In this paper we describe efforts toward a hyperspectral land remote sensing data analysis procedure that would be maximally effective for use by a broad community of future users. Though there would be dependence of performance achieved on the spectral subspace and the classification algorithm used, the major dependence is on how well the user quantitatively defines the classes desired. Thus the attempt is to measure this dependence for typical users and to introduce means that mitigate the problem of class and training definition.
Some algorithms, such as Gaussian Maximum Likelihood require the use of the second order statistics, e.g. the covariance matrix, to help characterize the target in addition to the mean. Also, models such as FASSP require the second order statistics of targets to predict the performance of algorithms even though the algorithm may not use the covariance matrix directly. However, many times the number of samples available to make a good estimate of the covariance matrix is small. The Leave-One-Out Covariance (LOOC) estimator can be used to estimate the covariance matrix when the number of samples available is less than the normal minimum required. The normal minimum number of samples needed for a sample class covariance matrix is p+1 samples for p-dimensional data. For the LOOC estimator, in theory, as few as 3 samples are all that are needed. However, what are the affects of using such a low number in practice? This paper presents the results of an experiment that was conducted to measure what the affect may be in one specific instance. Sometimes as few as 0.1 p samples produce reasonably satisfactory results; other times 0.4p or more samples are needed.
Multispectral image data has been a key data type for land observational remote sensing from aircraft and spacecraft since the 1960's. Sensor technology was a primary limiting factor for many years for this method, as sensors such as Landsat could only collect data in four to seven spectral bands at once. In the last few years, advances in sensor technology have mae possible the collection of such image data in as many as several hundred spectral bands at once. In this paper, some results obtained in the study of data analysis methods for such high dimensional data will be overviewed. They show that such data have substantially increased potential for deriving more detailed and more accurate information, but to achieve it, the primary limiting factor has become the precision with which a user can specify the analysis classes of interest. Some methods and procedures for mitigating this limitation in practical circumstances will be described.
Hyperspectral data potentially contain more information than multispectral data because of higher dimensionality. Information extraction algorithm performance is strongly related to the quantitative precision with which the desired classes are defined, a characteristic which increase rapidly with dimensionality. Due to the limited number of training samples used in defining classes, the information extraction of hyperspectral data may not perform as well as needed. In this paper, schemes for statistics enhancement are investigated for alleviating this problem. Previous works including the EM algorithm and the Leave-One-Out covariance estimator are discussed. The HALF covariance estimator is proposed for two-class problems by using the symmetry property of the normal distribution. A spectral-spatial labeling scheme is proposed to increase the training sample sizes automatically. We also seek to combine previous works with the proposed methods so as to take full advantage of statistics enhancement. Using these techniques, improvement in classification accuracy has been observed.
A focused research program has been under way for several years to discover optimally effective means for analysis of multispectral and hyperspectral data. The methods pursued are based upon fundamental principles of signal theory and signal processing. The basic approach revolves around viewing N spectral bands of data from a pixel as a single point in N dimensional space, thus, an important aspect of the work has been to discover unique aspects of higher dimensional spaces which can be exploited for their information-bearing aspects. Substantial progress on this problem has been made in the last several years, with several key algorithms having been defined. Among these are algorithms for transforms which define optimal case-specific features, and which improve the ability of the classifier to generalize. A more fundamental finding has been to understand the characteristics of high dimensional space and the significance of design samples and their use in defining the classifier. These results have been published in separate papers over the last several years. The purpose of this paper is to survey these results and to show how they relate to one another in achieving an effective overall analysis procedure for analyzing a hyperspectral image data set.
Analysis methods for multispectral data have been under study for at least three decades. In spite of that fact, the state of the technology is still far from satisfactory for conventional multispectral data, and the advent of hyperspectral sensor systems raises the challenge substantially. Thus a focused effort was begun a few years ago to advance the technology of multispectral analysis to a more effective level, and especially to prepare suitable methods to yield full information extraction capabilities from the new hyperspectral data. This paper outlines some of what has been learned about this problem from the research effort.
A new method for classification of multi-spectral data is proposed. This method is based on fitting mixtures of multivariate Gaussian components to training and unlabeled samples by using the EM algorithm. Through a backtracking search strategy with appropriate depth bounds, a series of mixture models are compared. The validity of the candidate models are evaluated by considering their description lengths and allocation rates. The most suitable model is selected and the multi-spectral data are classified accordingly. The EM algorithm is mapped onto a massively parallel computer system to reduce the computational cost. Experimental results show that the proposed algorithm is more robust against variations in training samples than the conventional supervised Gaussian maximum likelihood classifier.
The effect of additional unlabeled samples in improving the supervised learning process is studied in this paper. Three learning processes, supervised, unsupervised, and combined supervised-unsupervised, are compared by studying the asymptotic behavior of the estimates obtained under each process. Upper and lower bounds on the asymptotic covariance matrices are derived. It is shown that under a normal mixture density assumption for the probability density function of the feature space, the combined supervised-unsupervised learning is always superior to the supervised learning in achieving better estimates. Experimental results are provided to verify the theoretical concepts.
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