A method of the vectorial representation for splitting the calculation of the nonseparable three-dimensional discrete Hartley transform (3D DHT) into a set of one-dimensional (1D) DHTs is presented. The method is base...
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A method of the vectorial representation for splitting the calculation of the nonseparable three-dimensional discrete Hartley transform (3D DHT) into a set of one-dimensional (1D) DHTs is presented. The method is based on the vectorial, or tensor form of representation of a 3D image and can be applied to any orders of the transform. The case of the N/spl times/N&N-point DHT, for N=2/sup r/ (r>1), is considered in detail. The number of multiplications required for calculating the 3D DHT by the method of vectorial representation equals 7[8/sup r-1/(r-3)+4/sup r-1/] that is the best estimate of all existent algorithms. The improvement of this method, the recurrent algorithm, that reduces about 1.6 times the number of multiplications is also described.
This paper presents a physically based time series model that relates groundwater level fluctuations to precipitation and evapotranspiration. The model is based on the nonlinear relation between the degree of water sa...
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An algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey (BM) algorithm. By applying a technique developed by R. He et al. (see IEEE Trans. Inf. Theory, vol.47, p.1181...
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An algebraic decoding method is proposed for the quadratic residue codes that utilize the Berlekamp-Massey (BM) algorithm. By applying a technique developed by R. He et al. (see IEEE Trans. Inf. Theory, vol.47, p.1181-6, 2001), one can express unknown syndromes as functions of known syndromes. An efficient algorithm is also developed to determine the unknown syndromes. With the appearance of unknown syndromes, one obtains the consecutive syndromes that are needed for the application of the inverse-free BM algorithm. The new decoding scheme can be used to implement the (79,40,15) quadratic residue (QR) code which has not been treated so far. It is verified by a computer program that uses the C++ language.
Rate and diversity impose a fundamental trade-off in space-time coding. High-rate space-time codes come at a cost of lower diversity, and high reliability (diversity) implies a lower rate. We explore a different point...
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Rate and diversity impose a fundamental trade-off in space-time coding. High-rate space-time codes come at a cost of lower diversity, and high reliability (diversity) implies a lower rate. We explore a different point of view where we design high-rate space-time codes that have a high-diversity code embedded within them. This allows a form of communication where the high-rate code opportunistically takes advantage of good channel realizations whereas the embedded high-diversity code ensures that at least part of the information is received reliably. We explore this point of view with design issues, along with some preliminary progress on code constructions and some information-theoretic considerations.
Proper initialization of neural networks is critical for a successful training of its weights. Many methods have been proposed to achieve this, including heuristic least squares approaches. In this paper, inspired by ...
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Proper initialization of neural networks is critical for a successful training of its weights. Many methods have been proposed to achieve this, including heuristic least squares approaches. In this paper, inspired by these previous attempts to train (or initialize) neural networks, we formulate a mathematically sound algorithm based on backpropagating the desired output through the layers of a multilayer perceptron. The approach is accurate up to local first order approximations of the nonlinearities. It is shown to provide successful weight initialization for many data sets by Monte Carlo experiments.
We consider the long time dependence for the moments of displacement 〈|r|q〉 of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find 〈|r|q〉∼tγq (...
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We consider the long time dependence for the moments of displacement 〈|r|q〉 of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find 〈|r|q〉∼tγq (up to factors of lnt). The time exponent, γq, is piecewise linear and equal to q/2 for q<2 and q−1 for q>2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle’s velocity vector.
In this paper we present a controller that solves the problem of position coordination of two (or more) robotic systems, under a master-slave scheme, in the case when only position measurements are available. The cont...
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In this paper we present a controller that solves the problem of position coordination of two (or more) robotic systems, under a master-slave scheme, in the case when only position measurements are available. The controller consists of a feedback control law and two nonlinear observers. It is shown that the controller yields semi-global ultimate uniformly boundedness of the closed loop errors and a relation between the bound of the errors and the gains on the controller is established. Experimental results show, despite obvious model uncertainties, a good agreement with the predicted convergence.
We cast the problem of inferring the 3D shape of a scene from a collection of defocused images in the framework of anisotropic diffusion. We propose an algorithm that can estimate the shape of a scene by inferring the...
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We cast the problem of inferring the 3D shape of a scene from a collection of defocused images in the framework of anisotropic diffusion. We propose an algorithm that can estimate the shape of a scene by inferring the diffusion coefficient of a heat equation. The method is optimal, as we pose it as the minimization of a certain cost functional based on the input images, and fast. Furthermore, we also extend our algorithm to the case of multiple images, and derive a 3D scene segmentation algorithm that can work in the presence of pictorial camouflage.
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