Results 1  10
of
57
Efficient numerical methods in nonuniform sampling theory
, 1995
"... We present a new “second generation” reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a bandlimited function from its nonuniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named ..."
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Cited by 80 (9 self)
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We present a new “second generation” reconstruction algorithm for irregular sampling, i.e. for the problem of recovering a bandlimited function from its nonuniformly sampled values. The efficient new method is a combination of the adaptive weights method which was developed by the two first named authors and the method of conjugate gradients for the solution of positive definite linear systems. The choice of ”adaptive weights” can be seen as a simple but very efficient method of preconditioning. Further substantial acceleration is achieved by utilizing the Toeplitztype structure of the system matrix. This new algorithm can handle problems of much larger dimension and condition number than have been accessible so far. Furthermore, if some gaps between samples are large, then the algorithm can still be used as a very efficient extrapolation method across the gaps.
Hardware Assisted Volume Rendering of Unstructured Grids by Incremental Slicing
, 1996
"... Some of the more important research results in computational science rely on the use of simulation methods that operate on unstructured grids. However, these grids, composed of a set of convex polyhedra, introduce exceptional problems with respect to data visualization. Volume rendering techniques ..."
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Cited by 68 (0 self)
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Some of the more important research results in computational science rely on the use of simulation methods that operate on unstructured grids. However, these grids, composed of a set of convex polyhedra, introduce exceptional problems with respect to data visualization. Volume rendering techniques, originally developed to handle rectangular grids, show significant promise for general use with unstructured grids as well. The main disadvantage of this approach, compared to isosurfaces, particles or other visualization tools is its noninteractive performance. We describe an efficient method for rendering unstructured grids that is based on incremental slicing and hardware polygon rendering. For a given view direction, the grid vertices are transformed to image space using available graphics hardware. We then incrementally compute the 2D polygonmeshes that result from letting a set of equidistant planes, parallel to the screen plane, intersect (slice) the transformed grid. Final...
A Banach space of test functions for Gabor analysis
 IN &QUOT;GABOR ANALYSIS AND ALGORITHMS: THEORY AND APPLICATIONS
, 1998
"... We introduce the Banach space S 0 # L which has a variety of properties making it a useful tool in Gabor analysis. S 0 can be characterized as the smallest timefrequency homogeneous Banach space of (continuous) functions. We also present other characterizations of S 0 turning it into a very ..."
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Cited by 38 (9 self)
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We introduce the Banach space S 0 # L which has a variety of properties making it a useful tool in Gabor analysis. S 0 can be characterized as the smallest timefrequency homogeneous Banach space of (continuous) functions. We also present other characterizations of S 0 turning it into a very flexible tool for Gabor analysis and allowing for simplifications of various proofs. A careful
Perfect Recovery and Sensitivity Analysis of Time Encoded Bandlimited Signals
 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMSI: REGULAR PAPERS
, 2004
"... A time encoding machine is a realtime asynchronous
mechanism for encoding amplitude information into a time se
quence. We investigate the operating characteristics of a machine
consisting of a feedback loop containing an adder, a linear filter,
and a noninverting Schmitt trigger. We ..."
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Cited by 29 (19 self)
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A time encoding machine is a realtime asynchronous
mechanism for encoding amplitude information into a time se
quence. We investigate the operating characteristics of a machine
consisting of a feedback loop containing an adder, a linear filter,
and a noninverting Schmitt trigger. We show that the amplitude
information of a bandlimited signal can be perfectly recovered
if the difference between any two consecutive values of the time
sequence is bounded by the inverse of the Nyquist rate. We also
show how to build a nonlinear inverse time decoding machine
(TDM) that perfectly recovers the amplitude information from
the time sequence. We demonstrate the close relationship between
the recovery algorithms for time encoding and irregular sampling.
We also show the close relationship between time encoding and
a number of nonlinear modulation schemes including FM and
asynchronous sigma–delta modulation. We analyze the sensitivity
of the time encoding recovery algorithm and demonstrate how to
construct a TDM that perfectly recovers the amplitude informa
tion from the time sequence and is trigger parameter insensitive.
We derive bounds on the error in signal recovery introduced by
the quantization of the time sequence. We compare these with the
recovery error introduced by the quantization of the amplitude
of the bandlimited signal when irregular sampling is employed.
Under Nyquisttype rate conditions, quantization of a bandlimited
signal in the time and amplitude domains are shown to be largely
equivalent methods of information representation.
Reconstruction of Irregularly Sampled DiscreteTime Bandlimited Signals with Unknown Sampling Locations
, 2000
"... The purpose of this paper is to develop methods that can reconstruct a bandlimited discretetime signal from an irregular set of samples at unknown locations. We define a solution to the problem using first a geometric and then an algebraic point of view. We find the locations of the irregular set o ..."
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Cited by 23 (7 self)
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The purpose of this paper is to develop methods that can reconstruct a bandlimited discretetime signal from an irregular set of samples at unknown locations. We define a solution to the problem using first a geometric and then an algebraic point of view. We find the locations of the irregular set of samples by treating the problem as a combinatorial optimization problem. We employ an exhaustive method and two descent methods: the random search and cyclic coordinate methods. The numerical simulations were made on three types of irregular sets of locations: random sets; sets with jitter around a uniform set; and periodic nonuniform sets. Furthermore, for the periodic nonuniform set of locations, we develop a fast scheme that reduces the computational complexity of the problem by exploiting the periodic nonuniform structure of the sample locations in the DFT.
Time Encoding with an IntegrateandFire Neuron with a Refractory Period
 Neurocomputing
, 2004
"... Time encoding is a formal method of mapping amplitude information into a time sequence. We shaw that under simple conditions, bandlimited stimuli encoded with an integrateandfire neuron with an absolute refractory period can be recovered lossfree from the neural spike train at its output. We p ..."
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Cited by 21 (14 self)
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Time encoding is a formal method of mapping amplitude information into a time sequence. We shaw that under simple conditions, bandlimited stimuli encoded with an integrateandfire neuron with an absolute refractory period can be recovered lossfree from the neural spike train at its output. We provide an algorithm for perfect recovery and derive conditions for its convergence.
A randomized Kaczmarz algorithm with exponential convergence
"... The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical estimates for its rate of convergence are still scarce. We i ..."
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Cited by 21 (1 self)
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The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical estimates for its rate of convergence are still scarce. We introduce a randomized version of the Kaczmarz method for consistent, overdetermined linear systems and we prove that it converges with expected exponential rate. Furthermore, this is the first solver whose rate does not depend on the number of equations in the system. The solver does not even need to know the whole system, but only a small random part of it. It thus outperforms all previously known methods on general extremely overdetermined systems. Even for moderately overdetermined systems, numerical simulations as well as theoretical analysis reveal that our algorithm can converge faster than the celebrated conjugate gradient algorithm. Furthermore, our theory and numerical simulations confirm a prediction of Feichtinger et al. in the context of reconstructing bandlimited functions from nonuniform sampling. ∗ T.S. was supported by NSF DMS grant 0511461. R.V. was supported by the Alfred P.
Time Encoding and Perfect Recovery of Bandlimited Signals
 Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, April 610, 2003, Hong Kong
, 2003
"... A Time Encoding Machine is a realtime asynchronous mechanism for encoding amplitude information into a time sequence. We investigate the operating characteristics of a machine consisting of a feedback loop containing an adder, a linear filter and a Schmmitt trigger. We show how to recover the ampl ..."
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Cited by 16 (9 self)
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A Time Encoding Machine is a realtime asynchronous mechanism for encoding amplitude information into a time sequence. We investigate the operating characteristics of a machine consisting of a feedback loop containing an adder, a linear filter and a Schmmitt trigger. We show how to recover the amplitude information of a bandlimited signal from the time sequence lossfree.
An energy conservation method for wireless sensor networks employing a blue noise spatial sampling technique
 In Information Processing in Sensor Networks
, 2004
"... In this work, we present a method for the selection of a subset of nodes in a wireless sensor network whose application is to reconstruct the image of a (spatially) bandlimited physical value (e.g., temperature). The selection method creates a sampling pattern based on blue noise masking and guarant ..."
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Cited by 15 (1 self)
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In this work, we present a method for the selection of a subset of nodes in a wireless sensor network whose application is to reconstruct the image of a (spatially) bandlimited physical value (e.g., temperature). The selection method creates a sampling pattern based on blue noise masking and guarantees a near minimal number of activated sensors for a given signaltonoise ratio. The selection method is further enhanced to guarantee that the sensor nodes with the least residual energy are the primary candidates for deselection, while enabling a tradeoff between sensor selection optimality and balanced load distribution. Simulation results show the effectiveness of these selection methods in improving signaltonoise ratio and reducing the necessary number of active sensors compared with simpler selection approaches.
Interpolation in the Time and Frequency Domains
 IEEE SIGNAL PROCESSING LETTERS
, 1996
"... In this letter, we clarify the connections between two recently proposed and apparently unrelated approaches to bandlimited interpolation by showing that, in a certain sense made precise below, they are the dual of each other. The advantages of recognizing this duality are discussed. ..."
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Cited by 14 (11 self)
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In this letter, we clarify the connections between two recently proposed and apparently unrelated approaches to bandlimited interpolation by showing that, in a certain sense made precise below, they are the dual of each other. The advantages of recognizing this duality are discussed.