High-resolution spectral analysis with arbitrary spectral centers and arbitrary spectral resolutions

Spectral decomposition via banks of narrowband filters is a classic method of analyzing broadband acoustic signals. FFT algorithms and hardware efficiently perform narrowband analysis but are limited to constant bandwidths at fixed spectral center frequencies. We develop a technique for processing FFT outputs to realize banks of narrowband filters for which spectral band centers and spectral bandwidths may be arbitrarily assigned. In particular we present spectral analyzer configurations with spectral centers uniformily spaced on a logarithmic scale and with bandwidths proportional to center frequencies (constant Q filters) or with bandwidths proportional to the square root of center frequencies (root-proportional filters for linear FM line tracking).     

High-resolution spectral video acquisition

Compared with conventional cameras, spectral imagers provide many more features in the spectral domain. They have been used in various fields such as material identification, remote sensing, precision agriculture, and surveillance. Traditional imaging spectrometers use generally scanning systems. They cannot meet the demands of dynamic scenarios. This limits the practical applications for spectral imaging. Recently, with the rapid development in computational photography theory and semiconductor techniques, spectral video acquisition has become feasible. This paper aims to offer a review of the state-of-the-art spectral imaging technologies, especially those capable of capturing spectral videos. Finally, we evaluate the performances of the existing spectral acquisition systems and discuss the trends for future work.     

基于多尺度图谱和局部谱的目标提取算法

针对多尺度图谱算法不能有效提取含有较多纹理或包含差异较大区域的目标物体, 提出了一种结合图像平滑、多尺度图谱和局部谱的目标提取方法。首先对图像进行l0梯度最小化平滑处理, 锐化边缘的同时消除图像的部分纹理信息; 其次通过多尺度图谱方法对图像进行分割, 该算法结合了归一化割算法的高精确度和多尺度算法的高效率性; 最后结合局部谱理论, 将人工选取的种子区域作为约束条件, 进行有偏割向量估计, 通过最大类间方差法将该向量分割成目标和背景。实验表明, 该方法弥补了多尺度图谱算法的不足, 并能产生很好的目标提取效果。     

Computing spectral sequences

John McCleary insisted in his interesting textbook entitled “User’s guide to spectral sequences” on the fact that the tool “spectral sequence” is not in the general situation an algorithm allowing its user to compute the looked-for homology groups. The present article explains how the notion of “Object with Effective Homology” on the contrary allows the user to recursively obtain all the components of the Serre and Eilenberg–Moore spectral sequences, when the data are objects with effective homology. In particular the computability problem of the higher differentials is solved, the extension problem at abutment is also recursively solved. Furthermore, these methods have been concretely implemented as an extension of the Kenzo computer program. Two typical examples of spectral sequence computations are reported.     

谱熵和谱减法在CMMB信道估计中的应用

基于谱熵和谱减法的信号检测方法在语音处理领域得到了广泛应用,但至今没有发现将这种方法应用于基于中国移动多媒体即CMMB（China Mobile Multimedia Broadcasting）标准的信道估计中。将这种方法用于基于CMMB标准的系统信道估计中;仿真结果表明,该方法在信噪比很低时,较传统的CMMB系统信道估计方法有较好的效果。     

Parallelism in spectral methods

Several strategies of parallelism for spectral algorithms are discussed. The investigation shows that, despite the intrinsic lack of locality of spectral methods, they are amenable to parallel implementations, even on fine grain architectures. Typical algorithms for the spectral approximation of the viscous, incompressible Navier-Stokes equations serve as examples in the discussion.     

并行谱聚类算法

谱聚类算法是建立在谱图理论上的一种点对聚类算法,具有实现简单、理论基础扎实和适应任意数据空间的优点,因而成为机器学习领域的研究热点.谱聚类算法最大的问题在于计算复杂度过高,而并行计算可以提高解题效率,因此本文采用最为流行的并行计算框架MAP/REDUCE在Hadoop环境中实现了并行谱聚类算法,大大改善了谱聚类算法在大规模数据环境中的聚类效率问题.     

改进的多尺度图谱和局部谱的目标提取算法

当目标对象与背景的纹理较多或两者纹理较接近时,基于多尺度图谱和局部谱的目标提取算法不能很好地提取目标,主要由于在计算相似度度量时,金字塔多尺度图谱算法特征选取较简单。针对算法不足,提出基于改进的金字塔多尺度图谱和局部谱相结合的目标提取算法,主要通过改进多尺度图谱中干涉轮廓权重构造方法,原算法中是基于拉普拉斯边缘图和梯度图,改进后是基于多尺度边缘概率检测算子和方向分水岭算法产生的边缘强度图。多尺度边缘概率检测算子可以有效地解决纹理较复杂图像分割不佳问题,方向分水岭算法可以有效解决由于目标和背景部分边界信息较接近导致的分割不佳问题。实验结果表明改进算法有效地弥补了原算法的不足,并且具有良好的目标提取效果。     

Semidefinite spectral clustering

Multi-way partitioning of an undirected weighted graph where pairwise similarities are assigned as edge weights, provides an important tool for data clustering, but is an NP-hard problem. Spectral relaxation is a popular way of relaxation, leading to spectral clustering where the clustering is performed by the eigen-decomposition of the (normalized) graph Laplacian. On the other hand, semidefinite relaxation, is an alternative way of relaxing a combinatorial optimization, leading to a convex optimization. In this paper we employ a semidefinite programming (SDP) approach to the graph equipartitioning for clustering, where sufficient conditions for strong duality hold. The method is referred to as semidefinite spectral clustering, where the clustering is based on the eigen-decomposition of the optimal feasible matrix computed by SDP. Numerical experiments with several data sets, demonstrate the useful behavior of our semidefinite spectral clustering, compared to existing spectral clustering methods.     

A spectral matching quality indicator for material mapping using spectral library search methods

Spectral library search methods are being used increasingly as an efficient approach for exploiting hyperspectral remotely sensed data in material identification and mapping applications. The aim of this study was to develop a quantitative method, using an indicator called the Quality factor (Q-factor), for providing quantitative information on the reliability of spectral identifications in the interpretation (classification) of unknown spectra by library search methods. This was achieved by summing the two main requirements of a typical reflectance spectral library search for material mapping: (1) a reliable correlation between spectral matching scores and material similarity, and (2) a reliable separation ability between the relevant and non-relevant parts of the candidate reference spectra. These form a metric whose values reflect the closeness of the output reference spectra to the input unknown spectra for a chosen library search method. The Q-factor was tested as an indicator of the reliability of the material identifications by the library search for a range of unknown reflectance spectra of various types of vegetation, soils and minerals collected from the US Geological Survey (USGS) Spectral Library and from our in-house spectral database. The results indicate that this approach has the potential to separate correct and incorrect spectral identifications resulting from a particular spectral library search method using a reference similarity logic. The method may be applied to any combination of deterministic spectral matching alternatives using reflectance spectra. Spectrum-level quality information provided by the Q-factor is useful for optimizing a particular search method or for choosing the most appropriate method for distinct identification and classification problems.     

Algebraic spectral multigrid methods

For the Helmholtz equation a spectral discretization with a symmetric and sparse matrix is presented. Certain algebraic spectral multigrid methods can be efficiently used for solving the linear systems.     

A comparison of error metrics and constraints for multiple endmember spectral mixture analysis and spectral angle mapper

Spectral matching algorithms can be used for the identification of unknown spectra based on a measure of similarity with one or more known spectra. Two popular spectral matching algorithms use different error metrics and constraints to determine the existence of a spectral match. Multiple endmember spectral mixture analysis (MESMA) is a linear mixing model that uses a root mean square error (RMSE) error metric. Spectral angle mapper (SAM) compares two spectra using a spectral angle error metric. This paper compares two endmember MESMA and SAM using a spectral library containing six land cover classes. RMSE and spectral angle for models within each land cover class were directly compared. The dependence of RMSE on the albedo of the modeled spectrum was also explored. RMSE and spectral angle were found to be closely related, although not equivalent, due to variations in the albedo of the modeled spectra. Error constraints applied to both models resulted in large differences in the number of spectral matches. Using MESMA, the number of spectra modeled within the error constraint increased as the albedo of the modeled spectra decreased. The value of the error constraint used was shown to make a much larger difference in the number of spectra modeled than the choice of spectral matching algorithm.     

Shock capturing by the spectral viscosity method

A main disadvantage of using spectral methods for nonlinear conservation laws lies in the formation of Gibbs phenomenon, once spontaneous shock discontinuities appear in the solution. The global nature of spectral methods then pollutes the unstable Gibbs oscillations over all the computational domain, and the lack of entropy dissipation prevents convergences in these cases. In this paper, we discuss the spectral viscosity method, which is based on high frequency-dependent vanishing viscosity regularization of the classical spectral methods. We show that this method enforces the convergence of nonlinear spectral approximations without sacrificing their overall spectral accuracy.     

多尺度的谱聚类算法

提出了一种多尺度的谱聚类算法。与传统谱聚类算法不同,多尺度谱聚类算法用改进的k-means算法对未经规范的Laplacian矩阵的特征向量进行聚类。与传统k-means算法不同,改进的k-means算法提出一种新颖的划分数据点到聚类中心的方法,通过比较聚类中心与原点的距离和引入尺度参数来计算数据点与聚类中心的距离。实验表明,改进算法在人工数据集上取得令人满意的结果,在真实数据集上聚类结果较优。     

Bipolar spectral associative memories

Nonlinear spectral associative memories are proposed as quantized frequency domain formulations of nonlinear, recurrent associative memories in which volatile network attractors are instantiated by attractor waves. In contrast to conventional associative memories, attractors encoded in the frequency domain by convolution may be viewed as volatile online inputs, rather than nonvolatile, off-line parameters. Spectral memories hold several advantages over conventional associative memories, including decoder/attractor separability and linear scalability, which make them especially well suited for digital communications. Bit patterns may be transmitted over a noisy channel in a spectral attractor and recovered at the receiver by recurrent, spectral decoding. Massive nonlocal connectivity is realized virtually, maintaining high symbol-to-bit ratios while scaling linearly with pattern dimension. For n-bit patterns, autoassociative memories achieve the highest noise immunity, whereas heteroassociative memories offer the added flexibility of achieving various code rates, or degrees of extrinsic redundancy. Due to linear scalability, high noise immunity and use of conventional building blocks, spectral associative memories hold much promise for achieving robust communication systems. Simulations are provided showing bit error rates for various degrees of decoding time, computational oversampling, and signal-to-noise ratio.     

Robust path-based spectral clustering

Spectral clustering and path-based clustering are two recently developed clustering approaches that have delivered impressive results in a number of challenging clustering tasks. However, they are not robust enough against noise and outliers in the data. In this paper, based on M-estimation from robust statistics, we develop a robust path-based spectral clustering method by defining a robust path-based similarity measure for spectral clustering under both unsupervised and semi-supervised settings. Our proposed method is significantly more robust than spectral clustering and path-based clustering. We have performed experiments based on both synthetic and real-world data, comparing our method with some other methods. In particular, color images from the Berkeley segmentation data set and benchmark are used in the image segmentation experiments. Experimental results show that our method consistently outperforms other methods due to its higher robustness.     

m序列频谱免疫度的研究

频谱免疫度是度量周期序列抵抗离散傅里叶频谱攻击的重要指标。周期序列的频谱免疫度越大,抵抗离散傅里叶频谱攻击的能力越强。通过搜索[m]序列的零化子,计算其频谱重量,提出猜想：[n]级[m]序列的零化子最低频谱重量是[n+1],而该[m]序列的补序列恰恰是其一个最低频重零化子。研究了[m]序列零化子及其补序列的性质,从理论上证明了该猜想。分析了[m]序列补序列的零化子性质,得出结论：[n]级[m]序列的频谱免疫度为[n];说明了[m]序列难以抵抗离散傅里叶频谱攻击。     

Canopy blockage and scattering effects on apparent soil spectral reflectance and its consequence in spectral mixture analysis of vegetated surfaces

Remote sensing technique has become the most efficient and common approach to estimate surface vegetation cover. Among various remote sensing algorithms, spectral mixture analysis (SMA) is the most common approach to obtain sub‐pixel surface coverage. In the SMA, spectral endmembers (the number of endmembers may vary), with invariant spectral reflectance across the whole image, are needed to conduct the mixture procedure. Although the nonlinear effect in quantifying vegetation spectral reflectance was noticed and sometimes addressed in the SMA analysis, the nonlinear effect in soil spectral reflectance is seldom discussed in the literature. In this paper, we investigate the effects of vegetation canopy on the inter‐canopy soil spectral reflectance via mathematical modelling and field measurements. We identify two mechanisms that lead to the difference between remotely sensed apparent soil spectral reflectance and actual soil spectral reflectance. One is a canopy blockage effect, leading to a reduced apparent soil spectral reflectance. The other is a canopy scattering effect, leading to an increased apparent soil spectral reflectance. Without correction, the first (second) mechanism causes an overestimated (underestimated) areal coverage of the low‐spectral‐reflectance endmember. The overall effect of canopy to soil, however, tends to overestimate fractional vegetation cover due to the relative significance of the canopy blockage effect, even though the two mechanisms vary with spectral wavelengths and spectral difference between different vegetation and soil. For the SMA of vegetated surface using multiple‐spectral remote sensing imagery (e.g., LandSat), it is recommended that infrared bands of low vegetation spectral reflectance (e.g. band 7) be first considered; if both visible and infrared bands are used, combination of bands 3, 4, and 5 is appropriate, while use of all six bands could overestimate fraction vegetation cover.     

Non-negative and sparse spectral clustering

Spectral clustering aims to partition a data set into several groups by using the Laplacian of the graph such that data points in the same group are similar while data points in different groups are dissimilar to each other. Spectral clustering is very simple to implement and has many advantages over the traditional clustering algorithms such as k-means. Non-negative matrix factorization (NMF) factorizes a non-negative data matrix into a product of two non-negative (lower rank) matrices so as to achieve dimension reduction and part-based data representation. In this work, we proved that the spectral clustering under some conditions is equivalent to NMF. Unlike the previous work, we formulate the spectral clustering as a factorization of data matrix (or scaled data matrix) rather than the symmetrical factorization of the symmetrical pairwise similarity matrix as the previous study did. Under the NMF framework, where regularization can be easily incorporated into the spectral clustering, we propose several non-negative and sparse spectral clustering algorithms. Empirical studies on real world data show much better clustering accuracy of the proposed algorithms than some state-of-the-art methods such as ratio cut and normalized cut spectral clustering and non-negative Laplacian embedding.     

Impacts of spectral band difference effects on radiometric cross-calibration between satellite sensors in the solar-reflective spectral domain

In order for quantitative applications to make full use of the ever-increasing number of Earth observation satellite systems, data from the various imaging sensors involved must be on a consistent radiometric scale. This paper reports on an investigation of radiometric calibration errors due to differences in spectral response functions between satellite sensors when attempting cross-calibration based on near-simultaneous imaging of common ground targets in analogous spectral bands, a commonly used post-launch calibration methodology. Twenty Earth observation imaging sensors (including coarser and higher spatial resolution sensors) were considered, using the Landsat solar reflective spectral domain as a framework. Scene content was simulated using spectra for four ground target types (Railroad Valley Playa, snow, sand and rangeland), together with various combinations of atmospheric states and illumination geometries. Results were obtained as a function of ground target type, satellite sensor comparison, spectral region, and scene content. Overall, if spectral band difference effects (SBDEs) are not taken into account, the Railroad Valley Playa site is a “good” ground target for cross calibration between most but not all satellite sensors in most but not all spectral regions investigated. “Good” is defined as SBDEs within ± 3%. The other three ground target types considered (snow, sand and rangeland) proved to be more sensitive to uncorrected SBDEs than the RVPN site overall. The spectral characteristics of the scene content (solar irradiance, surface reflectance and atmosphere) are examined in detail to clarify why spectral difference effects arise and why they can be significant when comparing different imaging sensor systems. Atmospheric gas absorption features are identified as being the main source of spectral variability in most spectral regions. The paper concludes with recommendations on spectral data and tools that would facilitate cross-calibration between multiple satellite sensors.