Over the past decade, manifold and graph representations of hyperspectral imagery (HSI) have been explored widely in HSI applications. Among many data-driven approaches to deriving manifold coordinate representations including Isometric Mapping (ISOMAP), Local Linear Embedding (LLE), Laplacian Eigenmaps (LE), and Diffusion Kernels (DK), ISOMAP is the only global method that well represents the large scale nonlinear geometric structure of the data. In recent years, methods such as ENH-ISOMAP as well as its parallel computing accelerations makes ISOMAP practical for hyperspectral image dimensionality reduction. However, the noise problem in these methods has not been well addressed, which is critical to classification accuracy based on the manifold coordinates derived from these methods. While standard linear techniques to reduce the effects of noise can be applied as a preliminary step, these are based on global statistics and are applied globally across the entire data set, resulting in the risk of losing subtle nonlinear features before classification. To solve this problem, in this paper, we explore several approaches to modeling and mitigating noise in HSI in a local sense to improve the performance of the ENH-ISOMAP algorithm, aiming to reduce the noise effect on the manifold representations of the HSI. A new method to split data into local spectral subsets is introduced. Based on the local spectral subsets obtained with this method, a local noise model guided landmark selection scheme is proposed. In addition, a new robust adaptive neighborhood method using intrinsic dimensionality information to construct the k-Nearest Neighbor graph is introduced to increase the fidelity of the graph, based on the same framework of local spectral subsetting. The improved algorithm produces manifold coordinates with less noise, and shows a better classification accuracy using k-Nearest Neighbor classifier.
Over the past decade, manifold and graph representations of hyperspectral imagery (HSI) have been explored widely in HSI applications. There are a large number of data-driven approaches to deriving manifold coordinate representations including Isometric Mapping (ISOMAP)1, Local Linear Embedding (LLE)2, Laplacian Eigenmaps (LE)3, Diffusion Kernels (DK)4, and many related methods. Improvements to specific algorithms have been developed to ease computational burden or otherwise improve algorithm performance. For example, the best way to estimate the size of the locally linear neighborhoods used in graph construction have been addressed6 as well as the best method of linking the manifold representation with classifiers in applications. However, the problem of how to model and mitigate noise in manifold representations of hyperspectral imagery has not been well studied and remains a challenge for graph and manifold representations of hyperspectral imagery and their application. It is relatively easy to apply standard linear methods to remove noise from the data in advance of further processing, however, these approaches by and large treat the noise model in a global sense, using statistics derived from the entire data set and applying the results globally over the data set. Graph and manifold representations by their nature attempt to find an intrinsic representation of the local data structure, so it is natural to ask how can one best represent the noise model in a local sense. In this paper, we explore the approaches to modeling and mitigating noise at a local level, using manifold coordinates of local spectral subsets. The issue of landmark selection of the current landmark ISOMAP algorithm5 is addressed and a workflow is proposed to make use of manifold coordinates of local spectral subsets to make optimal landmark selection and minimize the effect of local noise.
We present several advanced techniques for evaluating the quality of fiber gyro coils, including characterizing the
temperature and vibration transient characteristics of fiber coils, monitoring polarization-maintaining fiber (PMF) coil
winding quality using distributed polarization crosstalk analyzer (DPXA) during production, and the defect detection of
fiber coil using optical coherence tomography (OCT). To the best of authors' knowledge, this is the first report of using
OCT for fiber coil inspection. The use of these new techniques can effectively improve and guarantee the quality of the
fiber gyro coils.
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