encoding algorithms can be stopped at any compressed file size or let run until the compressed file is a representation of a nearly lossless image. The experimental results on test images show that compared with SPIHT algorithm, the PSNRs of the proposed algorithm are superior by about 0.5 dB at the same bit rates and the subjective quality of reconstructed images is also better. [ABSTRACT FROM AUTHOR]

While in the process of decomposition of the Mallat discrete wavelet transform (DWT) fast algorithm, the algorithm has a drawback, that is, there is frequency distortion in the high frequency subband. In this paper, a new algorithm of decomposition and reconstruction in the discrete wavelet is presented. The algorithm can solve the frequency distortion in the high frequency subband in the process of decimation in each level. The simulation of numerical value example tests the validity of the algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the application of neural networks to design intelligent nonlinear predictive controllers. Predictive controllers are now widely used in many industrial applications. They have been used for linear systems in early applications and then some methods based on predictive control theory were proposed to govern the dynamics of nonlinear systems. In this paper, we will make use of multi-layer perceptron neurofuzzy models with Locally Linear Model Tree (LoLiMoT) learning algorithm as a part of intelligent predictive control system, which has shown excellent performance in identifying of nonlinear systems. The nonlinear dynamics of the system is identified using the neural network based method and then the identified model is used as a part of predictive control algorithm. The proposed method is used to solve the control problems in some benchmark systems. As a first study, the viscosity control in a Continuous Stirred Tank Reactor (CSTR) plant is considered. The mathematical model of the plant is used to generate the input output data set and then the dynamic behavior of the system is identified using a proper multi-layer perceptron neural network, which is used in the predictive control loop. Also, the predictive control based on the locally linear neurofuzzy model is applied to temperature control of an electrically heated micro heat exchanger. The dynamic behavior of the heat exchanger is identified based on some experimental data of the real plant. Comparing the identification results obtained by the neurofuzzy model with those of some linear models such as ARX and BJ, confirms the superior performance for the locally linear neurofuzzy model. Then, the predictive control is applied to the identified model to obtain a satisfactory performance in the output temperature that should track a desired reference signal. As another application, the algorithm is applied to temperature control of a solution polymerization methyl methacrylate in a batch reactor. The results show also somehow satisfactory performance for this highly nonlinear system. All the simulation results reveal the effectiveness of the proposed intelligent control strategy. [ABSTRACT FROM AUTHOR]

Face tracking has many visual applications such as human-computer interfaces, video communications and surveillance. Color-based particle trackers have been proved robust and versatile for a modest computational cost. In this paper, a probabilistic method for integrating multi-camera information is introduced to track human face 3D-pose variations. The proposed method fuses information coming from several calibrated cameras via one color-based particle filter. The algorithm relies on the following novelties. First, the human head other than face is defined as the target of our algorithm. To distinguish the face region and hair region, a dual-color-ball is utilized to model the human head in 3D space. Second, to enhance the robustness to illumination variety, the Fisher criterion is applied to measure the separability of the face region and the hair region on the color histogram. Consequently, the color distribution template can be adapted at the proper time. Finally, the algorithm is performed based on the distributed framework, therefore the computation is implemented equally by all client processors. To demonstrate the performance of the proposed algorithm, several scenarios of visual tracking are tested in an office environment with three to four calibrated cameras. Experiments show that accurate tracking results are achieved, even in some difficult scenarios, such as the complete occlusion and the temptation of anything with skin color. Furthermore, the additional information of our track results, including the head posture and the face orientation schemes, can be used for further work such as face recognition and eye gaze estimation, which is also explained by elaborated designed experiments. [ABSTRACT FROM AUTHOR]

This paper describes an application of the wavelet transform in in-line solder paste inspection. In the development of a three-dimensional (3D) automatic inspection device of solder paste, it is necessary to detect the characteristic positions in images. In this paper, on the basis of the property of local wavelet transform modulus maximum (WTMM) and the deference filter, a practical algorithm is proposed for the detection of the characteristic positions. The proposed algorithm is applied to more than 20 actual images obtained from the 3D automatic inspection device. The detected errors are smaller than the maximum permissible error of 5 pixels. Also, the proposed algorithm is verified in-line. The experimental results show that the quality of solder paste can be successfully judged in-line. The proposed algorithm is superior to other possible techniques reported so far because of its implementation in assembly lines. [ABSTRACT FROM AUTHOR]

By integrating the Fourier techniques and the edge information obtained using the radial symmetric functions, we propose in this paper an invariant feature extraction algorithm. Unlike the Gabor feature extraction method, the present method does not use direction dependent filters, nor does it use the images in polar form, for rotation invariance. Besides, the present Fourier-Radial invariant feature extraction algorithm, suitable for both the texture and non-texture images, has functional analogy with the Gabor feature extraction method, and hence, is easily implementable. It is mathematically proved, and justified through computations, that the method can generate the invariant and discriminative feature vectors. Our simulation results demonstrate that the method can be used for such applications as content-based image retrieval. [ABSTRACT FROM AUTHOR]

In Global Positioning System (GPS), receivers use FFT-based convolvers to acquire the signals. This paper shows a robust substitute algorithm for calculating the convolution that is less sensitive to additive noise. [ABSTRACT FROM AUTHOR]