Comparison between orthogonal subspace projection and background subtraction techniques applied to remote-sensing data

The basic measurement equation r = B + alphad + n is solved for alpha (the weight or abundance of the spectral target vector d) by two methods: (a) by subtracting the stochastic spectral background vector B from the spectral measurement's vector r (subtraction solution) and (b) by orthogonal subspace projection (OSP) of the measurements to a subspace orthogonal to B (the OSP solution). The different geometry of the two solutions and in particular the geometry of the noise vector n is explored. The angular distribution of the noise angle between B and n is the key factor for determining and predicting which solution is better. When the noise-angle distribution is uniform, the subtraction solution is always superior regardless of the orientation of the spectral target vector d. When the noise is more concentrated in the direction orthogonal to B, the OSP solution becomes better (as expected). Simulations and one-dimensional hyperspectral measurements of vapor concentration in the presence of background radiation and noise are given to illustrate these two solutions.     

Reflectance recovery for airborne sensor images of 3D scenes

An airborne sensor measures the radiance spectrum, which is dependent on the spectral reflectance of the ground material, the orientation of the material surface, and the atmospheric and illumination conditions. We present an algorithm to estimate the surface spectral reflectance, given the sensor radiance spectrum corresponding to a single pixel. The algorithm uses a nonlinear physics-based image formation model. A low-dimensional linear subspace model is used for the reflectance spectra. The solar radiance, sky radiance, and path-scattered radiance are dependent on the environmental conditions and viewing geometry, and this interdependence is considered by using a coupled-subspace model for these spectra. The algorithm uses the Levenberg-Marquardt method to estimate the subspace model parameters. We have applied the algorithm to a large set of synthetic and real data.     

Stochastic spectral unmixing with enhanced endmember class separation

Improvements to an algorithm for performing spectral unmixing of hyperspectral imagery based on the stochastic mixing model (SMM) are presented. The SMM provides a method for characterizing both subpixel mixing of the pure image constituents, or endmembers, and statistical variation in the endmember spectra that is due, for example, to sensor noise and natural variability of the pure constituents. Modifications of the iterative, expectation maximization approach to deriving the SMM parameter estimates are proposed, and their effects on unmixing performance are characterized. These modifications specifically concern algorithm initialization, random class assignment, and mixture constraints. The results show that the enhanced stochastic mixing model provides a better statistical representation of hyperspectral imagery from the perspective of achieving greater endmember class separation.     

基于CEM的高光谱图像小目标检测算法

针对高光谱图像中小目标检测问题,提出了一种基于约束能量最小化(Constrained Energy Minimization,CEM)的目标检测算法.该算法首先对原始图像进行背景信息抑制从而抑制背景地物、突出低概率的小目标,用迭代误差分析的自动端元提取算法找出目标的端元光谱,然后把目标端元光谱代入CEM滤波器得到该目标的检测结果图.用高光谱数据进行了实验研究,并与CEM滤波器进行了比较.结果表明,其检测性能与直接采用CEM方法的检测性能相当,但是相对于CEM方法,该算法不需要目标的先验光谱信息,更具有实用性.     

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.     

Constrained nonlinear method for estimating component spectra from multicomponent mixtures

A method is described for estimating the spectra of pure components from the spectra of unknown mixtures with various relative concentrations. This method is based on principal component analysis and a constrained nonlinear optimization technique and is applicable to qualitative analysis of mixtures of more than three components. The method gives two curves as the estimate of a component spectrum: one consists of the set of the maxima and the other consists of the set of the minima for all sampling points subject to a priori information. Experimental results of the estimation of the infrared absorption spectra of xylene-isomer mixtures are shown; the noise problem with this method is also discussed.     

Kernel-based spectral color image segmentation

In this work, we propose a new algorithm for spectral color image segmentation based on the use of a kernel matrix. A cost function for spectral kernel clustering is introduced to measure the correlation between clusters. An efficient multiscale method is presented for accelerating spectral color image segmentation. The multiscale strategy uses the lattice geometry of images to construct an image pyramid whose hierarchy provides a framework for rapidly estimating eigenvectors of normalized kernel matrices. To prevent the boundaries from deteriorating, the image size on the top level of the pyramid is generally required to be around 75 x 75, where the eigenvectors of normalized kernel matrices would be approximately solved by the Nystr?m method. Within this hierarchical structure, the coarse solution is increasingly propagated to finer levels and is refined using subspace iteration. In addition, to make full use of the abundant color information contained in spectral color images, we propose using spectrum extension to incorporate the geometric features of spectra into similarity measures. Experimental results have shown that the proposed method can perform significantly well in spectral color image segmentation as well as speed up the approximation of the eigenvectors of normalized kernel matrices.     

Characterization and mapping of carotenoids in the algae Dunaliella and Phaeodactylum using Raman and target orthogonal partial least squares

A method was developed for the characterisation of carotenoid pigments in algal species using Raman spectroscopy in combination with multivariate hyperspectral analysis. Target orthogonal partial least squares (T-OPLS) operates by designating one known reference spectrum as the target. The target spectrum is put as the single y column in an OPLS regression model where the X matrix consists of the unfolded image spectra as variables in its columns. The spectral shape of the OPLS first orthogonal target score enabled us to verify the peak positions of the standard, and detect new peaks, not present in the reference standard. It was shown that the mixture of carotenoids present in the algae did not fully match the reference spectrum, however, the method provided enough information to make an analysis possible also in this case. The image results were constructed from the OPLS loading vectors that were showing a correlation map for the reference spectrum from the predictive loadings and maps of the occurrence of deviations from the orthogonal loadings.     

Band-target entropy minimization (BTEM) applied to hyperspectral Raman image data

Band-target entropy minimization (BTEM) has been applied to extraction of component spectra from hyperspectral Raman images. In this method singular value decomposition is used to calculate the eigenvectors of the spectroscopic image data set. Bands in non-noise eigenvectors that would normally be used for recovery of spectra are examined for localized spectral features. For a targeted (identified) band, information entropy minimization or a closely related algorithm is used to recover the spectrum containing this feature from the non-noise eigenvectors, plus the next 5-30 eigenvectors, in which noise predominates. Tests for which eigenvectors to include are described. The method is demonstrated on one synthesized Raman image data set and two bone tissue specimens. By inclusion of small amounts of signal that would be unused in other methods, BTEM enables the extraction of a larger number of component spectra than are otherwise obtainable. An improvement in signal/noise ratio of the recovered spectra is also obtained.     

人体血糖无创测量中净信号的提取方法

提出了基于背景光谱构建噪声子空间提取葡萄糖净信号的方法,该方法不受参考浓度误差以及偶然相关因素的影响．对葡萄糖水溶液,以纯水为背景提取的葡萄糖净信号与传统方法的结果非常接近,相关系数达到0．9,且反映了葡萄糖的特征吸收信息．最后,在严格控制的实验条件下,对正常志愿者进行了活体口服葡萄糖耐量实验,并从生理状态不变的光谱构建的噪声子空间提取了血糖浓度变化导致的净信号．结果表明,口服葡萄糖耐量实验的漫反射光谱中的葡萄糖净信号,反映了葡萄糖分子在其一级倍频区域的特征吸收．这证实了左手掌部位采集的近红外光谱中确实携带了血糖浓度变化的信息．     

Recovering fluorescent spectra with an RGB digital camera and color filters using different matrix factorizations

The aim of a multispectral system is to recover a spectral function at each image pixel, but when a scene is digitally imaged under a light of unknown spectral power distribution (SPD), the image pixels give incomplete information about the spectral reflectances of objects in the scene. We have analyzed how accurately the spectra of artificial fluorescent light sources can be recovered with a digital CCD camera. The red-green-blue (RGB) sensor outputs are modified by the use of successive cutoff color filters. Four algorithms for simplifying the spectra datasets are used: nonnegative matrix factorization (NMF), independent component analysis (ICA), a direct pseudoinverse method, and principal component analysis (PCA). The algorithms are tested using both simulated data and data from a real RGB digital camera. The methods are compared in terms of the minimum rank of factorization and the number of sensors required to derive acceptable spectral and colorimetric SPD estimations; the PCA results are also given for the sake of comparison. The results show that all the algorithms surpass the PCA when a reduced number of sensors is used. The experimental results suggest a significant loss of quality when more than one color filter is used, which agrees with the previous results for reflectances. Nevertheless, an RGB digital camera with or without a prefilter is found to provide good spectral and colorimetric recovery of indoor fluorescent lighting and can be used for color correction without the need of a telespectroradiometer.     

Band-target entropy minimization. A robust algorithm for pure component spectral recovery. Application to complex randomized mixtures of six components

A newly developed self-modeling curve resolution method, band-target entropy minimization (BTEM), is described. This method starts with the data decomposition of a set of spectroscopic mixture data using singular value decomposition. It is followed by the transformation of the orthonormal basis vectors/loading vectors into individual pure component spectra one at a time. The transformation is based in part on some seminal ideas borrowed from information entropy theory with the desire to maximize the simplicity of the recovered pure component spectrum. Thus, the proper estimate is obtained via minimization of the proposed information entropy function or via minimization of derivative and area of the spectral estimate. Nonnegativity constraints are also imposed on the recovered pure component spectral estimate and its corresponding concentrations. As its name suggests, in this method, one targets a spectral feature readily observed in loading vectors to retain, and then combinations of the loading vectors are searched to achieve the global minimum value of an appropriate objective function. The major advantage of this method is its one spectrum at a time approach and its capability of recovering minor components having low spectroscopic signals. To illustrate the application of BTEM, spectral resolution was performed on FT-IR measurements of very highly overlapping mixture spectra containing six organic species with a two-component background interference (air). BTEM estimates were also compared with the estimates obtained using other self-modeling curve resolution techniques, i.e., SIMPLISMA, IPCA, OPA-ALS, and SIMPLISMA-ALS.     

Spectral pattern recognition of in situ FT-IR spectroscopic reaction data using minimization of entropy and spectral similarity (MESS): application to the homogeneous rhodium catalyzed hydroformylation of isoprene

An improved algorithm using minimization of entropy and spectral similarity (MESS) was tested to recover pure component spectra from in situ experimental Fourier transform infrared (FT-IR) reaction spectral data, which were collected from a homogeneous rhodium catalyzed hydroformylation of isoprene. The experimental spectra are complicated and highly overlapping because of the presence of multiple intermediate products in this reaction system. The traditional entropy minimization method fails to resolve real reaction mixture spectra, but MESS can successfully reconstruct pure component spectra of unknown intermediate products for real reaction systems by the addition of minimization of spectral similarity. The quantitative measure of spectral similarity between two spectra was given by their inner products. The results indicate that MESS is a stable and useful algorithm for spectral pattern recognition of highly overlapped experimental reaction spectra. Comparison is also made between MESS, entropy minimization, simple-to-use interactive self-modeling mixture analysis (SIMPLISMA), interactive principle component analysis (IPCA), and orthogonal projection approach-alternating least squares (OPA-ALS).     

Quantitative real-time blood flow estimation with intravascular ultrasound in the presence of in-plane flow

Previously, we showed a source of error in blood flow estimation introduced by in-plane flow using a slow-time finite-impulse response (FIR) filter-bank method measuring blood flow through the image plane of an intravascular ultrasound (IVUS) catheter array. There is a monotonic relationship between flow velocity and the normalized second moment of the slow-time spectrum when flow is orthogonal to the image plane of a side-looking catheter array. However, this relationship changes in the presence of in-plane flow, as slow-time spectra shift and spread with varying in-plane and out-of-plane components. These two effects increase the normalized spectral second moment, resulting in flow overestimates. However, by resampling the received signal with variable time delay from pulse to pulse (i.e., tilting the slow-time signals), the slow-time spectrum shifts back to direct current (DC), and the orthogonal estimation method can be used. We present a method to correct this overestimation and accurately estimate blood flow through the image plane in real time. Initially, the tilt delay needed to shift the slow-time spectrum back to DC at each point within the flow field is calculated. Knowing this tilt delay, a tilted slow-time signal is obtained for the velocity component normal to the image plane, and its spectrum is estimated using a filter-bank. That spectrum then is used to estimate the flow speed using a mapping function closely related to the monotonic relationship between the slow-time spectrum and flow speed observed for orthogonal flow. To accurately estimate flow angles, we modified the filter-bank algorithm, applying slow-time filter coefficients in a tilted arrangement and studying the slow-time spectral energy as a function of tilt. The slow-time spectral estimate is constructed with the tilted output of eight narrow, band-pass filters from a filter-bank. Independent simulations show that, for blood slowing at angles between +/-6 degrees and +/-15 degrees at a speed of 300 mm/s, flow velocity would be overestimated by as much as 38.79% and 249%, respectively, using the direct filter-bank approach. However, this error can be corrected using the modified method presented here, reducing the maximum overestimation error by a factor of 2.69 and 10.88 for those angles, respectively. Although the remaining error is not negligible, the volume flow rate, calculated by integrating the flow velocity over the entire vessel lumen, differs by only 3% or less from the true value over the angular range considered here. This represents an improvement of a factor of 40 over uncompensated estimates at maximum flow angles. Consequently, the modified real-time method can quantitatively measure flow in most IVUS applications in which the catheter's image plane is not precisely orthogonal to the flow direction.     

New indicator for optimal preprocessing and wavelength selection of near-infrared spectra

Preprocessing of near-infrared spectra to remove unwanted, i.e., non-related spectral variation and selection of informative wavelengths is considered to be a crucial step prior to the construction of a quantitative calibration model. The standard methodology when comparing various preprocessing techniques and selecting different wavelengths is to compare prediction statistics computed with an independent set of data not used to make the actual calibration model. When the errors of reference value are large, no such values are available at all, or only a limited number of samples are available, other methods exist to evaluate the preprocessing method and wavelength selection. In this work we present a new indicator (SE) that only requires blank sample spectra, i.e., spectra of samples that are mixtures of the interfering constituents (everything except the analyte), a pure analyte spectrum, or alternatively, a sample spectrum where the analyte is present. The indicator is based on computing the net analyte signal of the analyte and the total error, i.e., instrumental noise and bias. By comparing the indicator values when different preprocessing techniques and wavelength selections are applied to the spectra, the optimal preprocessing technique and the optimal wavelength selection can be determined without knowledge of reference values, i.e., it minimizes the non-related spectral variation. The SE indicator is compared to two other indicators that also use net analyte signal computations. To demonstrate the feasibility of the SE indicator, two near-infrared spectral data sets from the pharmaceutical industry were used, i.e., diffuse reflectance spectra of powder samples and transmission spectra of tablets. Especially in pharmaceutical spectroscopic applications, it is expected beforehand that the non-related spectral variation is rather large and it is important to remove it. The indicator gave excellent results with respect to wavelength selection and optimal preprocessing. The SE indicator performs better than the two other indicators, and it is also applicable to other situations where the Beer-Lambert law is valid.     

Fast self-quotient image method for lighting normalization based on modified Gaussian filter kernel

ABSTRACT

The Self-Quotient Image (SQI) Method [Wang H, Li SZ, Wang Y, et al. Self quotient image for face recognition. International Conference on Image Processing (ICIP’04); 2004;Vol. 2. p. 1397–1400; Wang H, Li SZ, Wang Y. Generalized quotient image. IEEE CVPR; 2004; Vol. 2. p. 498–505] is a simple method for lighting normalization based on the Quotient Image method [Shashua A, Riklin-Raviv T. The quotient image: class-based re-rendering and recognition with varying illuminations. T Pattern Anal Mach Intel. 2001;23(2):129–139; Riklin-Raviv T, Shashua A. The quotient image: class based recognition and synthesis under varying illumination. Proceedings of the 1999 Conference on Computer Vision and Pattern Recognition; 1999; Fort Collins (CO). p. 566–571]. The main advantage of the SQI is the use of only one image for lighting normalization. Nevertheless, the SQI still has few disadvantages which make hard to use it in some face recognition systems. In this paper, we introduce the modified version of the SQI method based on globally modified Gaussian filter kernel. In this modification, we tried to solve the disadvantages of the original SQI method, simplify the computational process, and increase the quality of illumination normalization. We have investigated two modification of the original SQI method and shown how they normalize different shadow regions.     

N-PSO: endmember extraction using advance particle swarm optimization for NLMM

This paper presents a fully unsupervised endmember extraction technique for hyperspectral image unmixing using nonlinear mixing model. The underlying idea of the model is that the pixel reflectances are nonlinear functions of pure spectral components contaminated by an additive noise. These nonlinear functions are approximated using polynomial functions, leading to a polynomial post-nonlinear mixing model (PPNM). In an unknown environment, the evaluation of the parameters involved in PPNM model is a tedious task, which is categorized as an NP hard problem. A method based on the combination of swarm intelligence, least-square (LS) and sub-gradient-based optimization (SO) is proposed to estimate the parameters involved in the model. The particle swarm optimization (PSO) is used to search the optimal endmember combination in the feasible solution space. The nonlinearity and respective abundances are evaluated using the LS and SO method, respectively. The proposed method is equipped with an adaptive tuning parameter-free mechanism and modified updating strategy. This strategy not only improves the result in terms of overall accuracy but also maintains physical constraints on the value of the resultant endmember set. The proposed method has been evaluated using simulated and real hyperspectral scenes. The experimental results on the hyperspectral scenes show that the proposed method obtains a higher extraction precision than those of the existing endmember extraction algorithms. Statistical analysis on a real hyperspectral image shows that the results obtain using N-PSO are 20–40% better than those from the existing approaches.     

Skin color correction for tissue spectroscopy: demonstration of a novel approach with tissue-mimicking phantoms

The application of partial least squares (PLS) regression to visible-near-infrared (VIS-NIR) spectroscopy for modeling important blood and tissue parameters is generally complicated by the variation in skin pigmentation (melanin) across the human population. An orthogonal correction method for removing the influence of skin pigmentation has been demonstrated in diffuse reflectance spectra from two-layer tissue-mimicking phantoms. The absorption properties of the phantoms were defined by lyophilized human hemoglobin (bottom layer) and synthetic melanin (top layer). Tissue-like scattering was simulated in both layers with intralipid. The approach uses principal components analysis (PCA) loading vectors from a separate set of phantom spectra that encode the unwanted melanin variation to remove the effect of melanin from the test phantoms. The preprocessing of phantom spectra using this orthogonal correction method resulted in PLS models with reduced complexity and enhanced prediction performance. Preliminary results from a separate study that evaluates the feasibility of defining skin color variation in an experiment with a single human subject are also presented.     

Transflectance spectra of faceted diamonds acquired by infrared microscopy

A novel transflectance technique using an infrared microscope was employed for spectral acquisition of loose and mounted faceted diamonds. The observed transflectance spectrum shows the same spectral features as those of the well-accepted diffuse reflectance spectrum. Unlike the diffuse reflectance spectrum, the transflectance spectrum was not affected by the diamond arrangements. The technique can be employed for direct spectra acquisition of mounted diamonds without taking the diamonds out of the jewelry bodies. Moreover, an individual diamond on a complex jewelry setting can be selectively measured. Infrared absorption bands unique to the chemical compositions, impurities, and treatment processes of the diamonds are discussed. The observed transflectance spectra can be exploited for diamond classification.     

基于全相位预处理的时域多重信号分类波达方向估计方法

低信噪比下,针对宽带短脉冲情况下频域多重信号分类(MUSIC)中噪声子空间估计不稳定问题,提出一种基于全相位预处理的时域多重信号分类波达方向(DOA)估计方法。①对线列阵接收数据进行分组处理;②按搜索角度对各组数据进行相移预处理,并对各组数据预处理结果进行相加,得到一组新数据;③对线列阵接收数据在时域构建相移后的协方差矩阵,在更短数据长度下,稳定实现噪声子空间估计,并依据估计出的噪声子空间含有的正交特性,通过单位矩阵加法器得到相应空间谱估计值,实现波达方向估计。数值仿真和实测数据处理结果表明,相比频域MUSIC方法,该方法有效提高了线列阵接收数据协方差矩阵中信号含有量和信噪比,能够在更短数据长度情况下实现对噪声子空间的稳定估计,具有较好的稳定性和检测性能,提高了MUSIC方法在实际波达方向估计中的鲁棒性。