Multivariate numerical differentiation

We present an innovative method for multivariate numerical differentiation i.e. the estimation of partial derivatives of multidimensional noisy signals. Starting from a local model of the signal consisting of a truncated Taylor expansion, we express, through adequate differential algebraic manipulations, the desired partial derivative as a function of iterated integrals of the noisy signal. Iterated integrals provide noise filtering. The presented method leads to a family of estimators for each partial derivative of any order. We present a detailed study of some structural properties given in terms of recurrence relations between elements of a same family. These properties are next used to study the performance of the estimators. We show that some differential algebraic manipulations corresponding to a particular family of estimators lead implicitly to an orthogonal projection of the desired derivative in a Jacobi polynomial basis functions, yielding an interpretation in terms of the popular least squares. This interpretation allows one to (1) explain the presence of a spatial delay inherent to the estimators and (2) derive an explicit formula for the delay. We also show how one can devise, by a proper combination of different elementary estimators of a given order derivative, an estimator giving a delay of any prescribed value. The simulation results show that delay-free estimators are sensitive to noise. Robustness with respect to noise can be highly increased by utilizing voluntary-delayed estimators. A numerical implementation scheme is given in the form of finite impulse response digital filters. The effectiveness of our derivative estimators is attested by several numerical simulations.     

QRS complex detection based on multi wavelet packet decomposition

We present in this paper a wavelet packet based QRS complex detection algorithm. Our proposed algorithm consists of a particular combination of two vectors obtained by applying a designed routine of QRS detection process using ‘haar’ and ‘db10’ wavelet functions respectively. The QRS complex detection routine is based on the histogram approach where our key idea was to search for the node with highest number of histogram coefficients, at center, which we assume that they are related to the iso-electric baseline whereas the remaining least number coefficients reflect the R waves peaks. Following a classical approach based of a calculated fixed threshold, the possible QRS complexes will be determined. The QRS detection complex algorithm has been applied to the whole MIT-BIH arrhythmia Database to assess its robustness. The algorithm reported a global sensitivity of 98.68%, positive predictive value of 97.24% and a percentage error of 04.12%. Eventhough, the obtained global results are not as excellent as expected, we have demonstrate that our designed QRS detection algorithm performs good on a partial selected high percentage of the whole database, e.g., the partial results, obtained when applying the algorithm on 85.01% of the whole MIT-BIH arrhythmia Database, are 99.14% of sensitivity, 98.94% of positive predictive value and 01.92% of percentage error.     

Signal reconstruction in wireless sensor networks based on a cubature Kalman particle filter

For solving the issues of the signal reconstruction of nonlinear non-Gaussian signals in wireless sensor networks(WSNs), a new signal reconstruction algorithm based on a cubature Kalman particle filter(CKPF) is proposed in this paper.We model the reconstruction signal first and then use the CKPF to estimate the signal. The CKPF uses a cubature Kalman filter(CKF) to generate the importance proposal distribution of the particle filter and integrates the latest observation, which can approximate the true posterior distribution better. It can improve the estimation accuracy. CKPF uses fewer cubature points than the unscented Kalman particle filter(UKPF) and has less computational overheads. Meanwhile, CKPF uses the square root of the error covariance for iterating and is more stable and accurate than the UKPF counterpart. Simulation results show that the algorithm can reconstruct the observed signals quickly and effectively, at the same time consuming less computational time and with more accuracy than the method based on UKPF.     

Finite element and finite volume‐element simulation of pseudo‐ECGs and cardiac alternans

In this paper, we are interested in the spatio‐temporal dynamics of the transmembrane potential in paced isotropic and anisotropic cardiac tissues. In particular, we observe a specific precursor of cardiac arrhythmias that is the presence of alternans in the action potential duration. The underlying mathematical model consists of a reaction–diffusion system describing the propagation of the electric potential and the nonlinear interaction with ionic gating variables. Either conforming piecewise continuous finite elements or a finite volume‐element scheme are employed for the spatial discretization of all fields, whereas operator splitting strategies of first and second order are used for the time integration. We also describe an efficient mechanism to compute pseudo‐ECG signals, and we analyze restitution curves and alternans patterns for physiological and pathological cardiac rhythms. Copyright © 2014 John Wiley & Sons, Ltd.     

一种基于简正波模态频散的远距离宽带海底参数反演方法

在浅海环境中, 海底环境参数对声传播有着重要的影响. 由于利用单个宽带声源进行海底参数反演时, 随着距离的增大, 误差变大, 本文提出利用warping变换对在浅海波导中传播的, 不同距离上的两个宽带爆炸声源进行简正波的有效分离, 实现了宽带爆炸声源的远距离海底参数反演. 采用全局寻优遗传算法对提取出的模态频散到达时间差与理论计算的模态频散到达时间差进行匹配处理, 并结合随距离连续变化的声传播损失, 实现了利用单水听器进行海底参数的反演. 实验结果表明: 运用反演出的海底参数提取模态频散时间差和实测数据提取出的模态频散时间差吻合得较好; 而通过传播损失反演得到的海底衰减系数与频率呈指数关系. 最后, 对反演结果进行了后验概率分析, 并将本组爆炸声源的反演结果用于另一组不同距离上爆炸声源时仍然有效, 来评价反演结果的有效性.     

基于冗余紧框架的?2/?1极小化块稀疏压缩感知

压缩感知是(近似)稀疏信号处理的研究热点之一,它突破了Nyquist/Shannon采样率,实现了信号的高效采集和鲁棒重构.本文采用l2/l1极小化方法和BlockD-RIP理论研究了在冗余紧框架下的块稀疏信号,所获结果表明,当BlockD-RIP常数δ2k/τ满足0<δ2k/τ<0.2时,l2/l1极小化方法能够鲁棒重构原始信号,同时改进了已有的重构条件和误差上界.基于离散傅里叶变换(DFT)字典,执行了一系列仿真实验充分证实了理论结果.     

靶材对激光等离子体诱导靶上电势信号的影响

将高功率脉冲激光分别作用于Cu、Fe、Al三种金属靶材,通过实验测试激光等离子体在这三种金属靶上产生的电势信号,讨论了靶材料对电势信号的影响.实验结果表明：靶上电势信号早期阶段受靶材料的影响比较显著,早期信号峰值大小随靶材变化顺序依次为：IFe>ICu>IAl,而峰值到达时间依次为：tAl相似文献   

Generalized analytic signal associated with linear canonical transform

Analytic signal is tightly associated with Hilbert transform and Fourier transform. The linear canonical transform is the generalization of many famous linear integral transforms, such as Fourier transform, fractional Fourier transform and Fresnel transform. Based on the parameter (a, b)-Hilbert transform and the linear canonical transform, in this paper, we develop some issues on generalized analytic signal. The generalized analytic signal can suppress the negative frequency components in the linear canonical transform domain. Furthermore, we prove that the kernel function of the inverse linear canonical transform satisfies the generalized analytic condition and get the generalized analytic pairs. We show the generalized Bedrosian theorem is valid in the linear canonical transform domain.     

An Overview of Variational Autoencoders for Source Separation,Finance, and Bio-Signal Applications

Autoencoders are a self-supervised learning system where, during training, the output is an approximation of the input. Typically, autoencoders have three parts: Encoder (which produces a compressed latent space representation of the input data), the Latent Space (which retains the knowledge in the input data with reduced dimensionality but preserves maximum information) and the Decoder (which reconstructs the input data from the compressed latent space). Autoencoders have found wide applications in dimensionality reduction, object detection, image classification, and image denoising applications. Variational Autoencoders (VAEs) can be regarded as enhanced Autoencoders where a Bayesian approach is used to learn the probability distribution of the input data. VAEs have found wide applications in generating data for speech, images, and text. In this paper, we present a general comprehensive overview of variational autoencoders. We discuss problems with the VAEs and present several variants of the VAEs that attempt to provide solutions to the problems. We present applications of variational autoencoders for finance (a new and emerging field of application), speech/audio source separation, and biosignal applications. Experimental results are presented for an example of speech source separation to illustrate the powerful application of variants of VAE: VAE, β-VAE, and ITL-AE. We conclude the paper with a summary, and we identify possible areas of research in improving performance of VAEs in particular and deep generative models in general, of which VAEs and generative adversarial networks (GANs) are examples.     

Multi-Class Classification of Medical Data Based on Neural Network Pruning and Information-Entropy Measures

Medical data includes clinical trials and clinical data such as patient-generated health data, laboratory results, medical imaging, and different signals coming from continuous health monitoring. Some commonly used data analysis techniques are text mining, big data analytics, and data mining. These techniques can be used for classification, clustering, and machine learning tasks. Machine learning could be described as an automatic learning process derived from concepts and knowledge without deliberate system coding. However, finding a suitable machine learning architecture for a specific task is still an open problem. In this work, we propose a machine learning model for the multi-class classification of medical data. This model is comprised of two components—a restricted Boltzmann machine and a classifier system. It uses a discriminant pruning method to select the most salient neurons in the hidden layer of the neural network, which implicitly leads to a selection of features for the input patterns that feed the classifier system. This study aims to investigate whether information-entropy measures may provide evidence for guiding discriminative pruning in a neural network for medical data processing, particularly cancer research, by using three cancer databases: Breast Cancer, Cervical Cancer, and Primary Tumour. Our proposal aimed to investigate the post-training neuronal pruning methodology using dissimilarity measures inspired by the information-entropy theory; the results obtained after pruning the neural network were favourable. Specifically, for the Breast Cancer dataset, the reported results indicate a 10.68% error rate, while our error rates range from 10% to 15%; for the Cervical Cancer dataset, the reported best error rate is 31%, while our proposal error rates are in the range of 4% to 6%; lastly, for the Primary Tumour dataset, the reported error rate is 20.35%, and our best error rate is 31%.