An infinite sum that appears in the error term for variational estimates of eigenvalues of the Helmholtz equation is examined. The sum is evaluated directly, confirming a result based on a higher-order variational ana...
An infinite sum that appears in the error term for variational estimates of eigenvalues of the Helmholtz equation is examined. The sum is evaluated directly, confirming a result based on a higher-order variational analysis. Use of this method for evaluating related infinite sums is discussed.
The classical theorem of Shannon enables one to reconstruct a finite-energy, bandlimited signal from a set of regularly spaced samples. Recently, Benedetto and Heller applied the theory of frames to derive a series of...
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The classical theorem of Shannon enables one to reconstruct a finite-energy, bandlimited signal from a set of regularly spaced samples. Recently, Benedetto and Heller applied the theory of frames to derive a series of sampling theorems with irregularly spaced sampling sequences. In this paper, we study one of these theorems with emphasis on its implementation. To implement the theorem, sampling sequences and sampled coefficients are required. Here, general schemes to construct sampling sequences, and to evaluate sampled coefficients, are established. In addition, we provide an error analysis on the approximation of sampled coefficients. Numerical results are furnished to illustrate the theory and to study various related issues. These issues include the choice of sampling sequences and functions, the effect of truncating the sampling formula, and the influence of the irregularity of sampling sequences.
The authors derive a closed form expression for the pixel variance in the iterative ML-EM reconstruction of a uniform circular source embedded in a uniformly attenuating circular object. The derivation includes both t...
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The authors derive a closed form expression for the pixel variance in the iterative ML-EM reconstruction of a uniform circular source embedded in a uniformly attenuating circular object. The derivation includes both the photon noise in the projection data and the noise in the attenuation map used for attenuation correction. The variance is found to increase with the number of iterations, but converges to a finite value. The noise to signal ratio at convergence is the sum of two terms which correspond to the contributions from the photon noise in the projection data and the attenuation map noise. The noise component due to the photon noise varies inversely with the total number of detected counts in the projection data. The relative variance at infinite iterations is similar in magnitude to that obtained for the filtered backprojection algorithm. The component due to attenuation map noise is proportional to the relative variance of the attenuation coefficient in the attenuation map. These observations are consistent with the results of the authors' previous computer simulation and experimental studies.
Dual-energy X-ray Computed Tomography (DECT) is a technique which is designed to allow the determination of energy-independent material properties. In this study, results of computer simulation show that energy-depend...
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Dual-energy X-ray Computed Tomography (DECT) is a technique which is designed to allow the determination of energy-independent material properties. In this study, results of computer simulation show that energy-dependent systematic errors exist in the values of attenuation coefficient synthesized using the basis material decomposition technique with acrylic and aluminum as the basis materials, especially when iodine (e.g., from radiographic contrast media) is present in the body. The errors are reduced when acrylic and an iodine-water mixture are used as the basis materials. The authors propose a simple model for the calculation of energy-dependent systematic errors using effective energies at the lower and higher energy windows of the X-ray spectrum used in the DECT system. The calculated errors agree well with the errors observed in the simulation. These results suggest that the observed systematic errors are predominantly due to the energy dependence of the basis material coefficients.
Though GIS technology has progressed rapidly during the past decade, the focus of most research and development activity has been placed on the development of single-user systems. A mismatch exists, however, between t...
Reports on the development of a scalable multiple-instruction multiple-data (MIMD) concurrent architecture which is intended to serve as an effective alternative for solving stochastic differential and optimization sy...
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Reports on the development of a scalable multiple-instruction multiple-data (MIMD) concurrent architecture which is intended to serve as an effective alternative for solving stochastic differential and optimization systems. This architecture has in turn motivated the application of group theory and invariance analysis to acquire further insights in understanding the original problem. The speed-up ratios attained by this architecture can realistically justify its potential deployment in certain real-time applications. A case study related to real-time stochastic control and optimization serve to illustrate this possibility.< >
A computationally relevant theory of lexical semantics must take into consideration both the form and the content of three different static knowledge sources - the lexicon, the ontological domain model and a text mean...
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For speech translation to be practical and useful, speech translation systems should be portable to multiple languages without substantial modification. We present the results of expanding the English-based JANUS spee...
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For speech translation to be practical and useful, speech translation systems should be portable to multiple languages without substantial modification. The authors present results of expanding the English-based JANUS...
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For speech translation to be practical and useful, speech translation systems should be portable to multiple languages without substantial modification. The authors present results of expanding the English-based JANUS speech translation system to translate from spoken German sentences to English and Japanese utterances. The authors also report the results of implementing part of the linked predictive neural network (LPNN) speech recognition module on a massively parallel machine. The JANUS approach generalizes well, with overall system performance of 97%. This surpasses English-based JANUS performance.< >
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