Kernel decomposition of time-frequency distributions

Bilinear time-frequency distributions (TFDs) offer improved time-frequency resolution over linear representations, but suffer from difficult interpretation, higher implementation cost, and the lack of associated low-cost signal synthesis algorithms. In the paper, the authors introduce some new tools for the interpretation and quantitative comparison of high-resolution TFDs. These tools are used in related work to define low-cost high-resolution TFDs and to define linear, low-cost signal synthesis algorithms associated with high-resolution TFDs. First, each real-valued TFD is associated with a self-adjoint linear operator ψ. The spectral representation of ψ expresses the TFD as a weighted sum of spectrograms (SPs). It is shown that the SP decomposition and Weyl correspondence do not yield useful interpretations for high-resolution TFDs due to the fact that ψ is not positive     

Vector-valued time-frequency representations

Cohen's (1989) class of time frequency distributions (TFDs), which includes the spectrogram (SP), Wigner distribution (WD), and reduced interference distributions (RIDs) has become widely known as a useful signal analysis tool. It has been shown that every real-valued TFD can be written as a weighted sum of SPs. The “SP decomposition” has been used to construct fast approximations to desirable TFDs using the SP building block, for which there exist accessible and efficient hardware and software implementations. We introduce a class of linear, vector-valued time-frequency representations (TFRs) that are easily related to associated bilinear TFDs through the SP decomposition. We solve a least-squares signal synthesis problem on modified vector-valued TFRs that are associated with nonnegative TFDs as a weighted sum of least-squares short-time Fourier transform (STFT) signal synthesis schemes. We extend the solution to vector-valued TFRs associated with high-resolution TFDs in order to define a high-resolution alternative to STFT signal synthesis, as demonstrated by desirable properties and examples. The resulting signal synthesis methods can be realized as a weighted sum of STFT synthesis schemes, for which there exist accessible and efficient hardware and software implementations     

Direction of arrival estimation using adaptive directional time-frequency distributions

Time-frequency distributions (TFDs) allow direction of arrival (DOA) estimation algorithms to be used in scenarios when the total number of sources are more than the number of sensors. The performance of such time–frequency (t–f) based DOA estimation algorithms depends on the resolution of the underlying TFD as a higher resolution TFD leads to better separation of sources in the t–f domain. This paper presents a novel DOA estimation algorithm that uses the adaptive directional t–f distribution (ADTFD) for the analysis of close signal components. The ADTFD optimizes the direction of kernel at each point in the t–f domain to obtain a clear t–f representation, which is then exploited for DOA estimation. Moreover, the proposed methodology can also be applied for DOA estimation of sparse signals. Experimental results indicate that the proposed DOA algorithm based on the ADTFD outperforms other fixed and adaptive kernel based DOA algorithms.     

Weighted least squares implementation of Cohen-Posch time-frequencydistributions

We present an improvement of the least-squares method of Sang et al. (see Proc. IEEE-SP Int. Symp. Time-Freq./Time-Scale Anal., p.165-8, 1996) for constructing nonnegative joint time-frequency distributions (TFDs) satisfying the time and frequency marginals (i.e., Cohen-Posch (1985) distributions). The proposed technique is a positivity constrained iterative weighted least-squares (WLS) algorithm used to modify an initial TFD (e.g., any bilinear TFD) to obtain a Cohen-Posch TFD. The new algorithm solves the “leakage” problem of the least-squares approach and is computationaly faster. Examples illustrating the performance of the new algorithm are presented. The results for the WLS method compare favorably with the minimum cross-entropy method previously developed by Loughlin et al. (1992)     

Adaptive instantaneous frequency estimation of multicomponent FMsignals using quadratic time-frequency distributions

An adaptive approach to the estimation of the instantaneous frequency (IF) of nonstationary mono- and multicomponent FM signals with additive Gaussian noise is presented. The IF estimation is based on the fact that quadratic time-frequency distributions (TFDs) have maxima around the IF law of the signal. It is shown that the bias and variance of the IF estimate are functions of the lag window length. If there is a bias-variance tradeoff, then the optimal window length for this tradeoff depends on the unknown IF law. Hence, an adaptive algorithm with a time-varying and data-driven window length is needed. The adaptive algorithm can utilize any quadratic TFD that satisfies the following three conditions: First, the IF estimation variance given by the chosen distribution should be a continuously decreasing function of the window length, whereas the bias should be continuously increasing so that the algorithm will converge at the optimal window length for the bias-variance tradeoff, second, the time-lag kernel filter of the chosen distribution should not perform narrowband filtering in the lag direction in order to not interfere with the adaptive window in that direction; third, the distribution should perform effective cross-terms reduction while keeping high resolution in order to be efficient for multicomponent signals. A quadratic distribution with high resolution, effective cross-terms reduction and no lag filtering is proposed. The algorithm estimates multiple IF laws by using a tracking algorithm for the signal components and utilizing the property that the proposed distribution enables nonparametric component amplitude estimation. An extension of the proposed TFD consisting of the use of time-only kernels for adaptive IF estimation is also proposed     

基于时频分布的欠定混叠盲分离

针对欠定混合信号的盲分离问题,提出了基于时频分布的欠定盲分离算法,首先计算信号的时频分布矩阵并找出信号的自源时频点,然后把自源点对应的时频分布矩阵表示成三阶张量并通过张量分解估计出混合矩阵,最后通过计算矩阵的伪逆和时频合成来完成源信号的恢复.该算法不需要假设源信号是稀疏的或相互独立的.仿真结果表明与已有算法相比本文方法...     

Exploiting In Situ Redox and Diffusion of Molybdenum to Enable Thin‐Film Circuitry for Low‐Cost Wireless Energy Harvesting

Direct additive fabrication of thin‐film electronics using a high‐mobility, wide‐bandgap amorphous oxide semiconductor (AOS) can pave the way for integration of efficient power circuits with digital electronics. For power rectifiers, vertical thin‐film diodes (V‐TFDs) offer superior efficiency and higher frequency operation compared to lateral thin‐film transistors (TFTs). However, the AOS V‐TFDs reported so far require additional fabrication steps and generally suffer from low voltage handling capability. Here, these challenges are overcome by exploiting in situ reactions of molybdenum (Mo) during the solution‐process deposition of amorphous zinc tin oxide film. The oxidation of Mo forms the rectifying contact of the V‐TFD, while the simultaneous diffusion of Mo increases the diode's voltage range of operation. The resulting V‐TFDs are demonstrated in a full‐wave rectifier for wireless energy harvesting from a commercial radio‐frequency identification reader. Finally, by using the same Mo film for V‐TFD rectifying contacts and TFT gate electrodes, this process allows simultaneous fabrication of both devices without any additional steps. The integration of TFTs alongside V‐TFDs opens a new fabrication route for future low‐cost and large‐area thin‐film circuitry with embedded power management.     

Underdetermined Blind Separation of Nondisjoint Sources in the Time-Frequency Domain

This paper considers the blind separation of nonstationary sources in the underdetermined case, when there are more sources than sensors. A general framework for this problem is to work on sources that are sparse in some signal representation domain. Recently, two methods have been proposed with respect to the time-frequency (TF) domain. The first uses quadratic time-frequency distributions (TFDs) and a clustering approach, and the second uses a linear TFD. Both of these methods assume that the sources are disjoint in the TF domain; i.e., there is, at most, one source present at a point in the TF domain. In this paper, we relax this assumption by allowing the sources to be TF-nondisjoint to a certain extent. In particular, the number of sources present at a point is strictly less than the number of sensors. The separation can still be achieved due to subspace projection that allows us to identify the sources present and to estimate their corresponding TFD values. In particular, we propose two subspace-based algorithms for TF-nondisjoint sources: one uses quadratic TFDs and the other a linear TFD. Another contribution of this paper is a new estimation procedure for the mixing matrix. Finally, then numerical performance of the proposed methods are provided highlighting their performance gain compared to existing ones     

New Time-Frequency Distribution

Cross terms are an inherent consequence of the second order nature of Cohen's class TFDs (Time-Frequency Distributions) [5], [6]. They are manifest in a TFD of multicomponent signals as spurious artifacts arising from interactions between the various signal components, and they can often appear at times and/or frequencies inconsistent with the underlying physical nature of the signal, causing misinterpretation [2], [3], [4]. There are many time frequency distributions that avoid the cross term effect; the best are the Choi-Williams ED (Exponential Distribution) [1] and Levin's IPS (Instantaneous Power Spectrum) [9]. In this paper we combine the cross term reducing philosophy of the ED and IPS to obtain a new TFD that most effectively reduces the cross term effect. Surprisingly, the new TFD also satisfies most desired TFD properties.     

基于条件对抗生成时频分布的多分量信号瞬时频率估计

瞬时频率（Instantaneous Frequency,IF）估计在多分量信号处理中具有重要意义,而现有方法在信号分量的IF曲线相近或相交时估计准确度不佳。针对这一问题,本文提出一种基于条件对抗生成时频分布的多分量信号IF估计方法。该方法首先采用时频分析产生信号的时频图像（例如掩膜维格纳分布）作为条件生成对抗网络（Conditional Generative Adversarial Networks, CGAN）的原始数据集,通过训练CGAN进行学习之后生成接近理想时频分布的时频图像。根据这些图像,本文利用一种改进的维特比算法提取出不同分量的IF曲线。其改进点在于增加了一个线段梯度的惩罚项,使维特比算法在分量相交的时频区域仍有准确的IF估计。实验结果表明,该方法能够有效且准确地估计分量相近或相交情况下信号的IF信息。      

An adaptive optimal-kernel time-frequency representation

Time-frequency representations with fixed windows or kernels figure prominently in many applications, but perform well only for limited classes of signals. Representations with signal-dependent kernels can overcome this limitation. However, while they often perform well, most existing schemes are block-oriented techniques unsuitable for on-line implementation or for tracking signal components with characteristics that change with time. The time-frequency representation developed in the present paper, based on a signal-dependent radially Gaussian kernel that adapts over time, surmounts these difficulties. The method employs a short-time ambiguity function both for kernel optimization and as an intermediate step in computing constant-time slices of the representation. Careful algorithm design provides reasonably efficient computation and allows on-line implementation. Certain enhancements, such as cone-kernel constraints and approximate retention of marginals, are easily incorporated with little additional computation. While somewhat more expensive than fixed kernel representations, this new technique often provides much better performance. Several examples illustrate its behavior on synthetic and real-world signals     

Multiple kernel relevance vector machine for geospatial objects detection in high-resolution remote sensing images

Geospatial objects detection within complex environment is a challenging problem in remote sensing area. In this paper, we derive an extension of the Relevance Vector Machine (RVM) technique to multiple kernel version. The proposed method learns an optimal kernel combination and the associated classifier simultaneously. Two feature types are extracted from images, forming basis kernels. Then these basis kernels are weighted combined and resulted the composite kernel exploits interesting points and appearance information of objects simultaneously. Weights and the detection model are finally learnt by a new algorithm. Experimental results show that the proposed method improve detection accuracy to above 88%, yields good interpretation for the selected subset of features and appears sparser than traditional single-kernel RVMs.     

基于能量峰区域时频滤波的信号估计

本文提出了一种基于能量峰时频区域滤波的信号估计方法。首先,设计了一种基于能量阈值的时频区域提取方法,识别出信号在时频面上的能量峰,并提取出能量峰所占据的时频区域;利用线性时频滤波器获取信号中的分量,将这些分量的时频分布叠加得到改善的时频分布。仿真结果表明,对于由时频不相交分量组成的信号,本方法可以分离出其中的信号分量,并能得到较优的时频分布。     

3-D shape estimation of DNA molecules from stereo cryo-electron micro-graphs using a projection-steerable snake.

We introduce a three-dimensional (3-D) parametric active contour algorithm for the shape estimation of DNA molecules from stereo cryo-electron micrographs. We estimate the shape by matching the projections of a 3-D global shape model with the micrographs; we choose the global model as a 3-D filament with a B-spline skeleton and a specified radial profile. The active contour algorithm iteratively updates the B-spline coefficients, which requires us to evaluate the projections and match them with the micrographs at every iteration. Since the evaluation of the projections of the global model is computationally expensive, we propose a fast algorithm based on locally approximating it by elongated blob-like templates. We introduce the concept of projection-steerability and derive a projection-steerable elongated template. Since the two-dimensional projections of such a blob at any 3-D orientation can be expressed as a linear combination of a few basis functions, matching the projections of such a 3-D template involves evaluating a weighted sum of inner products between the basis functions and the micrographs. The weights are simple functions of the 3-D orientation and the inner-products are evaluated efficiently by separable filtering. We choose an internal energy term that penalizes the average curvature magnitude. Since the exact length of the DNA molecule is known a priori, we introduce a constraint energy term that forces the curve to have this specified length. The sum of these energies along with the image energy derived from the matching process is minimized using the conjugate gradients algorithm. We validate the algorithm using real, as well as simulated, data and show that it performs well.     

Spatial averaging of time-frequency distributions for signalrecovery in uniform linear arrays

This paper presents a new approach based on spatial time-frequency averaging for separating signals received by a uniform linear antenna array. In this approach, spatial averaging of the time-frequency distributions (TFDs) of the sensor data is performed at multiple time-frequency points. This averaging restores the diagonal structure of the source TFD matrix necessary for source separation. With spatial averaging, cross-terms move from their off-diagonal positions in the source TFD matrix to become part of the matrix diagonal entries. It is shown that the proposed approach yields improved performance over the case when no spatial averaging is performed. Further, we demonstrate that in the context of source separation, the spatially averaged Wigner-Ville distribution outperforms the combined spatial-time-frequency averaged distributions, such as the one obtained by using the Choi-Williams (1989) distribution. Simulation examples involving the separation of two sources with close AM and FM modulations are presented     

Fast implementations of generalized discrete time-frequencydistributions

Cohen's class of time-frequency distributions (TFDs) have significant potential for the analysis of complex signals. In order to evaluate the TFD of a signal using its samples, discrete-time TFDs (DTFDs) have been defined as the Fourier transform of a smoothed discrete autocorrelation. Existing algorithms evaluate real-valued DTFDs using FFTs of the conjugate-symmetric autocorrelation. Although the computation required to smooth the autocorrelation is often greater than that for the FFT, there are no widely applicable fast algorithms for this part of the processing. Since the FFT is relatively inexpensive, downsampling is ineffective for reducing computation. If the DTFD needs only to be evaluated at a few frequencies for each time instant, the cost per time-frequency sample can be extremely high. The authors introduce two approaches for reducing the computation time of DTFDs. First, they define approximations to real-valued DTFDs, using spectrograms, that admit fast, space-saving evaluations. Frequency downsampling reduces the computation time of these approximations. Next, they define DTFDs that admit fast evaluations over sparse sets of time-frequency samples. A single short time Fourier transform is calculated in order for DTPD time-frequency samples to be evaluated at an additional, fixed cost per sample     

一种面向间隙核函数的快速算法

间隙核是一种应用非常广泛的字符串核,在文本分类和蛋白质分类中都取得了很好的效果.本文提出了一种应用在入侵检测领域的间隙核,称为长度加权核.并且提出了一种基于后缀核的动态规划算法,能够有效计算变长度加权核.另外,本文提出了一种位并行算法,能够加速定长度加权核的计算.实验表明在满足位并行的条件下这种快速算法比现有的几种计算间隙核的算法更为快速,而且应用在入侵检测中能够取得较好的效果.     

The running time-frequency distributions

This paper introduces the running kernels that yield recursive structures for time-frequency distributions (TFDs). The running kernels offer important properties not possessed by the commonly used block distribution kernels. The introduced kernels allow an invariance in computations with respect to the extent of the kernel in the time or the lag variable. However, contrary to the wide class of block kernels that satisfy the desired timefrequency (t-f) properties, most recursive (running) time-frequency distributions (RTFDs) violate the marginal and the support properties. This paper considers both the direct and the indirect types of recursion and presents examples for illustration.This research was supported in part by the US Air Force, grant no. AFOSR F49620-93-C0063 and a grant from the Office of Research and Sponsored Projects at Villanova University.     

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.     

基于熵调整模糊c-均值聚类的时频能量混合模型

本文提出了一种改进由时频不相交分量组成信号的双线性时频分布的分辨率和可读性的方法。用修正的Xie-Beni聚类有效性指标对熵调整模糊c-均值聚类算法进行拓展将模糊聚类与密度估计相结合,实现了信号时频分量的识别和建模;信号的时频能量混合模型给出了信号分量的数目及其在时频面上所占据的区域。这些信息可以用于分离信号分量,设计适合于每个分离分量的光滑核。仿真结果表明,对于由时频不相交分量组成的信号,本方法可以识别出其中的信号分量,并得到较优的时频分布。