14,652 research outputs found
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Astrophysical Supercomputing with GPUs: Critical Decisions for Early Adopters
General purpose computing on graphics processing units (GPGPU) is
dramatically changing the landscape of high performance computing in astronomy.
In this paper, we identify and investigate several key decision areas, with a
goal of simplyfing the early adoption of GPGPU in astronomy. We consider the
merits of OpenCL as an open standard in order to reduce risks associated with
coding in a native, vendor-specific programming environment, and present a GPU
programming philosophy based on using brute force solutions. We assert that
effective use of new GPU-based supercomputing facilities will require a change
in approach from astronomers. This will likely include improved programming
training, an increased need for software development best-practice through the
use of profiling and related optimisation tools, and a greater reliance on
third-party code libraries. As with any new technology, those willing to take
the risks, and make the investment of time and effort to become early adopters
of GPGPU in astronomy, stand to reap great benefits.Comment: 13 pages, 5 figures, accepted for publication in PAS
Analyze Large Multidimensional Datasets Using Algebraic Topology
This paper presents an efficient algorithm to extract knowledge from high-dimensionality, high- complexity datasets using algebraic topology, namely simplicial complexes. Based on concept of isomorphism of relations, our method turn a relational table into a geometric object (a simplicial complex is a polyhedron). So, conceptually association rule searching is turned into a geometric traversal problem. By leveraging on the core concepts behind Simplicial Complex, we use a new technique (in computer science) that improves the performance over existing methods and uses far less memory. It was designed and developed with a strong emphasis on scalability, reliability, and extensibility. This paper also investigate the possibility of Hadoop integration and the challenges that come with the framework
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Experimental investigation of an interior search method within a simple framework
A steepest gradient method for solving Linear Programming (LP) problems, followed by a procedure for purifying a non-basic solution to an improved extreme point solution have been embedded within an otherwise simplex based optimiser. The algorithm is designed to be hybrid in nature and exploits many aspects of sparse matrix and revised simplex technology. The interior search step terminates at a boundary point which is usually non-basic. This is then followed by a series of minor pivotal steps which lead to a basic feasible solution with a superior objective function value. It is concluded that the procedures discussed in this paper are likely to have three possible applications, which are
(i) improving a non-basic feasible solution to a superior extreme point solution,
(iii) an improved starting point for the revised simplex method, and
(iii) an efficient implementation of the multiple price strategy of the revised simplex method
Segmentation of Three-dimensional Images with Parametric Active Surfaces and Topology Changes
In this paper, we introduce a novel parametric method for segmentation of
three-dimensional images. We consider a piecewise constant version of the
Mumford-Shah and the Chan-Vese functionals and perform a region-based
segmentation of 3D image data. An evolution law is derived from energy
minimization problems which push the surfaces to the boundaries of 3D objects
in the image. We propose a parametric scheme which describes the evolution of
parametric surfaces. An efficient finite element scheme is proposed for a
numerical approximation of the evolution equations. Since standard parametric
methods cannot handle topology changes automatically, an efficient method is
presented to detect, identify and perform changes in the topology of the
surfaces. One main focus of this paper are the algorithmic details to handle
topology changes like splitting and merging of surfaces and change of the genus
of a surface. Different artificial images are studied to demonstrate the
ability to detect the different types of topology changes. Finally, the
parametric method is applied to segmentation of medical 3D images
ColDICE: a parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation
Resolving numerically Vlasov-Poisson equations for initially cold systems can
be reduced to following the evolution of a three-dimensional sheet evolving in
six-dimensional phase-space. We describe a public parallel numerical algorithm
consisting in representing the phase-space sheet with a conforming,
self-adaptive simplicial tessellation of which the vertices follow the
Lagrangian equations of motion. The algorithm is implemented both in six- and
four-dimensional phase-space. Refinement of the tessellation mesh is performed
using the bisection method and a local representation of the phase-space sheet
at second order relying on additional tracers created when needed at runtime.
In order to preserve in the best way the Hamiltonian nature of the system,
refinement is anisotropic and constrained by measurements of local Poincar\'e
invariants. Resolution of Poisson equation is performed using the fast Fourier
method on a regular rectangular grid, similarly to particle in cells codes. To
compute the density projected onto this grid, the intersection of the
tessellation and the grid is calculated using the method of Franklin and
Kankanhalli (1993) generalised to linear order. As preliminary tests of the
code, we study in four dimensional phase-space the evolution of an initially
small patch in a chaotic potential and the cosmological collapse of a
fluctuation composed of two sinusoidal waves. We also perform a "warm" dark
matter simulation in six-dimensional phase-space that we use to check the
parallel scaling of the code.Comment: Code and illustration movies available at:
http://www.vlasix.org/index.php?n=Main.ColDICE - Article submitted to Journal
of Computational Physic
Restricted Value Iteration: Theory and Algorithms
Value iteration is a popular algorithm for finding near optimal policies for
POMDPs. It is inefficient due to the need to account for the entire belief
space, which necessitates the solution of large numbers of linear programs. In
this paper, we study value iteration restricted to belief subsets. We show
that, together with properly chosen belief subsets, restricted value iteration
yields near-optimal policies and we give a condition for determining whether a
given belief subset would bring about savings in space and time. We also apply
restricted value iteration to two interesting classes of POMDPs, namely
informative POMDPs and near-discernible POMDPs
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