Browsing by Author "Hegde, Chinmay"

Now showing 1 - 4 of 4
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    An Introduction to Compressive Sensing
    (Rice University, 2014-08-26) Baraniuk, Richard; Davenport, Mark A.; Duarte, Marco F.; Hegde, Chinmay
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    Nonlinear Signal Models: Geometry, Algorithms, and Analysis
    (2013-07-24) Hegde, Chinmay; Baraniuk, Richard G.; Veeraraghavan, Ashok; Yin, Wotao
    Traditional signal processing systems, based on linear modeling principles, face a stifling pressure to meet present-day demands caused by the deluge of data generated, transmitted and processed across the globe. Fortunately, recent advances have resulted in the emergence of more sophisticated, nonlinear signal models. Such nonlinear models have inspired fundamental changes in which information processing systems are designed and analyzed. For example, the sparse signal model serves as the basis for Compressive Sensing (CS), an exciting new framework for signal acquisition. In this thesis, we advocate a geometry-based approach for nonlinear modeling of signal ensembles. We make the guiding assumption that the signal class of interest forms a nonlinear low-dimensional manifold belonging to the high-dimensional signal space. A host of traditional data models can be essentially interpreted as specific instances of such manifolds. Therefore, our proposed geometric approach provides a common framework that can unify, analyze, and significantly extend the scope of nonlinear models for information acquisition and processing. We demonstrate that the geometric approach enables new algorithms and analysis for a number of signal processing applications. Our specific contributions include: (i) new convex formulations and algorithms for the design of linear systems for data acquisition, compression, and classification; (ii) a general algorithm for reconstruction, deconvolution, and denoising of signals, images, and matrix-valued data; (iii) efficient methods for inference from a small number of linear signal samples, without ever resorting to reconstruction; and, (iv) new signal and image representations for robust modeling and processing of large-scale data ensembles.
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    Sampling and recovery of pulse streams
    (2010) Hegde, Chinmay; Baraniuk, Richard G.
    Compressive Sensing (CS) is a new technique for the efficient acquisition of signals, images, and other data that have a sparse representation in some basis, frame, or dictionary. By sparse we mean that the N -dimensional basis representation has just K << N significant coefficients; in this case, the CS theory maintains that just M = O (K log N) random linear signal measurements will both preserve all of the signal information and enable robust signal reconstruction in polynomial time. In this paper, we extend the CS theory to pulse stream data, which correspond to S-sparse signals/images that are convolved with an unknown F-sparse pulse shape. Ignoring their convolutional structure, a pulse stream signal is K = SF sparse. Such signals figure prominently in a number of applications, from neuroscience to astronomy. Our specific contributions are threefold. First, we propose a pulse stream signal model and show that it is equivalent to an infinite union of subspaces. Second, we derive a lower bound on the number of measurements M required to preserve the essential information present in pulse streams. The bound is linear in the total number of degrees of freedom S + F, which is significantly smaller than the naive bound based on the total signal sparsity K = SF. Third, we develop an efficient signal recovery algorithm that infers both the shape of the impulse response as well as the locations and amplitudes of the pulses. The algorithm alternatively estimates the pulse locations and the pulse shape in a manner reminiscent of classical deconvolution algorithms. Numerical experiments on synthetic and real data demonstrate the advantages of our approach over standard CS.
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    A Theoretical Analysis of Joint Manifolds
    (2009-01) Davenport, Mark A.; Hegde, Chinmay; Duarte, Marco; Baraniuk, Richard G.
    The emergence of low-cost sensor architectures for diverse modalities has made it possible to deploy sensor arrays that capture a single event from a large number of vantage points and using multiple modalities. In many scenarios, these sensors acquire very high-dimensional data such as audio signals, images, and video. To cope with such high-dimensional data, we typically rely on low-dimensional models. Manifold models provide a particularly powerful model that captures the structure of high-dimensional data when it is governed by a low-dimensional set of parameters. However, these models do not typically take into account dependencies among multiple sensors. We thus propose a new joint manifold framework for data ensembles that exploits such dependencies. We show that simple algorithms can exploit the joint manifold structure to improve their performance on standard signal processing applications. Additionally, recent results concerning dimensionality reduction for manifolds enable us to formulate a network-scalable data compression scheme that uses random projections of the sensed data. This scheme efficiently fuses the data from all sensors through the addition of such projections, regardless of the data modalities and dimensions.