Acoustic Modelling Using Continuous Rational Kernels

Many discriminative classification algorithms are designed for tasks where samples can be represented by fixed-length vectors. However, many examples in the fields of text processing, computational biology and speech recognition are best represented as variable-length sequences of vectors. Although several dynamic kernels have been proposed for mapping sequences of discrete observations into fixed-dimensional feature-spaces, few kernels exist for sequences of continuous observations. This paper introduces continuous rational kernels, an extension of standard rational kernels, as a general framework for classifying sequences of continuous observations. In addition to allowing new task-dependent kernels to be defined, continuous rational kernels allow existing continuous dynamic kernels, such as Fisher and generative kernels, to be calculated using standard weighted finite-state transducer algorithms. Preliminary results on both a large vocabulary continuous speech recognition (LVCSR) task and the TIMIT database are presented.     

Mapping and pseudoinverse algorithms for ocean data assimilation

Among existing ocean data assimilation methodologies, reduced-state Kalman filters are a widely studied compromise between resolution, optimality, error specification, and computational feasibility. In such reduced-state filters, the measurement update takes place on a coarser grid than that of the general circulation model (GCM); therefore, these filters require mapping operators from the GCM grid to the reduced state and vice versa. The general requirements are that the state-reduction and interpolation operators be pseudoinverses of each other, that the coarse state define a closed dynamical system, that the mapping operations be insensitive to noise, and that they be appropriate for regions with irregular coastlines and bathymetry. In this paper, we describe three efficient algorithms for computing the pseudoinverse: a fast Fourier transform algorithm that serves for illustration purposes, an exact implicit method that is recommended for most applications, and an efficient iterative algorithm that can be used for the largest problems. The mapping performance of 11 interpolation kernels is evaluated. Surprisingly, common kernels such as bilinear, exponential, Gaussian, and sinc perform only moderately well. We recommend instead three kernels, smooth, thin-plate, and optimal interpolation, which have superior properties. This study removes the computational bottleneck of mapping and pseudoinverse algorithms and makes possible the application of reduced-state filters to global problems at state-of-the-art resolutions.     

Linear least-square estimation algorithms involving correlated signal and noise

Recursive algorithms are designed for the computation of the optimal linear filter and all types of predictors and smoothers of a signal vector corrupted by a white noise correlated with the signal. These algorithms are derived under both continuous and discrete time formulation of the problem. The only hypothesis imposed is that the correlation functions involved are factorizable kernels. The main contribution of this work with respect to previous studies lies in allowing correlation between the signal and the observation noise, which is useful in applications to feedback control and feedback communications. Moreover, recursive computational formulas are obtained for the error covariances associated with the above estimates.     

利用多尺度卷积神经网络的图像超分辨率算法

单幅图像超分辨率问题是典型的图像反问题。近年来深度学习广泛应用于图像超分辨率重建。为提高超分辨率算法的性能,本文利用多尺度和残差训练的思想,提出一种利用多尺度卷积神经网络的图像超分辨率算法。该算法采用多尺度的卷积核及收缩--扩展的网络结构来提取图像多尺度的信息,并在网络结构中使用跳跃连接,以便更好的传递信息并弥补由于使用下采样和上采样而造成的图像细节信息的损失,来提高图像的重建质量。通过与其它算法的对比实验表明了本文算法不仅可以取得更好的性能,并且训练的收敛速度较快。      

Nonuniform Interpolation of Noisy Signals Using Support Vector Machines

The problem of signal interpolation has been intensively studied in the information theory literature, in conditions such as unlimited band, nonuniform sampling, and presence of noise. During the last decade, support vector machines (SVM) have been widely used for approximation problems, including function and signal interpolation. However, the signal structure has not always been taken into account in SVM interpolation. We propose the statement of two novel SVM algorithms for signal interpolation, specifically, the primal and the dual signal model based algorithms. Shift-invariant Mercer's kernels are used as building blocks, according to the requirement of bandlimited signal. The sine kernel, which has received little attention in the SVM literature, is used for bandlimited reconstruction. Well-known properties of general SVM algorithms (sparseness of the solution, robustness, and regularization) are explored with simulation examples, yielding improved results with respect to standard algorithms, and revealing good characteristics in nonuniform interpolation of noisy signals.     

CORDIC-Based Unified Architectures for Computation of DCT/IDCT/DST/IDST

In this paper, CORDIC (coordinate rotation digital computer)-based Cooley-Tukey fast Fourier transform (FFT)-like algorithms for power-of-two point discrete cosine transform/discrete sine transform/inverse discrete cosine transform/inverse discrete sine transform are proposed and their corresponding unified architectures are developed by fully reusing the unique two basic processing elements. The proposed algorithms have some distinguished advantages, such as FFT-like regular data flow, unique post-scaling factor, and arithmetic-sequence rotation angles. The developed unified architectures can compute four different transforms by simple routing the data flow according to the specific transform without feeding different transform coefficients or different transform kernels. The unfolding technique is used to overcome the problem of difficult to realize pipeline that occur in iterative CORDIC algorithms. Compared to existing unified architectures, the proposed architectures have a superior performance in terms of hardware complexity, control complexity, throughput, scalability, modularity, and pipelinability.     

Nonlinear channel modeling and identification using baseband Volterra-Parafac models

Baseband Volterra models are very useful for representing nonlinear communication channels. These models present the specificity to include only odd-order nonlinear terms, with kernels characterized by a double symmetry. The main drawback is their parametric complexity. In this paper, we develop a new class of Volterra models, called baseband Volterra-Parafac models, with a reduced parametric complexity, by using a doubly symmetric Parafac decomposition of high order Volterra kernels viewed as tensors. Three adaptive algorithms are then proposed for estimating the parameters of these models. Some Monte Carlo simulation results are presented to compare the performance of the proposed estimation algorithms, in the case of third-order baseband Volterra systems excited by PSK and QAM inputs.     

An adaptive local-search algorithm for the channel-assignmentproblem (CAP)

The channel-assignment problem (CAP) for cellular radio networks is an NP-complete problem. Previous techniques for solving this problem have used graph-coloring algorithms, neural networks, simulated annealing, and pattern-based optimization procedures. We describe an efficient two-phase adaptive local-search algorithm for the channel-assignment problem. This algorithm has been applied to several existing benchmark problems with encouraging results. In many cases it outperforms the existing algorithms in the quality of the solution obtained. When used in conjunction with structured preprocessing, the algorithm can be applied to large networks. It is thus a practical tool for the planning of cellular radio networks     

基于脉冲序列核的脉冲神经元监督学习算法

脉冲神经元应用脉冲时间编码神经信息,监督学习的目标是对于给定的突触输入产生任意的期望脉冲序列.但由于神经元脉冲发放过程的不连续性,构建高效的脉冲神经元监督学习算法非常困难,同时也是该研究领域的重要问题.基于脉冲序列的核函数定义,提出了一种新的脉冲神经元监督学习算法,特点是应用脉冲序列核构造多脉冲误差函数和对应的突触学习规则,并通过神经元的实际脉冲发放频率自适应地调整学习率.将该算法用于脉冲序列的学习任务,期望脉冲序列采用Poisson过程或线性方法编码,并分析了不同的核函数对算法学习性能的影响.实验结果表明该算法具有较高的学习精度和良好的适应能力,在处理复杂的时空脉冲模式学习问题时十分有效.     

Atom specific multiple kernel dictionary based Sparse Representation Classifier for medium scale image classification

Kernel based Sparse Representation Classifier (KSRC) can classify images with acceptable performance. In addition, Multiple Kernel Learning based SRC (MKL-SRC) computes the weighted sum of multiple kernels in order to construct a unified kernel while the weight of each kernel is calculated as a fixed value in the training phase. In this paper, an MKL-SRC with non-fixed kernel weights for dictionary atoms is proposed. Kernel weights are embedded as new variables to the main KSRC goal function and the resulted optimization problem is solved to find the sparse coefficients and kernel weights simultaneously. As a result, an atom specific multiple kernel dictionary is computed in the training phase which is used by SRC to classify test images. Also, it is proved that the resulting optimization problem is convex and is solvable via common algorithms. The experimental results demonstrate the effectiveness of the proposed approach.     

Algorithm for global leaf area index retrieval using satellite imagery

Leaf area index (LAI) is one of the most important Earth surface parameters in modeling ecosystems and their interaction with climate. Based on a geometrical optical model (Four-Scale) and LAI algorithms previously derived for Canada-wide applications, this paper presents a new algorithm for the global retrieval of LAI where the bidirectional reflectance distribution function (BRDF) is considered explicitly in the algorithm and hence removing the need of doing BRDF corrections and normalizations to the input images. The core problem of integrating BRDF into the LAI algorithm is that nonlinear BRDF kernels that are used to relate spectral reflectances to LAI are also LAI dependent, and no analytical solution is found to derive directly LAI from reflectance data. This problem is solved through developing a simple iteration procedure. The relationships between LAI and reflectances of various spectral bands (red, near infrared, and shortwave infrared) are simulated with Four-Scale with a multiple scattering scheme. Based on the model simulations, the key coefficients in the BRDF kernels are fitted with Chebyshev polynomials of the second kind. Spectral indices - the simple ratio and the reduced simple ratio - are used to effectively combine the spectral bands for LAI retrieval. Example regional and global LAI maps are produced. Accuracy assessment on a Canada-wide LAI map is made in comparison with a previously validated 1998 LAI map and ground measurements made in seven Landsat scenes.     

Differentiation of discrete multidimensional signals

We describe the design of finite-size linear-phase separable kernels for differentiation of discrete multidimensional signals. The problem is formulated as an optimization of the rotation-invariance of the gradient operator, which results in a simultaneous constraint on a set of one-dimensional low-pass prefilter and differentiator filters up to the desired order. We also develop extensions of this formulation to both higher dimensions and higher order directional derivatives. We develop a numerical procedure for optimizing the constraint, and demonstrate its use in constructing a set of example filters. The resulting filters are significantly more accurate than those commonly used in the image and multidimensional signal processing literature.     

Multiple Fourier series procedures for extraction of nonlinearregressions from noisy data

Three nonparametric procedures for the extraction of nonlinear regressions from noisy data are proposed. The procedures are based on the Dirichlet, Fejer, and de la Vallee Poussin multiple kernels. Convergence properties are investigated. In particular, it is shown that the algorithms are convergent in the mean-integrated-square-error sense. The appropriate theorem establishes a relation between the order of kernels and the number of observations. Special attention is focused on the two-dimensional case. It is proved that the procedures attain the optimal rate of convergence, which cannot be exceeded by any other nonparametric algorithm     

Levinson-like and Schur-like fast algorithms for solvingblock-slanted Toeplitz systems of equations arising in wavelet-basedsolution of integral equations

The Wiener-Hopf integral equation of linear least-squares estimation of a wide-sense stationary random process and the Krein integral equation of one-dimensional (1-D) inverse scattering are Fredholm equations with symmetric Toeplitz kernels. They are transformed using a wavelet-based Galerkin method into a symmetric “block-slanted Toeplitz (BST)” system of equations. Levinson-like and Schur-like fast algorithms are developed for solving the symmetric BST system of equations. The significance of these algorithms is as follows. If the kernel of the integral equation is not a Calderon-Zygmund operator, the wavelet transform may not sparsify it. The kernel of the Krein and Wiener-Hopf integral equations does not, in general, satisfy the Calderon-Zygmund conditions. As a result, application of the wavelet transform to the integral equation does not yield a sparse system matrix. There is, therefore, a need for fast algorithms that directly exploit the (symmetric block-slanted Toeplitz) structure of the system matrix and do not rely on sparsity. The first such O(n²) algorithms, viz., a Levinson-like algorithm and a Schur (1917) like algorithm, are presented. These algorithms are also applied to the factorization of the BST system matrix. The Levinson-like algorithm also yields a test for positive definiteness of the BST system matrix. The results obtained are directly applicable to the problem of constrained deconvolution of a nonstationary signal, where the locations of the smooth regions of the signal being deconvolved are known a priori     

一种新的地震子波估计方法

地震子波估计问题是地震勘探信号处理和分析中的关键一环。本文基于遗传算法提出了一个新的地震子波估计方法。该方法用ARMA模型描述地震子波，用遗传算法交替迭代地估计AR和MA参数。与其它方法相比，本文提出的方法具有高度稳定性和很好的精度，并适应于估计非最小相位地震子波。     

Concentration maximization and local basis expansions (LBEX) for linear inverse problems

Linear inverse problems arise in biomedicine electroencephalography and magnetoencephalography (EEG and MEG) and geophysics. The kernels relating sensors to the unknown sources are Green's functions of some partial differential equation. This knowledge is obscured when treating the discretized kernels simply as matrices. Consequently, physical understanding of the fundamental resolution limits has been lacking. We relate the inverse problem to spatial Fourier analysis, and the resolution limits to uncertainty principles, providing conceptual links to underlying physics. Motivated by the spectral concentration problem and multitaper spectral analysis, our approach constructs local basis sets using maximally concentrated linear combinations of the measurement kernels.     

Algorithms for packet classification

The process of categorizing packets into “flows” in an Internet router is called packet classification. All packets belonging to the same flow obey a predefined rule and are processed in a similar manner by the router. For example, all packets with the same source and destination IP addresses may be defined to form a flow. Packet classification is needed for non-best-effort services, such as firewalls and quality of service; services that require the capability to distinguish and isolate traffic in different flows for suitable processing. In general, packet classification on multiple fields is a difficult problem. Hence, researchers have proposed a variety of algorithms which, broadly speaking, can be categorized as basic search algorithms, geometric algorithms, heuristic algorithms, or hardware-specific search algorithms. In this tutorial we describe algorithms that are representative of each category, and discuss which type of algorithm might be suitable for different applications     

基于0-1背包问题的两种算法

0-1背包问题是组合优化领域里的一个典型问题,是属于易于描述却难于解决的NP难题,有效解决0-1背包问题具有重要意义。首先给出了0-1背包问题的描述,然后详细介绍了回溯法和分支限界法的算法思想和搜索策略,并对两种算法进行了比较和分析。     

Efficient algorithms for burst error recovery using FFT and othertransform kernels

We show that the problem of signal reconstruction from missing samples can be handled by using reconstruction algorithms similar to the Reed-Solomon (RS) decoding techniques. Usually, the RS algorithm is used for error detection and correction of samples in finite fields. For the case of missing samples of a speech signal, we work with samples in the field of real or complex numbers, and we can use FFT or some new transforms in the reconstruction algorithm. DSP implementation and simulation results show that the proposed methods are better than the ones previously published in terms of the quality of recovered speech signal for a given complexity. The burst error recovery method using the FFT kernel is sensitive to quantization and additive noise like the other techniques. However, other proposed transform kernels are very robust in correcting bursts of errors with the presence of quantization and additive noise     

On applying molecular computation to binary linear codes

Adleman's (1994) successful solution of a seven-vertex instance of the NP-complete Hamiltonian directed path problem by a DNA algorithm initiated the field of biomolecular computing. In this correspondence, we describe DNA algorithms based on the sticker model to perform encoding, minimum-distance computation, and maximum-likelihood (ML) decoding of binary linear codes. We also discuss feasibility and limitations of the sticker algorithms