KEYWORDS: Probability theory, Data fusion, Monte Carlo methods, Sensor fusion, Binary data, Composites, Roads, Bayesian inference, Medical diagnostics, Biometrics
In this work we focus on the relationship between the Dempster-Shafer (DS) and Bayesian evidence accumulation.
While it is accepted that the DS theory is, in a certain sense, a generalization of the probability theory, the approaches
vary in several important respects, including the treatment of uncertain information and the way the evidence is
combined, making direct comparison of results of the two analyses difficult. In this work we ameliorate these
difficulties by proposing a mathematical framework within which the relationship between the two methods can be made
precise. The findings of the investigation elucidate the role uncertainty plays in the DS theory and enable evaluation of
relative fitness of the two techniques for practical data fusion scenarios.
KEYWORDS: Fourier transforms, Time-frequency analysis, Image segmentation, Space operations, Multidimensional signal processing, Curium, Signal processing, Associative arrays, Algorithms, Detection theory
We propose a new, time-frequency formulation of the Gerchberg-Papoulis algorithm for extrapolation of band- limited signals. The new formulation is obtained by translating the constituent operations of the Gerchberg- Papoulis procedure, the truncation and the Fourier transform, into the language of the finite Zak transform, a time-frequency tool intimately related to the Fourier transform. We will show that the use of the Zak transform results in a significant reduction of the computational complexity of the Gerchberg-Papoulis procedure and in an increased flexibility of the algorithm.
Recently, a new approach to hyperspectral imaging, relying on the theory of computed tomography, was proposed by researchers at the Air Force Research Laboratory. The approach allows all photons to be recorded and therefore increases robustness of the imaging system to noise and focal plane array non-uniformities. However, as all computed tomography systems, the approach suffers form the limited angle problem, which obstructs reconstruction of the hyperspectral information. In this work we present a direct, one-step algorithm for reconstruction of the unknown information based on a priori knowledge about the hyperspectral image.
This paper reports on the design, performance and signal processing of a visible/near infrared (VIS-NIR) chromotomographic hyperspectral imaging sensor. The sensor consists of a telescope, a direct vision prism, and a framing video camera. The direct vision prism is a two-prism set, arranged such that one wavelength passes undeviated, while the other wavelengths are dispersed along a line. The prism is mounted on a bearing so that it can be rotated on the optical axis of the telescope. As the prism is rotated, the projected image is multiplexed on elements of the focal plane array. Computational methods are used to reconstruct the scene at each wavelength; an approach similar to the limited-angle tomography techniques used in medicine. The sensor covers the visible through near infrared spectrum of silicon photodiodes. The sensor weighs less than 6 pounds has under 300 in3 volume and requires 20 watts. It produces image cubes, with 64 spectral bands, at rates up to 10 Hz. By operating in relatively fast framing mode, the sensor allows characterization of transient events. We will describe the sensor configuration and method of operation. We also present examples of sensor spectral image data.
We present a new algorithm for chromotomographic image restoration. The main stage of the algorithm employs the iterative method of projections onto convex sets, utilizing a new constraint operator. The constraint takes advantage of hyperspectral data redundancy and information compacting ability of singular value decomposition to reduce noise and artifacts. Results of experiments on both in-house and AVIRIS data demonstrate that the algorithm converges rapidly and delivers high image fidelity.
Chromotomographic spectral imaging techniques offer high spatial resolution, moderate spectral resolution and high optical throughput. However, the performance of chromotomographic systems has historically been limited by the artifacts introduced by a cone of missing information. The recent successful application of principal component analysis to spectral imagery indicates that spectral imagery is inherently redundant. We have developed an iterative technique for filling in the missing cone that relies on this redundance. We demonstrate the effectiveness of our approach on measured data, and compare the results to those obtained with a scanned slit configuration.
We present a new algorithm for image restoration with application to image spectrometry, combining two radically different techniques: the singular value decomposition (SVD) and the method of projections onto convex sets (POCS). The SVD technique is used to obtain an initial estimate of the unknown image and to establish correspondence between the missing data and the spectral description of the image. The iterative method of convex projections is then applied to the estimate, regaining the missing data by enforcing a sequence of constraints on the reconstructed object. We report results of investigations of the SVD-POCS method and demonstrate that the new algorithm leads to significant improvements in the recovered image.
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