Comments on "comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data"

Ben-David and Ren [Appl. Opt. 44, 3846 (2005)] discussed methods of estimating the concentration of chemical vapor plumes in hyperspectral images. The authors of that paper concluded that a technique called orthogonal subspace projection (OSP) produces better concentration estimates than background subtraction when certain stochastic noise conditions are present in the data. While that conclusion is correct, it is worth noting that the data can be whitened to improve the performance of the background subtraction method. In particular, if the noise is multivariate Gaussian, then whitening will ensure that the background subtraction method is superior to OSP.     

Highlight detection and removal from spectral image

We present a constrained spectral unmixing method to remove highlight from a single spectral image. In the constrained spectral unmixing method, the constraints have been imposed so that all the fractions of diffuse and highlight reflection sum up to 1 and are positive. As a result, the spectra of the diffuse image are always positive. The spectral power distribution (SPD) of the light source has been used as the pure highlight spectrum. The pure diffuse spectrum of the measured spectrum has been chosen from the set of diffuse spectra. The pure diffuse spectrum has a minimum angle among the angles calculated between spectra from a set of diffuse spectra and the measured spectrum projected onto the subspace orthogonal to the SPD of the light source. The set of diffuse spectra has been collected by an automated target generation program from the diffuse part in the image. Constrained energy minimization in a finite impulse response linear filter has been used to detect the highlight and diffuse parts in the image. Results by constrained spectral unmixing have been compared with results by the orthogonal subspace projection (OSP) method [Proceedings of International Conference on Pattern Recognition (2006), pp. 812-815] and probabilistic principal component analysis (PPCA) [Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (2005), paper 15]. Constrained spectral unmixing outperforms OSP and PPCA in the visual assessment of the diffuse results. The highlight removal method by constrained spectral unmixing is suitable for spectral images.     

Sparse Deconvolution Methods for Ultrasonic NDT

In this work we present two sparse deconvolution methods for nondestructive testing. The first method is a special matching pursuit (MP) algorithm in order to deconvolve the mixed data (signal and noise), and thus to remove the unwanted noise. The second method is based on the approximate Prony method (APM). Both methods employ the sparsity assumption about the measured ultrasonic signal as prior knowledge. The MP algorithm is used to derive a sparse representation of the measured data by a deconvolution and subtraction scheme. An orthogonal variant of the algorithm (OMP) is presented as well. The APM technique also relies on the assumption that the desired signals are sparse linear combinations of (reflections of) the transmitted pulse. For blind deconvolution, where the transducer impulse response is unknown, we offer a general Gaussian echo model whose parameters can be iteratively adjusted to the real measurements. Several test results show that the methods work well even for high noise levels. Further, an outlook for possible applications of these deconvolution methods is given.     

Comparison of methods for reducing the effects of scattering in spectrophotometry

Light scattering provides a problem in optical spectroscopy as the relationship between attenuation and absorption in the presence of scattering is nonlinear. Three simple methods of reducing the effects of scattering and hence returning to an approximately linear relationship are considered in this paper, namely, extracting light that has maintained its original polarization state through subtraction of orthogonal polarization states, use of an added absorber, and spatial filtering. These can all be applied relatively easily to conventional spectrophotometers. However, there is an inevitable trade-off between the accuracy of the measurement and the signal-to-noise ratio as scattered light is rejected from the detector. It is demonstrated that polarization subtraction is the most efficient technique at selecting weakly scattered photons from a scattered light background as it enables the relationship between attenuation and absorption coefficient to become more linear while maintaining a higher number of detected photons. In practical use, the drawback of polarization subtraction over added absorber and spatial filtering methods is that a large dc background light level is maintained, which contributes to a higher shot noise. This means that when the scattering coefficient is high (micros > or = 7 mm(-1)) the added absorber method offers better performance for shot noise limited detection.     

非一致性噪声条件下的特征空间波束形成

由于水声环境的复杂性,阵列的噪声分布可能是非一致性的。当阵元噪声功率各不相同时,阵列协方差矩阵特征分解得到的特征子空间与真实目标的特征子空间之间存在误差,导致特征子空间波束形成算法的性能衰减。文章提出了一种新的非一致性噪声条件下特征子空间的估计方法,将阵列协方差矩阵对角线置0,进行特征分解估计的特征子空间将不受阵元噪声非一致性的影响。将该方法应用到特征空间波束形成算法,提高了非一致性噪声条件下特征空间波束形成算法的方位分辨能力。仿真和实验结果验证了所提方法的可行性和有效性。     

Distortions of the extinction coefficient profile caused by systematic errors in lidar data

The influence of lidar data systematic errors on the retrieved particulate extinction coefficient profile in clear atmospheres is investigated. Particularly, two sources of the extinction coefficient profile distortions are analyzed: (1) a zero-line offset remaining after subtraction of an inaccurately determined signal background component and (2) a far-end incomplete overlap due to poor adjustment of the lidar system optics. Inversion results for simulated lidar signals, obtained with the near- and far-end solutions, are presented that show advantages of the near-end solution for clear atmospheres.     

一种低信噪比环境下的语音端点检测算法

端点检测技术是语音信号处理的关键技术之一，为提高低信噪比环境下端点检测的准确率和稳健性，提出了一种非平稳噪声抑制和调制域谱减结合功率归一化倒谱距离的端点检测算法。该算法首先通过抑制非平稳噪声再采用调制域谱减消除残余噪声来提升信噪比，减少语音失真。然后再提取每帧信号的功率归一化倒谱系数，计算每帧信号与背景噪声的功率归一化倒谱距离。最后将该倒谱距离作为检测参数，采用双门限判决方法进行端点检测。实验结果表明，该端点检测算法对语音帧和噪声帧具有较好的区分性。此外，在低信噪比环境下，所提出的算法对于不同类型的噪声都具有较好的稳健性。     

一种基于统计模型的改进谱减降噪算法

提出了基于语音和噪声的傅里叶系数服从统计模型分布的假设,将基于统计模型的信噪比更新和噪声更新的方法应用于谱减法,试图解决传统谱减法中存在的音乐噪声和语音失真的问题。将提出算法与多通道谱减法和基于对数的最小均方幅度谱估计方法进行客观评价分析。利用频率加权分段信噪比评价方法、语音质量感知评价及综合质量测量等3种指标进行去噪效果评价。结果表明,所提出的基于统计模型的降噪算法效果优于MBSS,且接近Log-MMSE。     

Object localization in the presence of a strong heterogeneous background in fluorescent tomography

We propose a method for object localization in fluorescent tomography (FT) in the presence of a highly heterogeneous background. Existing approaches typically assume a homogeneous background distribution; thus, they are incapable of accurately accounting for the more general case of an unconstrained, possibly heterogeneous, background. The proposed method iteratively solves the inverse problem over a solution space partitioned into a background subspace and an object subspace to simultaneously estimate the background and localize the target fluorescent objects. Simulation results of this algorithm applied to continuous-wave FT demonstrate effective localization of target objects in the presence of highly heterogeneous background distributions.     

插值正交向量尺度函数

插值正交尺度函数在抽样理论、信号处理和计算机图形学等方面有重要应用,本文给出了紧支撑正交插值向量尺度函数的定义,并对它们进行了刻画。我们证明了向量小波子空间的抽样定理问题能被转化为每个分量所在的闭空间的抽样定理问题。进一步,我们得到了向量小波子空间中抽样定理的具体表达形式。最后,我们构造了两个例子。     

I-V and low frequency noise characterization of poly and amorphous silicon Ti- and Co-salicide resistors

Accurate characterization of polysilicon resistors can help in the design and the fabrication of deep-sub-micron CMOS technologies. In this paper we have studied poly and amorphous silicon Ti- and Co-salicide resistors. In order to discriminate between contact and bulk material contribution transmission line model (TLM) test structures are well adapted for both current-voltage (I-V) and low frequency noise (LFN) characterization. Measurements are undertaken as a function of the geometry (inter-electrode length and electrode width) and of the bias current.From I-V measurements sheet resistance of the different bulk materials (poly or amorphous silicon) and contact resistances of the two different processes (TiSi₂ or CoSi₂) are extracted.Experimentally noise voltage spectral density is measured and converted in resistance spectral density. Noise spectra were always fitted with a 1/f component and white noise. Then, like for I-V characterization (i.e. analyzing the noise of different sample lengths), the contact and bulk 1/f noise contribution is extracted. When contact noise is found to be negligible, bulk material noise is directly modelled according to Hooge relation; otherwise we can only estimate the bulk material. Then the normalised α parameter is used to compare material quality.     

噪声背景下目标线谱提取方法研究

利用目标线谱与自噪声线谱在时间域和空间域上的差异,采用时空联合手段研究舰船噪声中目标线谱的提取方法。文中具体讨论了连续谱背景下线谱的提取方法以及舷侧阵中自噪声线谱与目标线谱的分离方法。海上实验数据处理结果表明了该方法的有效性。     

Detection,identification, and estimation of biological aerosols and vapors with a Fourier-transform infrared spectrometer

Two experiments were conducted with a Fourier-transform infrared (FTIR) spectrometer. The purpose of the first experiment was to detect and identify Bacillus subtilis subsp. niger (BG) bioaerosol spores and kaolin dust in an open-air release for which the thermal contrast between the aerosol temperature and background brightness temperature is small. The second experiment estimated the concentration of a small amount of triethyl phosphate (TEP) vapor in a closed chamber in which an external blackbody radiation source was used and where the thermal contrast was large. The deduced BG (TEP) extinction spectrum (identification) showed an excellent match to the library BG (TEP) extinction spectrum. Analysis of the time sequence of the measurements coincided well with the presence (detection) of the BG during the measurements, and the estimated concentration of time-dependent TEP vapor was excellent. The data were analyzed with hyperspectral detection, identification, and estimation algorithms. The algorithms were based on radiative transfer theory and statistical signal-processing methods. A subspace orthogonal projection operator was used to statistically subtract the large thermal background contribution to the measurements, and a robust maximum-likelihood solution was used to deduce the target (aerosol or vapor cloud) spectrum and estimate its mass-column concentration. A Gaussian-mixture probability model for the deduced mass-column concentration was computed with an expectation-maximization algorithm to produce the detection threshold, the probability of detection, and the probability of false alarm. The results of this study are encouraging, as they suggest for the first time to the authors' knowledge the feasibility of detecting biological aerosols with passive FTIR sensors.     

Interpreting anomalously low voltage noise in two-channel measurement systems

In this work we 1) analyze and give a theoretical explanation for the anomalously low cross-spectral density of voltage fluctuations that is observed when two thermal noise sources with matched intensities are coupled to the inputs of two-channel phase modulation (PM) or amplitude modulation (AM) noise measurement systems (NMS), 2) empirically evaluate spectral resolutions of different types of measurement systems, and 3) discuss noise measurement techniques involving cross-correlation signal processing. Our work shows that the statistical uncertainty, which sets the ultimate spectral resolution in the thermal noise limited regime, is approximately the same for both systems. However, in practical terms, the non-stationary nature of the noise, the temporal separation of calibration and measurement, and the difficulty of reproducing the calibrations for two measurements make it extremely difficult to resolve noise that is more than 10 dB below the noise floor in a single channel NMS. In a two-channel NMS, however, the calibrations of the two channels are carried out simultaneously, and one can take full advantage of a large number of averages and make reproducible noise measurements with resolution 10 dB below the noise floor of a single channel NMS     

Digital filtering implementations for the detection of broad spectral features by direct analysis of passive Fourier transform infrared interferograms

Finite impulse response (FIR) filters and finite impulse response matrix (FIRM) filters are evaluated for use in the detection of volatile organic compounds with wide spectral bands by direct analysis of interferogram data obtained from passive Fourier transform infrared (FT-IR) measurements. Short segments of filtered interferogram points are classified by support vector machines (SVMs) to implement the automated detection of heated plumes of the target analyte, ethanol. The interferograms employed in this study were acquired with a downward-looking passive FT-IR spectrometer mounted on a fixed-wing aircraft. Classifiers are trained with data collected on the ground and subsequently used for the airborne detection. The success of the automated detection depends on the effective removal of background contributions from the interferogram segments. Removing the background signature is complicated when the analyte spectral bands are broad because there is significant overlap between the interferogram representations of the analyte and background. Methods to implement the FIR and FIRM filters while excluding background contributions are explored in this work. When properly optimized, both filtering procedures provide satisfactory classification results for the airborne data. Missed detection rates of 8% or smaller for ethanol and false positive rates of at most 0.8% are realized. The optimization of filter design parameters, the starting interferogram point for filtering, and the length of the interferogram segments used in the pattern recognition is discussed.     

Model reduction from partial observations

This paper deals with model‐order reduction of parametric partial differential equations (PPDEs). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial information on the latter is available. We assume that 2 sources of information are available: (a) a “rough” prior knowledge taking the form of a manifold containing the target solution manifold and (b) partial linear measurements of the solutions of the PPDE (the term partial refers to the fact that observation operators cannot be inverted). We provide and study several tools to derive good approximation subspaces from these 2 sources of information. We first identify the best worst‐case performance achievable in this setup and propose simple procedures to approximate the corresponding optimal approximation subspace. We then provide, in a simplified setup, a theoretical analysis relating the achievable reduction performance to the choice of the observation operator and the prior knowledge available on the solution manifold.     

Partial least squares based decomposition of five spectrally overlapping factors

The development of a multi-sensory fiber-optic based fluence rate probe (MSP) for light monitoring and dosimetry during photodynamic therapy (PDT) created the need for a robust multivariate signal analysis algorithm capable of quantifying the intensity of five component spectra, representing the sensors, which display a large degree of spectral overlap. Partial least squares (PLS) analysis, as an option for such an analysis algorithm, was evaluated through simulations in the presence of three types of noise, which experimentally may limit the accuracy of PLS quantification of component spectra contributions. Random, or white noise, background was varied over a range of 0-15% relative intensity. A non-random (Gaussian) background vector was simulated, as an experimentally relevant spectral interferent, over a range of 0-7% relative intensity. Spectral variation was modeled by a spectral shift of +/-1-5 nm. Procedures for selecting preferred combinations of fluorophores, with minimum possible spectral overlap, were developed. To illustrate the importance of this selection process, PLS performance results were compared for two possible combinations of five fluorophores, as well as for the combination of three fluorophores currently in experimental use with MSPs. Experimentally anticipated worst-case quantifications were identified for all three types of simulated noise (5% random background, 0.5% Gaussian background, and +/-2 nm spectral shift). The effects of single and combined types of noise were evaluated by independently varying each type of simulated noise over the experimentally relevant range. The mean percentage error in determining the fluorophore contributions and hence quantification of the fluence rate were compared with the required performance standard of better than 10% error for optical power meters in medical use. The PLS algorithm provided an accuracy of 7 +/- 2% for five fluorophores and 3.3 +/- 0.8% for three fluorophores, indicating that PLS is an appropriate choice for this application.     

Invalidity of the spectral Fokker–Planck equation for Cauchy noise driven Langevin equation

The standard Langevin equation is a first order stochastic differential equation where the driving noise term is a Brownian motion. The marginal probability density is a solution to a linear partial differential equation called the Fokker–Planck equation. If the Brownian motion is replaced by so-called -stable noise (or Lévy noise) the Fokker–Planck equation no longer exists as a partial differential equation for the probability density because the property of finite variance is lost. Instead it has been attempted to formulate an equation for the characteristic function (the Fourier transform) corresponding to the density function. This equation is frequently called the spectral Fokker–Planck equation.

This paper raises doubt about the validity of the spectral Fokker–Planck equation in its standard formulation. The equation can be solved with respect to stationary solutions in the particular case where the noise is Cauchy noise and the drift function is a polynomial that allows the existence of a stationary probability density solution. The solution shows paradoxic properties by not being unique and only in particular cases having one of its solutions closely approximating the solutions to a corresponding Langevin difference equation. Similar doubt can be traced Grigoriu's work [Stochastic Calculus (2002)].     

In-band optical signal-to-noise ratio monitoring method based on high-resolution polarization analysis and induced differential group delay

We report on an in-band optical signal-to-noise ratio monitoring technique for wavelength division multiplexed channels. Our proposal relies on the different degree of polarization between the signal (highly polarized) and the noise (not polarized). Using this principle, we divide the signal under test into two orthogonal polarization components and induce a differential group delay via a controlled birefringence apparatus that produces a wavelength-dependent shift of the polarization state of the signal. After a linear polarizing filter, high-resolution spectral analysis allows measurement of the amplified spontaneous emission noise level. The method is tested by experimental measurements of a 40 Gbit/s differential phase-shift keying channel showing very good performance.     

An inverse Stokes problem using interior pressure data

An inverse boundary value problem associated to the Stokes equations in a domain of two dimensions is considered. This problem requires the determination of the unspecified surface fluid velocity, or one of its components, over a part of its boundary by introducing extra interior pressure measurements. The problem is discretised numerically using the boundary element method (BEM) and the resulting ill-conditioned system of linear algebraic equations is solved using the Tikhonov regularisation method, with the choice of the regularisation parameter based on the L-curve criterion. The numerical technique is validated for some test examples with known analytical solutions. The accuracy of the numerical solutions is checked by comparison with their corresponding exact values and an investigation into stability of the numerical solution is undertaken by the addition of random noise into the interior pressure measurements. It is shown that the BEM provides a stable numerical solution of the Stokes problem which converges to the exact solution as the magnitude of error in the interior data decreases.