The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
Antonio Ortega - One of the best experts on this subject based on the ideXlab platform.
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A probabilistic interpretation of Sampling Theory of graph signals
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Akshay Gadde, Antonio OrtegaAbstract:We give a probabilistic interpretation of Sampling Theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain conditions, reconstructing a graph signal from a subset of its samples by least squares is equivalent to performing MAP inference on an approximation of this GRF which has a low rank covariance matrix. We then show that a Sampling set of given size with the largest associated cut-off frequency, which is optimal from a Sampling theoretic point of view, minimizes the worst case predictive covariance of the MAP estimate on the GRF. This interpretation also gives an intuitive explanation for the superior performance of the Sampling theoretic approach to active semi-supervised classification.
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active semi supervised learning using Sampling Theory for graph signals
Knowledge Discovery and Data Mining, 2014Co-Authors: Akshay Gadde, Aamir Anis, Antonio OrtegaAbstract:We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on Sampling Theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The Sampling Theory for graph signals aims to extend the traditional Nyquist-Shannon Sampling Theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on Sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.
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KDD - Active semi-supervised learning using Sampling Theory for graph signals
Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, 2014Co-Authors: Akshay Gadde, Aamir Anis, Antonio OrtegaAbstract:We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on Sampling Theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The Sampling Theory for graph signals aims to extend the traditional Nyquist-Shannon Sampling Theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on Sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.
Jelena Kovacevic - One of the best experts on this subject based on the ideXlab platform.
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Sampling Theory for graph signals on product graphs
IEEE Global Conference on Signal and Information Processing, 2018Co-Authors: Rohan Varma, Jelena KovacevicAbstract:In this paper, we extend the Sampling Theory on graphs by constructing a framework that exploits the structure in product graphs for efficient Sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs that are composed from smaller graph atoms; we motivate how this model is a flexible and useful way to model richer classes of data that can be multi-modal in nature. Previous works have established a Sampling Theory on graphs for bandlimited signals. Importantly, the framework achieves significant savings in both sample complexity and computational complexity.
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GlobalSIP - Sampling Theory FOR GRAPH SIGNALS ON PRODUCT GRAPHS
2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP), 2018Co-Authors: Rohan Varma, Jelena KovacevicAbstract:In this paper, we extend the Sampling Theory on graphs by constructing a framework that exploits the structure in product graphs for efficient Sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs that are composed from smaller graph atoms; we motivate how this model is a flexible and useful way to model richer classes of data that can be multi-modal in nature. Previous works have established a Sampling Theory on graphs for bandlimited signals. Importantly, the framework achieves significant savings in both sample complexity and computational complexity.
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Sampling Theory for graph signals
International Conference on Acoustics Speech and Signal Processing, 2015Co-Authors: Siheng Chen, Aliaksei Sandryhaila, Jelena KovacevicAbstract:We propose a Sampling Theory for finite-dimensional vectors with a generalized bandwidth restriction, which follows the same paradigm of the classical Sampling Theory. We use this general result to derive a Sampling theorem for bandlimited graph signals in the framework of discrete signal processing on graphs. By imposing a specific structure on the graph, graph signals reduce to finite discrete-time or discrete-space signals, effectively ensuring that the proposed Sampling Theory works for such signals. The proposed Sampling Theory is applicable to both directed and undirected graphs, the assumption of perfect recovery is easy both to check and to satisfy, and, under that assumption, perfect recovery is guaranteed without any probability constraints or any approximation.
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ICASSP - Sampling Theory for graph signals
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Siheng Chen, Aliaksei Sandryhaila, Jelena KovacevicAbstract:We propose a Sampling Theory for finite-dimensional vectors with a generalized bandwidth restriction, which follows the same paradigm of the classical Sampling Theory. We use this general result to derive a Sampling theorem for bandlimited graph signals in the framework of discrete signal processing on graphs. By imposing a specific structure on the graph, graph signals reduce to finite discrete-time or discrete-space signals, effectively ensuring that the proposed Sampling Theory works for such signals. The proposed Sampling Theory is applicable to both directed and undirected graphs, the assumption of perfect recovery is easy both to check and to satisfy, and, under that assumption, perfect recovery is guaranteed without any probability constraints or any approximation.
Akshay Gadde - One of the best experts on this subject based on the ideXlab platform.
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A probabilistic interpretation of Sampling Theory of graph signals
2015 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2015Co-Authors: Akshay Gadde, Antonio OrtegaAbstract:We give a probabilistic interpretation of Sampling Theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain conditions, reconstructing a graph signal from a subset of its samples by least squares is equivalent to performing MAP inference on an approximation of this GRF which has a low rank covariance matrix. We then show that a Sampling set of given size with the largest associated cut-off frequency, which is optimal from a Sampling theoretic point of view, minimizes the worst case predictive covariance of the MAP estimate on the GRF. This interpretation also gives an intuitive explanation for the superior performance of the Sampling theoretic approach to active semi-supervised classification.
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active semi supervised learning using Sampling Theory for graph signals
Knowledge Discovery and Data Mining, 2014Co-Authors: Akshay Gadde, Aamir Anis, Antonio OrtegaAbstract:We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on Sampling Theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The Sampling Theory for graph signals aims to extend the traditional Nyquist-Shannon Sampling Theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on Sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.
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KDD - Active semi-supervised learning using Sampling Theory for graph signals
Proceedings of the 20th ACM SIGKDD international conference on Knowledge discovery and data mining, 2014Co-Authors: Akshay Gadde, Aamir Anis, Antonio OrtegaAbstract:We consider the problem of offline, pool-based active semi-supervised learning on graphs. This problem is important when the labeled data is scarce and expensive whereas unlabeled data is easily available. The data points are represented by the vertices of an undirected graph with the similarity between them captured by the edge weights. Given a target number of nodes to label, the goal is to choose those nodes that are most informative and then predict the unknown labels. We propose a novel framework for this problem based on our recent results on Sampling Theory for graph signals. A graph signal is a real-valued function defined on each node of the graph. A notion of frequency for such signals can be defined using the spectrum of the graph Laplacian matrix. The Sampling Theory for graph signals aims to extend the traditional Nyquist-Shannon Sampling Theory by allowing us to identify the class of graph signals that can be reconstructed from their values on a subset of vertices. This approach allows us to define a criterion for active learning based on Sampling set selection which aims at maximizing the frequency of the signals that can be reconstructed from their samples on the set. Experiments show the effectiveness of our method.
Mehdi Shahbazian - One of the best experts on this subject based on the ideXlab platform.
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nonlinear dynamic system control using wavelet neural network based on Sampling Theory
Systems Man and Cybernetics, 2009Co-Authors: Ehsan Hossainiasl, Mehdi ShahbazianAbstract:Wavelet neural network based on Sampling Theory has been found to have a good performance in function approximation. In this paper, this type of wavelet neural network is applied to modeling and control of a nonlinear dynamic system and some methods are employed to optimize the structure of wavelet neural network to prevent a large number of nodes. The direct inverse control technique is employed for investigating the ability of this network in control application. A variety of simulations are conducted for demonstrating the performance of the direct inverse control using wavelet neural network. The performance of this approach is compared with direct inverse control using multilayer perceptron neural network (MLP). Simulation results show that our proposed method reveals better stability and performance in reference tracking and control action.
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Non uniform noisy data training using wavelet neural network based on Sampling Theory
WSEAS TRANSACTIONS on SYSTEMS archive, 2008Co-Authors: Mehdi Shahbazian, Karim SalahshoorAbstract:Global convergence and overfitting are the main problem in neural network training. One of the new methods to overcome these problems is Sampling Theory that is applied in training of wavelet neural network. In this paper this new method is improved for training of wavelet neural network in non uniform and noisy data. The improvements include suggesting a method for finding the appropriate feedback matrix, addition of early stopping and wavelet thresholding to training procedure. Two experiments are conducted for one and two dimensional function. The results establish a satisfied performance of this algorithm in reduction of generalization error, reduction the complexity of wavelet neural network and mainly avoiding overfitting.
Ayush Bhandari - One of the best experts on this subject based on the ideXlab platform.
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a swiss army knife for finite rate of innovation Sampling Theory
International Conference on Acoustics Speech and Signal Processing, 2016Co-Authors: Ayush Bhandari, Yonina C EldarAbstract:Finite-Rate-of-Innovation (FRI) Sampling Theory prescribes a procedure for exact recovery of Dirac impulses from linear measurements in the form of orthogonal projections of streams of Dirac impulses onto the subspace of Fourier—bandlimited functions. This enables recovery of a continuous time sparse signals at sub-Nyquist rates. In many cases, the transform domain of interest may be more general than the Fourier domain. Recent work has extended FRI Sampling Theory to the spherical Fourier Transform, fractional Fourier Transform and the Laplace Transform. In this paper, we develop a broad FRI framework applicable to a general class of transformations that includes Fourier, Laplace, Fresnel, fractional Fourier, Bargmann and Gauss—Weierstrass transforms, among others. For this purpose, we consider the Special Affine Fourier Transform (SAFT) which parametrically generalizes a number of well known unitary transforms linked with signal processing and optics. We first derive a version of Shannon's Sampling Theory based on the convolution structure tailored for the SAFT domain. Having identified the subspace of SAFT—bandlimited functions, we apply FRI Sampling Theory to the SAFT and study recovery of sparse signals, thus providing a unified view of FRI Sampling Theory for a large class of disparately studied operations.
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super resolved time of flight sensing via fri Sampling Theory
International Conference on Acoustics Speech and Signal Processing, 2016Co-Authors: Ayush Bhandari, Andrew M Wallace, Ramesh RaskarAbstract:Optical time-of-flight (ToF) sensors can measure scene depth accurately by projection and reception of an optical signal. The range to a surface in the path of the emitted signal is proportional to the delay time of the light echo or the reflected signal. In practice, a diverging beam may be subject to multi-echo backscatter, and all these echoes must be resolved to estimate the multiple depths. In this paper, we propose a method for super-resolution of optical ToF signals. Our contributions are twofold. Starting with a general image formation model common to most ToF sensors, we draw a striking analogy of ToF systems with Sampling Theory. Based on our model, we reformulate the ToF super-resolution problem as a parameter estimation problem pivoted around the finite-rate-of-innovation framework. In particular, we show that super-resolution of multi-echo backscattered signal amounts to recovery of Dirac impulses from low-pass measurements. Our Theory is corroborated by analysis of data collected from a photon counting, LiDAR sensor, showing the effectiveness of our non-iterative and computationally efficient algorithm.
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ICASSP - A swiss army knife for finite rate of innovation Sampling Theory
2016 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 2016Co-Authors: Ayush Bhandari, Yonina C EldarAbstract:Finite-Rate-of-Innovation (FRI) Sampling Theory prescribes a procedure for exact recovery of Dirac impulses from linear measurements in the form of orthogonal projections of streams of Dirac impulses onto the subspace of Fourier—bandlimited functions. This enables recovery of a continuous time sparse signals at sub-Nyquist rates. In many cases, the transform domain of interest may be more general than the Fourier domain. Recent work has extended FRI Sampling Theory to the spherical Fourier Transform, fractional Fourier Transform and the Laplace Transform. In this paper, we develop a broad FRI framework applicable to a general class of transformations that includes Fourier, Laplace, Fresnel, fractional Fourier, Bargmann and Gauss—Weierstrass transforms, among others. For this purpose, we consider the Special Affine Fourier Transform (SAFT) which parametrically generalizes a number of well known unitary transforms linked with signal processing and optics. We first derive a version of Shannon's Sampling Theory based on the convolution structure tailored for the SAFT domain. Having identified the subspace of SAFT—bandlimited functions, we apply FRI Sampling Theory to the SAFT and study recovery of sparse signals, thus providing a unified view of FRI Sampling Theory for a large class of disparately studied operations.
