Shih-Yu Chen

Kinetics of synthesis of silicon carbide by carbothermal reduction of silicon dioxide

Abstract Carbothermal reduction of silicon dioxide in a flowing stream of inert gas was investigated by weight loss measurements, X-ray diffraction, and scanning electron microscopy. The results obtained indicate that the reaction rate can be increased by increasing either the sample size or reaction temperature. Furthermore, the reaction rate was found to increase on decreasing the inert gas flow rate, Si/C molar ratio, grain size of silicon dioxide or carbon, or the initial bulk density. Empirical equations for the consumption rates of SiO2 and C, as well as the production rate of SiC, were also determined. The results also indicate that Fe2O3 acts as a catalyst on the reaction and that both the amount and the Fe2O3 particle size may change the degree of influence on the reaction.

PPI-SVM-Iterative FLDA Approach to Unsupervised Multispectral Image Classification

This paper presents a new approach to unsupervised classification for multispectral imagery. It first implements the pixel purity index (PPI) which is commonly used in hyperspectral imaging for endmember extraction to find seed samples without prior knowledge, then uses the PPI-found samples as support vectors for a kernel-based support vector machine (SVM) to generate a set of initial training samples. In order to mitigate randomness caused by PPI and sensitivity of support vectors used by SVM it further develops an iterative Fishers linear discriminate analysis (IFLDA) that performs FLDA classification iteratively to produce a final set of training samples that will be used to perform a follow-up supervised classification. However, when the image is very large, which is usually the case in multispectral imagery, the computational complexity will be very high for PPI to process the entire image. To resolve this issue a Gaussian pyramid image processing is introduced to reduce image size. The experimental results show the proposed approach has great promise in unsupervised multispectral classification.

Comparative Study and Analysis Among ATGP, VCA, and SGA for Finding Endmembers in Hyperspectral Imagery

Endmember finding has become increasingly important in hyperspectral data exploitation because endmembers can be used to specify unknown particular spectral classes. Pixel purity index (PPI) and N-finder algorithm (N-FINDR) are probably the two most widely used techniques for this purpose where many currently available endmember finding algorithms are indeed derived from these two algorithms and can be considered as their variants. Among them are three well-known algorithms derived from imposing different abundance constraints, that is, abundance-unconstrained automatic target generation process (ATGP), abundance nonnegativity constrained vertex component analysis (VCA), and fully abundance constrained simplex growing algorithm (SGA). This paper explores relationships among these three algorithms and further shows that theoretically they are essentially the same algorithms in the sense of design rationale. The reason that these three algorithms perform differently is not because they are different algorithms, but rather because they use different preprocessing steps, such as initial conditions and dimensionality reduction transforms.

Recursive unsupervised fully constrained least squares methods

Linear spectral mixture analysis (LSMA) generally performs with signatures assumed to be known to form a linear mixing model to be known. Unfortunately, this is generally not the case in real world applications. An unsupervised fully constrained least squares (UFCLS) method has been proposed to find these desired signatures. Unfortunately, it requires prior knowledge about the number of signatures, p needed to be generated. The recently proposed virtual dimensionality (VD) can be used for this purpose. This paper develops a recursive UFCLS (RUFCLS) method to accomplish these two tasks in one-shot operation, viz., determine the value of p as well as find these p signatures simultaneously. Such RUFCLS can perform data unmixing progressively signature-by-signature via a recursive update equation with signatures used to form a linear mixing model for linear spectral unmixing generated by UFCLS. Most importantly, RUFCLS does not require any matrix inverse operation but only matrix multiplications and outer products of vectors. This significant advantage provides an effective computational means of determining the VD.

Low-rank decomposition-based anomaly detection

With high spectral resolution hyperspectral imaging is capable of uncovering many subtle signal sources which cannot be known a priori or visually inspected. Such signal sources generally appear as anomalies in the data. Due to high correlation among spectral bands and sparsity of anomalies, a hyperspectral image can be e decomposed into two subspaces: a background subspace specified by a matrix with low rank dimensionality and an anomaly subspace specified by a sparse matrix with high rank dimensionality. This paper develops an approach to finding such low-high rank decomposition to identify anomaly subspace. Its idea is to formulate a convex constrained optimization problem that minimizes the nuclear norm of the background subspace and little ι1 norm of the anomaly subspace subject to a decomposition of data space into background and anomaly subspaces. By virtue of such a background-anomaly decomposition the commonly used RX detector can be implemented in the sense that anomalies can be separated in the anomaly subspace specified by a sparse matrix. Experimental results demonstrate that the background-anomaly subspace decomposition can actually improve and enhance RXD performance.

Fully abundance-constrained endmember finding for hyperspectral images

Fully constrained least squares (FCLS) method has been widely used in linear spectral mixture analysis (LSMA). This paper presents two versions of FCLS, to be called SeQuential FCLS (SQ-FCLS) and SuCcessive FCLS (SC-FCLS) to find endmembers. In order to address random issues in initial conditions, two versions of FCLS, Iterative FCLS (I-FLCS) and Random FCLS (RFCLS) are also developed.

Progressive constrained energy minimization for subpixel detection

Constrained energy minimization (CEM) has been widely used for subpixel detection. It makes use of the sample correlation matrix R by suppressing the background thus enhancing detection of targets of interest. In many real world problems, implementing target detection on a timely basis is crucial, specifically moving targets. However, since the calculation of the sample correlation matrix R needs the complete data set prior to its use in detection, CEM is prevented from being implemented as a real time processing algorithm. In order to resolve this dilemma, the sample correlation matrix R must be replaced with a causal sample correlation matrix formed by only those data samples that have been visited and the currently being processed data sample. This causality is a pre-requisite to real time processing. By virtue of such causality, designing and developing a real time processing version of CEM becomes feasible. This paper presents a progressive CEM (PCEM) where the causal sample correlation matrix can be updated sample by sample. Accordingly, PCEM allows the CEM to be implemented as a causal CEM (C-CEM) as well as real time (RT) CEM via a recursive update equation in real time.

Recursive Automatic Target Generation Process in Subpixel Detection

Automatic target generation process (ATGP) has been used in a wide range of applications in hyperspectral image analysis. It performs a sequence of orthogonal subspace projections to extract potential targets of interest. This letter presents a recursive version of the ATGP, which is referred to as the recursive ATGP (RATGP) and has three advantages over the ATGP as follows: 1) there is no need of inverting a matrix as the ATGP does for finding each new target; 2) there is a significant reduction in the computational complexity in the hardware design due to its recursive structure; and 3) there is an automatic stopping rule that can be derived by the Neyman-Pearson detection theory to terminate the algorithm.

Endmember-specified virtual dimensionality in hyperspectral imagery

One key issue encountered in endmember extraction is to determine the number of endmembers, p, required to be extracted. Virtual dimensionality (VD) has been widely used for this purpose. However, VD was originally developed and defined as the number of spectrally distinct signatures which are not necessarily pure signatures. So, on some occasions the VD estimated value for p may not be accurate to be used for the number of endmembers. This paper develops an endmember-specified VD (ES-VD) which makes use of data sample vectors generated by a specific endemember finding algorithm (EFA) as target signal sources and then determine if these signal sources are indeed true endmember by a binary composite hypothesis testing to determine endmembers. As a result, ES-VD varies with different target signal sources produced by EFAs. Most importantly, ES-VD not only determines the value of VD and in the mean time it also finds desired endmembers.

Anomaly discrimination in hyperspectral imagery

Anomaly detection finds data samples whose signatures are spectrally distinct from their surrounding data samples. Unfortunately, it cannot discriminate the anomalies it detected one from another. In order to accomplish this task it requires a way of measuring spectral similarity such as spectral angle mapper (SAM) or spectral information divergence (SID) to determine if a detected anomaly is different from another. However, this arises in a challenging issue of how to find an appropriate thresholding value for this purpose. Interestingly, this issue has not received much attention in the past. This paper investigates the issue of anomaly discrimination which can differentiate detected anomalies without using any spectral measure. The ideas are to makes use unsupervised target detection algorithms, Automatic Target Generation Process (ATGP) coupled with an anomaly detector to distinguish detected anomalies. Experimental results show that the proposed methods are indeed very effective in anomaly discrimination.