Recent Submissions

  • A Theoretical Analysis of Joint Manifolds 

    Davenport, Mark A.; Hegde, Chinmay; Duarte, Marco; Baraniuk, Richard G. (2009-01)
    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 ...
  • Sparse Coding with Population Sketches 

    Dyer, Eva L.; Baraniuk, Richard G.; Johnson, Don H. (2009-07-13)
  • Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes 

    Baraniuk, Richard; Crouse, Matthew (2009-04-15)
    1/f noise and statistically self-similar random processes such as fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) are fundamental models for a host of real-world phenomena, from network traffic to DNA to the stock market. Synthesis algorithms play a key role by providing the feedstock of data necessary for running complex ...
  • Tuning support vector machines for minimax and Neyman-Pearson classification 

    Scott, Clayton D.; Baraniuk, Richard G.; Davenport, Mark A. (2008-08-19)
    This paper studies the training of support vector machine (SVM) classifiers with respect to the minimax and Neyman-Pearson criteria. In principle, these criteria can be optimized in a straightforward way using a cost-sensitive SVM. In practice, however, because these criteria require especially accurate error estimation, standard techniques for tuning ...
  • A simple proof of the restricted isometry property for random matrices 

    Baraniuk, Richard G.; Davenport, Mark A.; DeVore, Ronald A.; Wakin, Michael B. (2007-01-18)
    We give a simple technique for verifying the Restricted Isometry Property (as introduced by Candès and Tao) for random matrices that underlies Compressed Sensing. Our approach has two main ingredients: (i) concentration inequalities for random inner products that have recently provided algorithmically simple proofs of the Johnson–Lindenstrauss lemma; ...
  • Single-pixel imaging via compressive sampling 

    Duarte, Marco F.; Davenport, Mark A.; Takhar, Dharmpal; Laska, Jason N.; Sun, Ting; (2008-03-01)
  • Multiscale random projections for compressive classification 

    Duarte, Marco F.; Davenport, Mark A.; Wakin, Michael B.; Laska, Jason N.; Takhar, Dharmpal; (2007-09-01)
    We propose a framework for exploiting dimension-reducing random projections in detection and classification problems. Our approach is based on the generalized likelihood ratio test; in the case of image classification, it exploits the fact that a set of images of a fixed scene under varying articulation parameters forms a low-dimensional, nonlinear ...
  • Minimax support vector machines 

    Davenport, Mark A.; Baraniuk, Richard G.; Scott, Clayton D. (2007-08-01)
    We study the problem of designing support vector machine (SVM) classifiers that minimize the maximum of the false alarm and miss rates. This is a natural classification setting in the absence of prior information regarding the relative costs of the two types of errors or true frequency of the two classes in nature. Examining two approaches – one ...
  • The smashed filter for compressive classification and target recognition 

    Davenport, Mark A.; Duarte, Marco F.; Wakin, Michael B.; Laska, Jason N.; Takhar, Dharmpal; (2007-01-01)
    The theory of compressive sensing (CS) enables the reconstruction of a sparse or compressible image or signal from a small set of linear, non-adaptive (even random) projections. However, in many applications, including object and target recognition, we are ultimately interested in making a decision about an image rather than computing a reconstruction. ...
  • Regression level set estimation via cost-sensitive classification 

    Scott, Clayton D.; Davenport, Mark A. (2007-06-01)
    Regression level set estimation is an important yet understudied learning task. It lies somewhere between regression function estimation and traditional binary classification, and in many cases is a more appropriate setting for questions posed in these more common frameworks. This note explains how estimating the level set of a regression function ...
  • Detection and estimation with compressive measurements 

    Baraniuk, Richard G.; Davenport, Mark A.; Wakin, Michael B. (2006-11-01)
    The recently introduced theory of compressed sensing enables the reconstruction of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist rate samples. Interestingly, it has been shown that random projections are a satisfactory ...
  • Small-time scaling behaviors of Internet backbone traffic: An empirical study 

    Zhang, Zhi-Li; Ribeiro, Vinay Joseph; Moon, Sue; Diot, Christophe (2003-04-20)
    We study the small-time (sub-seconds) scaling behaviors of Internet backbone traffic, based on traces collected from OC3/12/48 links in a tier-1 ISP. We observe that for a majority of these traces, the (second-order) scaling exponents at small time scales (1ms - 100ms) are fairly close to 0.5, indicating that <i>traffic fluctuations</i> at these ...
  • Multiscale Density Estimation 

    Willett, Rebecca; Nowak, Robert David (2003-08-20)
    The nonparametric density estimation method proposed in this paper is computationally fast, capable of detecting density discontinuities and singularities at a very high resolution, spatially adaptive, and offers near minimax convergence rates for broad classes of densities including Besov spaces. At the heart of this new method lie multiscale signal ...
  • Multiscale Likelihood Analysis and Image Reconstruction 

    Willett, Rebecca; Nowak, Robert David (2003-08-20)
    The nonparametric multiscale polynomial and platelet methods presented here are powerful new tools for signal and image denoising and reconstruction. Unlike traditional wavelet-based multiscale methods, these methods are both well suited to processing Poisson or multinomial data and capable of preserving image edges. At the heart of these new methods ...
  • Platelets for Multiscale Analysis in Photon-Limited Imaging 

    Willett, Rebecca; Nowak, Robert David (2002-09-20)
    This paper proposes a new multiscale image decomposition based on platelets. Platelets are localized functions at various scales, locations, and orientations that produce piecewise linear image approximations. For smoothness measured in certain H¨older classes, the error of m-term platelet approximations can decay significantly faster than that of ...
  • Platelets for Multiscale Analysis in Medical Imaging 

    Willett, Rebecca; Nowak, Robert David (2002-04-20)
    This paper describes the development and use of multiscale, platelet-based image reconstruction algorithms in medical imaging. Such algorithms are effective because platelets approximate images in certain (piecewise) smoothness classes significantly more efficiently than sinusoids, wavelets, or wedgelets. Platelet representations are especially ...
  • Multiscale Analysis for Intensity and Density Estimation 

    Willett, Rebecca (2002-04-20)
    The nonparametric multiscale polynomial and platelet algorithms presented in this thesis are powerful new tools for signal and image denoising and reconstruction. Unlike traditional wavelet-based multiscale methods, these algorithms are both well suited to processing Poisson and multinomial data and capable of preserving image edges. At the heart of ...
  • Platelets: A Multiscale Approach for Recovering Edges and Surfaces in Photon-Limited Medical Imaging 

    Willett, Rebecca; Nowak, Robert David (2003)
    This paper proposes a new multiscale image decomposition based on platelets. Platelets are localized functions at various scales, locations, and orientations that produce piecewise linear image approximations. Platelets are well suited for approximating images consisting of smooth regions separated by smooth boundaries. For smoothness measured in ...
  • Multiresolution Nonparametric Intensity and Density Estimation 

    Willett, Rebecca; Nowak, Robert David (2002-05-20)
    This paper introduces a new multiscale method for nonparametric piecewise polynomial intensity and density estimation of point processes. Fast, piecewise polynomial, maximum penalized likelihood methods for intensity and density estimation are developed. The recursive partitioning scheme underlying these methods is based on multiscale likelihood ...
  • Multiresolution Intensity Estimation of Piecewise Linear Poisson Processes 

    Willett, Rebecca (2001-04-20)
    Given observations of a one-dimensional piecewise linear, length-M Poisson intensity function, our goal is to estimate both the partition points and the parameters of each segment. In order to determine where the breaks lie, we develop a maximum penalized likelihood estimator based on information-theoretic complexity penalization. We construct a ...

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