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1,596
On limits of wireless communications in a fading environment when using multiple antennas
 Wireless Personal Communications
, 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (M ..."
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Cited by 2181 (11 self)
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Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bitrates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multielement array (MEA) technology, that is processing the spatial dimension (not just the time dimension) to improve wireless capacities in certain applications. Specifically, we present some basic information theory results that promise great advantages of using MEAs in wireless LANs and building to building wireless communication links. We explore the important case when the channel characteristic is not available at the transmitter but the receiver knows (tracks) the characteristic which is subject to Rayleigh fading. Fixing the overall transmitted power, we express the capacity offered by MEA technology and we see how the capacity scales with increasing SNR for a large but practical number, n, of antenna elements at both transmitter and receiver. We investigate the case of independent Rayleigh faded paths between antenna elements and find that with high probability extraordinary capacity is available. Compared to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signaltonoise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take the cases n = 2, 4 and 16 at an average received SNR of 21 dB. For over 99%
Multiresolution grayscale and rotation invariant texture classification with local binary patterns
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... This paper presents a theoretically very simple, yet efficient, multiresolution approach to grayscale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions. The method is based on recognizing that certain ..."
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Cited by 1134 (36 self)
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This paper presents a theoretically very simple, yet efficient, multiresolution approach to grayscale and rotation invariant texture classification based on local binary patterns and nonparametric discrimination of sample and prototype distributions. The method is based on recognizing that certain local binary patterns, termed "uniform," are fundamental properties of local image texture and their occurrence histogram is proven to be a very powerful texture feature. We derive a generalized grayscale and rotation invariant operator presentation that allows for detecting the "uniform" patterns for any quantization of the angular space and for any spatial resolution and presents a method for combining multiple operators for multiresolution analysis. The proposed approach is very robust in terms of grayscale variations since the operator is, by definition, invariant against any monotonic transformation of the gray scale. Another advantage is computational simplicity as the operator can be realized with a few operations in a small neighborhood and a lookup table. Excellent experimental results obtained in true problems of rotation invariance, where the classifier is trained at one particular rotation angle and tested with samples from other rotation angles, demonstrate that good discrimination can be achieved with the occurrence statistics of simple rotation invariant local binary patterns. These operators characterize the spatial configuration of local image texture and the performance can be further improved by combining them with rotation invariant variance measures that characterize the contrast of local image texture. The joint distributions of these orthogonal measures are shown to be very powerful tools for rotation invariant texture analysis.
Sparse coding with an overcomplete basis set: a strategy employed by V1
 Vision Research
, 1997
"... The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive f ..."
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Cited by 910 (12 self)
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The spatial receptive fields of simple cells in mammalian striate cortex have been reasonably well described physiologically and can be characterized as being localized, oriented, and ban@ass, comparable with the basis functions of wavelet transforms. Previously, we have shown that these receptive field properties may be accounted for in terms of a strategy for producing a sparse distribution of output activity in response to natural images. Here, in addition to describing this work in a more expansive fashion, we examine the neurobiological implications of sparse coding. Of particular interest is the case when the code is overcompletei.e., when the number of code elements is greater than the effective dimensionality of the input space. Because the basis functions are nonorthogonal and not linearly independent of each other, sparsifying the code will recruit only those basis functions necessary for representing a given input, and so the inputoutput function will deviate from being purely linear. These deviations from linearity provide a potential explanation for the weak forms of nonlinearity observed in the response properties of cortical simple cells, and they further make predictions about the expected interactions among units in
New results in linear filtering and prediction theory
 Trans. ASME, Ser. D, J. Basic Eng
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 506 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary statistics. The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field. The Duality Principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed sidebyside. Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly. 1
A Maximum Entropy Approach to Adaptive Statistical Language Modeling
 Computer, Speech and Language
, 1996
"... An adaptive statistical languagemodel is described, which successfullyintegrates long distancelinguistic information with other knowledge sources. Most existing statistical language models exploit only the immediate history of a text. To extract information from further back in the document's h ..."
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Cited by 284 (12 self)
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An adaptive statistical languagemodel is described, which successfullyintegrates long distancelinguistic information with other knowledge sources. Most existing statistical language models exploit only the immediate history of a text. To extract information from further back in the document's history, we propose and use trigger pairs as the basic information bearing elements. This allows the model to adapt its expectations to the topic of discourse. Next, statistical evidence from multiple sources must be combined. Traditionally, linear interpolation and its variants have been used, but these are shown here to be seriously deficient. Instead, we apply the principle of Maximum Entropy (ME). Each information source gives rise to a set of constraints, to be imposed on the combined estimate. The intersection of these constraints is the set of probability functions which are consistent with all the information sources. The function with the highest entropy within that set is the ME solution...
Shape Distributions
 ACM Transactions on Graphics
, 2002
"... this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The pr ..."
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Cited by 279 (2 self)
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this paper, we propose and analyze a method for computing shape signatures for arbitrary (possibly degenerate) 3D polygonal models. The key idea is to represent the signature of an object as a shape distribution sampled from a shape function measuring global geometric properties of an object. The primary motivation for this approach is to reduce the shape matching problem to the comparison of probability distributions, which is simpler than traditional shape matching methods that require pose registration, feature correspondence, or model fitting
The analogues of entropy and of Fisher’s information measure in free probability theory
 I. Comm. Math. Phys
, 1993
"... Dedicated to Huzuhiro Araki Abstract. Analogues of the entropy and Fisher information measure for random variables in the context of free probability theory are introduced. Monotonicity properties and an analogue of the CramerRao inequality are proved. ..."
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Cited by 257 (12 self)
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Dedicated to Huzuhiro Araki Abstract. Analogues of the entropy and Fisher information measure for random variables in the context of free probability theory are introduced. Monotonicity properties and an analogue of the CramerRao inequality are proved.
Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross entropy
 IEEE Trans. Information Theory
, 1980
"... dple of min imum cromentropy (mhlmum dire&d dfvergenoe) are shown tobeunfquelycomxtmethodsforhductiveinf~whennewinformnt ionlsghninthefomlofexpe&edvalues.ReviousjILstit icatioaslLve ..."
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Cited by 255 (2 self)
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dple of min imum cromentropy (mhlmum dire&d dfvergenoe) are shown tobeunfquelycomxtmethodsforhductiveinf~whennewinformnt ionlsghninthefomlofexpe&edvalues.ReviousjILstit icatioaslLve
A Gaussian prior for smoothing maximum entropy models
, 1999
"... In certain contexts, maximum entropy (ME) modeling can be viewed as maximum likelihood training for exponential models, and like other maximum likelihood methods is prone to overfitting of training data. Several smoothing methods for maximum entropy models have been proposed to address this problem ..."
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Cited by 248 (2 self)
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In certain contexts, maximum entropy (ME) modeling can be viewed as maximum likelihood training for exponential models, and like other maximum likelihood methods is prone to overfitting of training data. Several smoothing methods for maximum entropy models have been proposed to address this problem, but previous results do not make it clear how these smoothing methods compare with smoothing methods for other types of related models. In this work, we survey previous work in maximum entropy smoothing and compare the performance of several of these algorithms with conventional techniques for smoothing ngram language models. Because of the mature body of research in ngram model smoothing and the close connection between maximum entropy and conventional ngram models, this domain is wellsuited to gauge the performance of maximum entropy smoothing methods. Over a large number of data sets, we find that an ME smoothing method proposed to us by Lafferty [1] performs as well as or better than all other algorithms under consideration. This general and efficient method involves using a Gaussian prior on the parameters of the model and selecting maximum a posteriori instead of maximum likelihood parameter values. We contrast this method with previous ngram smoothing methods to explain its superior performance.