Meiping Song

Real-Time Constrained Energy Minimization for Subpixel Detection

Constrained energy minimization (CEM) has been widely used in subpixel detection. This paper presents a new real-time processing of CEM according to two data acquisition formats, band-interleaved-pixel/sample (BIP/BIS) and band-interleaved line (BIL) where the global sample correlation matrix R must be replaced with a causal sample correlation matrix formed by only those data samples up to the pixel/sample currently being processed or a causal data line matrix formed by all data lines up to the data line being just completed. Both versions of CEM have not been investigated in the past. Its applications include detection of moving targets which can be only detected in real-time ongoing process, as well as subtle targets which is likely to be missed and overwhelmed by CEM in one-shot operation. Interestingly, while BIP/BIS and BIL look similar, their real-time implementations are quite different due to their use of causal sample correlation matrices, one updated by samples and the other updated by data lines. As a result, two different recursive equations are also derived for CEM using BIP/BIS and BIL, respectively, for real-time implementation.

Gram-Schmidt orthogonal vector projection for hyperspectral unmixing

Orthogonal subspace projection (OSP) requires inverting a matrix to eliminate effect of unwanted signal sources on unmixing of desired signal sources. When the number of such wanted signals sources is large, which is indeed the case for hyperspectra data, OSP will become slow due to its matrix inversion. This paper develops a simple alternative approach to OSP without computing matrix inversion, called Gram Schmidt orthogonal vector projection (GSOVP) which is also based on orthogonal projection. Instead of annihilating all unwanted signal sources and then extracting the desired signal as OSP does, GSOVP accomplishes these two tasks by simple inner products. As a result, computational complexity is significantly reduced and hardware design is further simplified.

Simplex volume analysis for finding endmembers in hyperspectral imagery

Using maximal simplex volume as an optimal criterion for finding endmembers is a common approach and has been widely studied in the literature. Interestingly, very little work has been reported on how simplex volume is calculated. It turns out that the issue of calculating simplex volume is much more complicated and involved than what we may think. This paper investigates this issue from two different aspects, geometric structure and eigen-analysis. The geometric structure is derived from its simplex structure whose volume can be calculated by multiplying its base with its height. On the other hand, eigen-analysis takes advantage of the Cayley-Menger determinant to calculate the simplex volume. The major issue of this approach is that when the matrix is ill-rank where determinant is desired. To deal with this problem two methods are generally considered. One is to perform data dimensionality reduction to make the matrix to be of full rank. The drawback of this method is that the original volume has been shrunk and the found volume of a dimensionality-reduced simplex is not the real original simplex volume. Another is to use singular value decomposition (SVD) to find singular values for calculating simplex volume. The dilemma of this method is its instability in numerical calculations. This paper explores all of these three methods in simplex volume calculation. Experimental results show that geometric structure-based method yields the most reliable simplex volume.

Recursive Geometric Simplex Growing Analysis for Finding Endmembers in Hyperspectral Imagery

Simplex growing algorithm (SGA) is an endmember finding algorithm which searches for endmembers one after another by growing simplexes one vertex at a time via maximizing simplex volume (SV). Unfortunately, several issues arise in calculating SV. One is the use of dimensionality reduction (DR) because the dimensionality of a simplex is usually much smaller than data dimensionality. Second, calculating SV requires calculating the determinant of an ill-ranked matrix in which case singular value decomposition (SVD) is generally required to perform DR. Both approaches generally do not produce true SV. Finally, the computing time becomes excessive and numerically instable as the number of endmembers grows. This paper develops a new theory, called geometric simplex growing analysis (GSGA), to resolve these issues. It can be considered as an alternative to SGA from a rather different point of view. More specifically, GSGA looks into the geometric structures of a simplex whose volume can be actually calculated by multiplication of its base and height. As a result, it converts calculating maximal SV to finding maximal orthogonal projection as its maximal height becomes perpendicular to its base. To facilitate GSGA in practical applications, GSGA is further used to extend SGA to recursive geometric simplex growing algorithm (RGSGA) which allows GSGA to be implemented recursively in a similar manner that a Kalman filter does. Consequently, RGSGA can be very easily implemented with significant saving of computing time. Best of all, RGSGA is also shown to be most efficient and effective among all SGA-based variants.

A Subpixel Target Detection Approach to Hyperspectral Image Classification

Hyperspectral image classification faces various levels of difficulty due to the use of different types of hyperspectral image data. Recently, spectral–spatial approaches have been developed by jointly taking care of spectral and spatial information. This paper presents a completely different approach from a subpixel target detection view point. It implements four stage processes, a preprocessing stage, which uses band selection (BS) and nonlinear band expansion, referred to as BS-then-nonlinear expansion (BSNE), a detection stage, which implements constrained energy minimization (CEM) to produce subpixel target maps, and an iterative stage, which develops an iterative CEM (ICEM) by applying Gaussian filters to capture spatial information, and then feeding the Gaussian-filtered CEM-detection maps back to BSNE band images to reprocess CEM in an iterative manner. Finally, in the last stage Otsu’s method is applied to converting ICEM-detected real-valued maps to discrete values for classification. The entire process is called BSNE-ICEM. Experimental results demonstrate BSNE-ICEM, which has advantages over support vector machine-based approaches in many aspects, such as easy implementation, fewer parameters to be used, and better false classification and precision rates.

Recursive Band Processing of Orthogonal Subspace Projection for Hyperspectral Imagery

Recursive band processing of orthogonal subspace projection (RBP-OSP) is developed according to the band sequential (BSQ) format acquired by a hyperspectral imaging sensor. It can be implemented band by band recursively without waiting for data being completely collected. This is particularly important for satellite communication when data download is limited by bandwidth and transmission. Unlike band selection which requires prior knowledge of how many bands are needed to be selected, RBP-OSP has capability which allows different process units to process data whenever bands are available. In addition, it also enables users to identify significant bands during data processing. Finally and most importantly, RBP can provide progressive profiles on OSP performance, which is the best advantage that RBP-OSP can offer and cannot be accomplished by any one-shot operator.

Recursive orthogonal vector projection algorithm for linear spectral unmixing

Orthogonal vector projection (OVP) is recently developed as a versatile technique which can used in various application in hyperspectral imaging such as subpixel detection, linear spectral unmixing and endmember finding. A great advantage of OVP is that only calculations of vector products are required with no need of matrix multiplications and inverse calculations. Furthermore, this paper develops a recursive version of OVP, to be called recursive OVP (ROVP) so that OVP can be performed vector by vector recursively without using previously processed vectors. As a result, the computational complexity of ROVP is much lower than other algorithms. Furthermore, the ROVP is much easier to be applied to hardware such as FPGA or GPU in the future.

A Hyperspectral Imaging Approach to White Matter Hyperintensities Detection in Brain Magnetic Resonance Images

White matter hyperintensities (WMHs) are closely related to various geriatric disorders including cerebrovascular diseases, cardiovascular diseases, dementia, and psychiatric disorders of elderly people, and can be generally detected on T2 weighted (T2W) or fluid attenuation inversion recovery (FLAIR) brain magnetic resonance (MR) images. This paper develops a new approach to detect WMH in MR brain images from a hyperspectral imaging perspective. To take advantage of hyperspectral imaging, a nonlinear band expansion (NBE) process is proposed to expand MR images to a hyperspectral image. It then redesigns the well-known hyperspectral subpixel target detection, called constrained energy minimization (CEM), as an iterative version of CEM (ICEM) for WMH detection. Its idea is to implement CEM iteratively by feeding back Gaussian filtered CEM-detection maps to capture spatial information. To show effectiveness of NBE-ICEM in WMH detection, the lesion segmentation tool (LST), which is an open source toolbox for statistical parametric mapping (SPM), is used for comparative study. For quantitative analysis, the synthetic images in BrainWeb provided by McGill University are used for experiments where our proposed NBE-ICEM performs better than LST in all cases, especially for noisy MR images. As for real images collected by Taichung Veterans General Hospital, the NBE-ICEM also shows its advantages over and superiority to LST.

Channel Capacity Approach to Hyperspectral Band Subset Selection

This paper develops an information theoretical approach using channel capacity as a criterion for band subset selection (BSS). It formulates a BSS problem as a channel capacity problem by constructing a band channel with the original full band set as a channel input space, a selected band subset as a channel output space and the channel transition specified by band discrimination between original bands and selected bands. Then BSS is selected by Blahuts algorithm that iteratively finds a best possible input space that yields the maximal channel capacity. As a result, there is no need of band prioritization and interband decorrelation generally required by traditional band selection (BS). Two iterative algorithms are developed for finding an optimal BSS, sequential channel capacity BSS (SQ-CCBSS) and successive CCBSS (SC-CCBSS), both of which avoid an exhaustive search for all possible band subset combinations. Experimental results demonstrate that using CCBSS-selected band subsets produce quite different and interesting results from multiple bands selected by traditional single BS (SBS) based methods.

Orthogonal projection-based fully constrained spectral unmixing

OSP has been used widely in detection and abundance estimation for about twenty years. But it can’t apply nonnegative and sum-to-one constraints when being used as an abundance estimator. Fully constrained least square algorithm does this well, but its time cost increases greatly as the number of endmembers grows. There are some tries for unmixing spectral under fully constraints from different aspects recently. Here in this paper, a new fully constrained unmixing algorithm is prompted based on orthogonal projection process, where a nearest projected point is defined onto the simplex constructed by endmembers. It is much easier, and it is faster than FCLS with the mostly same unmixing results. It is also compared with other two constrained unmixing algorithms, which shows its effectiveness too.