Hsiao-Chi Li

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.

Open chest cardiac massage offers no benefit over closed chest compressions in patients with traumatic cardiac arrest.

BACKGROUND Open chest cardiac massage (OCCM) is a commonly performed procedure after traumatic cardiac arrest (TCA). OCCM has been reported to be superior to closed chest compressions (CCC) in animal models and in non-TCA. The purpose of this study is to prospectively compare OCCM versus CCC in TCA using end-tidal carbon dioxide (ETCO2), the criterion standard for determining the effectiveness of chest compressions and detection of return of spontaneous circulation (ROSC), as the surrogate for cardiac output and marker for adequacy of resuscitation. METHODS This prospective observational study enrolled patients over a 9-month period directly presenting to a level 1 trauma center after TCA. Continuous high-resolution ETCO2 measurements were collected every 6 seconds for periods of CCC and OCCM, respectively. Patients receiving CCC only were compared with patients receiving CCC followed by OCCM. Students t tests were used to compare ETCO2 within and between groups. RESULTS Thirty-three patients were enrolled (16 OCCM, 17 CCC-only). Mean time of CCC before OCCM was 66 seconds. Within the OCCM group, final, peak, mean, and median ETCO2 levels significantly increased when comparing the initial CCC period to the OCCM interval. Using a time-matched comparison, significant increases were observed in the final and peak but not mean and median values when comparing the first minute of CCC to the remaining time in the CCC-only group. However, when periods of OCCM were compared with equivalent periods of CCC-only, there were no differences in the initial, final, peak, mean, or median ETCO2 values. Correspondingly, no difference in rates of ROSC was observed between groups (OCCM 23.5% vs. CCC 38.9%; p = 0.53). CONCLUSION Although we could not control for confounders, we found no significant improvement in ETCO2 or ROSC with OCCM. With newer endovascular techniques for aortic occlusion, thoracotomy solely for performing OCCM provides no benefit over CCC. LEVEL OF EVIDENCE Therapeutic study, level III.

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.

Recursive Orthogonal Projection-Based Simplex Growing Algorithm

The simplex growing algorithm (SGA) has been widely used for finding endmembers. It can be considered as a sequential version of the well-known endmember finding algorithm, N-finder algorithm (N-FINDR), which finds endmembers one at a time by growing simplexes. However, one of the major hurdles for N-FINDR and SGA is the calculation of simplex volume (SV) which poses a great challenge in designing any algorithm using SV as a criterion for finding endmembers. This paper develops an orthogonal projection (OP)-based SGA (OP-SGA) which essentially resolves this computational issue. It converts the issue of calculating SV to calculating the OP on previously found simplexes without computing matrix determinants. Most importantly, a recursive Kalman filter-like OP-SGA, to be called recursive OP-SGA (ROP-SGA), can be also derived to ease computation. By virtue of ROP-SGA, several advantages and benefits in computational savings and hardware implementation can be gained for which N-FINDR and SGA do not have.

Linear spectral unmixing using least squares error, orthogonal projection and simplex volume for hyperspectral images

Linear spectral unmixing (LSU) and Simplex Volume (SV) are closely related. The link between these two has been recognized recently by the fact that simplex can be realized by two physical abundance constraints, Abundance Sum-to-one Constraint (ASC) and Abundance Non-negativity Constraint (ANC). In other words, all data sample vectors are embraced by a simplex with vertices which are actually the set of signatures used to unmix data sample vectors where the data sample vectors outside the simplex are considered as unwanted sample vectors such as noisy samples, bad sample vectors. On the other hand, LSU is solved by Least Squares Error (LSE) which uses the principle of orthogonality to derive the solution. Therefore, LSU is also equivalent to being solved by Orthogonal Projection (OP). This paper explores applications of LSU using these criteria, simplex, LSE and OP in data unmixing.

Constrained multiple band selection for hyperspectral imagery

A recent developed band selection, called constrained band selection (CBS), makes use of constrained energy minimization (CEM) to constrain a single band to calculate its priority for band selection (BS). This paper extends such CEM-BS to a constrained multiple band selection (CMBS)-based method, to be called linearly constrained minimum variance multiple band-constrained selection (CMBS), which uses LCMV to constrain multiple bands to perform band subset selection. Since CMBS selects multiple bands as a band subset as a whole it does not require band prioritization (BP) or band de-correlation (BD) as traditional band selection (BS) usually does. However, CMBS is traded for one challenging issue, which is excessive computational complexity because it requires running through a total number of subsets in the power set of a full band set compared to BS which only needs to select one band at a time. In order to avoid exhaustive search for all band subsets in it power set, a sequential CMBS, successive CMBS (SC-CMBS) is developed to ease computational complexity.

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.