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

POSE: Pseudo Object Space Error for Initialization-Free Bundle Adjustment

Bundle adjustment is a nonlinear refinement method for camera poses and 3D structure requiring sufficiently good initialization. In recent years, it was experimentally observed that useful minima can be reached even from arbitrary initialization for affine bundle adjustment problems (and fixed-rank matrix factorization instances in general). The key success factor lies in the use of the variable projection (VarPro) method, which is known to have a wide basin of convergence for such problems. In this paper, we propose the Pseudo Object Space Error (pOSE), which is an objective with cameras represented as a hybrid between the affine and projective models. This formulation allows us to obtain 3D reconstructions that are close to the true projective reconstructions while retaining a bilinear problem structure suitable for the VarPro method. Experimental results show that using pOSE has a high success rate to yield faithful 3D reconstructions from random initializations, taking one step towards initialization-free structure from motion

FLOW INJECTION AND MULTIVARIATE CALIBRATION TECHNIQUES FOR PROCESS ANALYSIS

The role of process analytical chemistry is summarised in chapter one with particular emphasis on a multidisciplinary approach and the instrumental requirements for on-plant analysis. These concepts are extended to process FIA, highlighting its potential for simultaneous multicomponent determinations. The development of an automated FIA monitor for the on-line determination of sulphite in potassium chloride brine is covered in the second chapter. Reaction stability is demonstrated and the results of on-plant validation and on-line trials are presented. The next chapter deals with the concepts of multivariate calibration. Direct multicomponent analysis, principal components regression and partial least squares regression are critically examined in practical spectroscopic terms and statistical terms. The relative predictive abilities of these techniques are compared in chapter four for the resolution of a multicomponent UV-visible spectrophotometric data set. Chapter five describes the development of an automated FIA-diode array system for the simultaneous determination of phosphate and chlorine. The implications of combining reaction chemistries and the influence of a number of calibration parameters are considered in detail. Finally, the jackknife is presented as a means of dimensionality estimation' and bias correction in PLS modelling. Data sets from the literature are analysed and the results compared with those obtaining using commercial software.ICI Chemicals & Polymer