Sampling scheme optimization from hyperspectral data

This thesis presents statistical sampling scheme optimization for geo-environ-menta] purposes on the basis of hyperspectral data. It integrates derived products of the hyperspectral remote sensing data into individual sampling schemes. Five different issues are being dealt with.

First, the optimized sampling scheme is presented to select samples that represent different ontological categories. The iterated conditional modes algorithm (ICM) is used as an unsupervised segmentation technique. Within each cate-gory, simulated annealing is applied for minimizing the mean shortest distance (MMSD) between sampling points. The number of sampling points in each category is proportional to the size and variability' of the category. The combination of the ICM algorithm for image segmentation with simulated annealing for optimized sampling, results in an elegant and powerful tool in designing optimal sampling schemes using remote sensing images. A validation study conducted shows that the optimized sampling scheme gives best estimates for commonly used vegetation indices compared to simple random sampling and rectangular grid sampling.

Next, optimal sampling schemes, which focus on ground verification of minerals derived from hyperspectral data, are presented. Spectral angle mapper {SAM) and spectral feature fitting (SFF) classification techniques are applied to obtain rule mineral images. The rule images provide weights that are utilized in objective functions of the sampling schemes which are optimized by means of simulated annealing. Three weight, functions intensively sample areas where a high probability and abundance of al unite occurs. Weight function I uses binary weights derived from the SAM classification image, leading to an even distribution of sampling points over the region of interest. Weight function II uses scaled weights derived from the SAM rule image. Sample points are arranged more intensely in areas where there is an abundance of al unite. Weight function III combines information from several different rule image classifications. Sampling points are distributed more intensely in regions of high probable alu-nite as classified by both SAM and SFF, thus representing the purest of pixels. This method leads to an efficient distribution of sample points, on the basis of a user-defined objective.

This is followed by a quantitative method for optimally locating exploration targets based on a probabilistic mineral prospectivity map. which was created by means of weights-of-evidence (WofE) modeling. Locations of discovered mineral occurrences were used as a training set and a map of distances to faults/fractures and three channel ratio images of HyMap hyperspectral data were used as evidences. The WofE posterior probability map was applied to an objective function that optimized location of exploration targets. Optimized exploration target zones spatially coincide with undiscovered mineral occurrences, namely, those not used to train the WofE model input, and show other zones without mineral occurrences within delineated prospective ground. The results indicate usefulness of the described optimization method to allocate exploration targets for undiscovered mineral occurrence, based on probabilistic mineral prospectiv-ity maps.

A method for estimating the partial abundance of spectrally similar minerals in complex mixtures follows. Linear mixtures are generated with varying proportions of individual spectrum, from a spectral library, of a set of iron-bearing oxide/hydroxide/sulfate minerals. The first and second derivatives of each of the different sets of mixed spectra and the individual spectrum are evaluated. This method for spectral unmixing requires formulating a linear function of individual spectra of the minerals. The error between these derivative functions and the respective derivative function of the mixed spectrum is minimized by means of simulated annealing. Experiments are made on several different mixtures of selected end-members, which could plausibly occur in real situations. The variance of the differences between the second derivatives of the observed spectrum and the second derivatives of the end-member spectra give most precise estimates for the abundance of each end-member.

Lastly, a method by which an optimal ground sampling scheme can be obtained for a variable of interest is described. The variable of interest is the spatial distribution of a suite of heavy metals in mine tailings. Derivation of an optimal sampling scheme makes use of covariates of the spatial variable of interest, which are readily but less accurately obtainable by using airborne hyperspectral data. The covariates are abundances of secondary iron-bearing minerals estimated through spectral unmixing. Via simulated annealing, an optimal retrospective sampling scheme for a previously sampled area is derived having fewer samples but having almost equal mean kriging prediction error as the original ground samples. Via simulated annealing, an optimal prospective sampling scheme for a new unvisited area is derived based on the variogram model of a previously sampled area. The results of this study demonstrate potential application of hy-perspectral remote sensing and simulated annealing to surface characterization of large mine tailings having similar climatic and terrain characteristics to the mine tailings in the case study area.