Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches

Imaging spectrometers measure electromagnetic energy scattered in their instantaneous field view in hundreds or thousands of spectral channels with higher spectral resolution than multispectral cameras. Imaging spectrometers are therefore often referred to as hyperspectral cameras (HSCs). Higher spectral resolution enables material identification via spectroscopic analysis, which facilitates countless applications that require identifying materials in scenarios unsuitable for classical spectroscopic analysis. Due to low spatial resolution of HSCs, microscopic material mixing, and multiple scattering, spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus, accurate estimation requires unmixing. Pixels are assumed to be mixtures of a few materials, called endmembers. Unmixing involves estimating all or some of: the number of endmembers, their spectral signatures, and their abundances at each pixel. Unmixing is a challenging, ill-posed inverse problem because of model inaccuracies, observation noise, environmental conditions, endmember variability, and data set size. Researchers have devised and investigated many models searching for robust, stable, tractable, and accurate unmixing algorithms. This paper presents an overview of unmixing methods from the time of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models are first discussed. Signal-subspace, geometrical, statistical, sparsity-based, and spatial-contextual unmixing algorithms are described. Mathematical problems and potential solutions are described. Algorithm characteristics are illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensin

Fuzzy Piecewise Linear Regression

International audienceFuzzy regression using possibilistic concepts allows the identification of models from uncertain data sets. However, some limitations still exist about the possible evolution of the output spread with respect to inputs. We present here a modified form of fuzzy linear model whose output can have any kind of output spread tendency. The formulation of the linear program used to identify the model introduces a modified criterion that assesses the model fuzziness independently of the collected data. These concepts are used in a global identification process in charge of building a piecewise model able to represent every kind of output evolution

Mathematical programming for piecewise linear regression analysis

In data mining, regression analysis is a computational tool that predicts continuous output variables from a number of independent input variables, by approximating their complex inner relationship. A large number of methods have been successfully proposed, based on various methodologies, including linear regression, support vector regression, neural network, piece-wise regression, etc. In terms of piece-wise regression, the existing methods in literature are usually restricted to problems of very small scale, due to their inherent non-linear nature. In this work, a more efficient piece-wise linear regression method is introduced based on a novel integer linear programming formulation. The proposed method partitions one input variable into multiple mutually exclusive segments, and fits one multivariate linear regression function per segment to minimise the total absolute error. Assuming both the single partition feature and the number of regions are known, the mixed integer linear model is proposed to simultaneously determine the locations of multiple break-points and regression coefficients for each segment. Furthermore, an efficient heuristic procedure is presented to identify the key partition feature and final number of break-points. 7 real world problems covering several application domains have been used to demonstrate the efficiency of our proposed method. It is shown that our proposed piece-wise regression method can be solved to global optimality for datasets of thousands samples, which also consistently achieves higher prediction accuracy than a number of state-of-the-art regression methods. Another advantage of the proposed method is that the learned model can be conveniently expressed as a small number of if-then rules that are easily interpretable. Overall, this work proposes an efficient rule-based multivariate regression method based on piece-wise functions and achieves better prediction performance than state-of-the-arts approaches. This novel method can benefit expert systems in various applications by automatically acquiring knowledge from databases to improve the quality of knowledge base

Joint segmentation of multivariate time series with hidden process regression for human activity recognition

The problem of human activity recognition is central for understanding and predicting the human behavior, in particular in a prospective of assistive services to humans, such as health monitoring, well being, security, etc. There is therefore a growing need to build accurate models which can take into account the variability of the human activities over time (dynamic models) rather than static ones which can have some limitations in such a dynamic context. In this paper, the problem of activity recognition is analyzed through the segmentation of the multidimensional time series of the acceleration data measured in the 3-d space using body-worn accelerometers. The proposed model for automatic temporal segmentation is a specific statistical latent process model which assumes that the observed acceleration sequence is governed by sequence of hidden (unobserved) activities. More specifically, the proposed approach is based on a specific multiple regression model incorporating a hidden discrete logistic process which governs the switching from one activity to another over time. The model is learned in an unsupervised context by maximizing the observed-data log-likelihood via a dedicated expectation-maximization (EM) algorithm. We applied it on a real-world automatic human activity recognition problem and its performance was assessed by performing comparisons with alternative approaches, including well-known supervised static classifiers and the standard hidden Markov model (HMM). The obtained results are very encouraging and show that the proposed approach is quite competitive even it works in an entirely unsupervised way and does not requires a feature extraction preprocessing step

Fully automated segmentation and tracking of the intima media thickness in ultrasound video sequences of the common carotid artery

Abstract—The robust identification and measurement of the intima media thickness (IMT) has a high clinical relevance because it represents one of the most precise predictors used in the assessment of potential future cardiovascular events. To facilitate the analysis of arterial wall thickening in serial clinical investigations, in this paper we have developed a novel fully automatic algorithm for the segmentation, measurement, and tracking of the intima media complex (IMC) in B-mode ultrasound video sequences. The proposed algorithm entails a two-stage image analysis process that initially addresses the segmentation of the IMC in the first frame of the ultrasound video sequence using a model-based approach; in the second step, a novel customized tracking procedure is applied to robustly detect the IMC in the subsequent frames. For the video tracking procedure, we introduce a spatially coherent algorithm called adaptive normalized correlation that prevents the tracking process from converging to wrong arterial interfaces. This represents the main contribution of this paper and was developed to deal with inconsistencies in the appearance of the IMC over the cardiac cycle. The quantitative evaluation has been carried out on 40 ultrasound video sequences of the common carotid artery (CCA) by comparing the results returned by the developed algorithm with respect to ground truth data that has been manually annotated by clinical experts. The measured IMTmean ± standard deviation recorded by the proposed algorithm is 0.60 mm ± 0.10, with a mean coefficient of variation (CV) of 2.05%, whereas the corresponding result obtained for the manually annotated ground truth data is 0.60 mm ± 0.11 with a mean CV equal to 5.60%. The numerical results reported in this paper indicate that the proposed algorithm is able to correctly segment and track the IMC in ultrasound CCA video sequences, and we were encouraged by the stability of our technique when applied to data captured under different imaging conditions. Future clinical studies will focus on the evaluation of patients that are affected by advanced cardiovascular conditions such as focal thickening and arterial plaques

Conductance-based interface detection for multi-phase pipe flow

Sediment and flow depth monitoring in sewers is important for informing flow models and for predicting and mitigating against sewer blockage formation and surcharge. In this study, a novel sensor based on conductance measurement has been developed and tested under a laboratory environment and validated by a finite-element model. The relative conductance is measured between pairs of adjacent electrodes to provide a conductance profile along the sensor length. A piecewise linear relationship between conductance and electrode length was derived and the interface positions between sediment, water, and air can be determined from the profile. The results demonstrated that the root mean square error of the model and the measured interface level are within 1.4% and 2.6% of sensor’s measurement range. An error distribution of interface height shows that all anticipated errors are within the resolution of the electrode length increments. Furthermore, it was found that the conductivity of the measured medium is proportional to the gradient of the linear relationship of conductance and electrode length. It could therefore prove a valuable new tool for the accurate quantification of sediment and flow levels in sewer conduits, coastal environments, drainage systems for transport networks, and other industrial or academic applications