Now showing items 1-28 of 28

  • Analysis of the DCS one-stage Greedy Algorothm for Common Sparse Supports 

    Baron, Dror; Duarte, Marco F.; Wakin, Michael; Sarvotham, Shriram; Baraniuk, Richard G. (2005-11-01)
    Analysis of the DCS one-stage Greedy Algorothm for Common Sparse Supports
  • Approximation and Compression of Piecewise Smooth Images Using a Wavelet/Wedgelet Geometric Model 

    Romberg, Justin; Wakin, Michael; Baraniuk, Richard G. (2003-09-01)
    Inherent to photograph-like images are two types of structures: large smooth regions and geometrically smooth edge contours separating those regions. Over the past years, efficient representations and algorithms have been ...
  • Compressing Piecewise Smooth Multidimensional Functions Using Surflets: Rate-Distortion Analysis 

    Chandrasekaran, Venkat; Wakin, Michael; Baron, Dror; Baraniuk, Richard G. (2004-03-01)
    Discontinuities in data often represent the key information of interest. Efficient representations for such discontinuities are important for many signal processing applications, including compression, but standard Fourier ...
  • Compression of Higher Dimensional Functions Containing Smooth Discontinuities 

    Chandrasekaran, Venkat; Wakin, Michael; Baron, Dror; Baraniuk, Richard G. (2004-03-01)
    Discontinuities in data often represent the key information of interest. Efficient representations for such discontinuities are important for many signal processing applications, including compression, but standard Fourier ...
  • Distributed Compressed Sensing of Jointly Sparse Signals 

    Sarvotham, Shriram; Baron, Dror; Wakin, Michael; Duarte, Marco F.; Baraniuk, Richard G. (2005-11-01)
    Compressed sensing is an emerging field based on the revelation that a small collection of linear projections of a sparse signal contains enough information for reconstruction. In this paper we expand our theory for ...
  • Edge Characteristics in Wavelet-Based Image Coding 

    Wakin, Michael (2001-04-20)
    Accurate prediction of wavelet coefficients relies on an understanding of the phase effects of edge alignment. This research examines techniques for uncovering edge information based on the available coefficients. These ...
  • A Geometric Hidden Markov Tree Wavelet Model 

    Romberg, Justin; Wakin, Michael; Choi, Hyeokho; Baraniuk, Richard G. (2003-08-01)
    In the last few years, it has become apparent that traditional wavelet-based image processing algorithms and models have significant shortcomings in their treatment of edge contours. The standard modeling paradigm exploits ...
  • Geometric Methods for Wavelet-Based Image Compression 

    Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G. (2003-08-01)
    Natural images can be viewed as combinations of smooth regions, textures, and geometry. Wavelet-based image coders, such as the space-frequency quantization (SFQ) algorithm, provide reasonably efficient representations for ...
  • Geometric Tools for Image Compression 

    Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G. (2002-11-01)
    Images typically contain strong geometric features, such as edges, that impose a structure on pixel values and wavelet coefficients. Modeling the joint coherent behavior of wavelet coefficients is difficult, and standard ...
  • High-Resolution Navigation on Non-Differentiable Image Manifolds 

    Wakin, Michael; Donoho, David; Choi, Hyeokho; Baraniuk, Richard G. (2005-03-01)
    The images generated by varying the underlying articulation parameters of an object (pose, attitude, light source position, and so on) can be viewed as points on a low-dimensional <i>image parameter articulation manifold</i> ...
  • Image Compression using an Efficient Edge Cartoon + Texture Model 

    Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G. (2002-04-01)
    Wavelet-based image coders optimally represent smooth regions and isolated point singularities. However, wavelet coders are less adept at representing perceptually important edge singularities, and coding performance ...
  • Image Compression using Multiscale Geometric Edge Models 

    Wakin, Michael (2002-05-20)
    Edges are of particular interest for image compression, as they communicate important information, contribute large amounts of high-frequency energy, and can generally be described with few parameters. Many of today's most ...
  • A Markov Chain Analysis of Blackjack Strategy 

    Wakin, Michael; Rozell, Chris (2004-07-01)
    Blackjack receives considerable attention from mathematicians and entrepreneurs alike, due to its simple rules, its inherent random nature, and the abundance of "prior" information available to an observant player. Many ...
  • Multiscale Geometric Image Processing 

    Romberg, Justin; Wakin, Michael; Baraniuk, Richard G. (2003-07-01)
    Since their introduction a little more than 10 years ago, wavelets have revolutionized image processing. Wavelet based algorithms define the state-of-the-art for applications including image coding (JPEG2000), restoration, ...
  • The Multiscale Structure of Non-Differentiable Image Manifolds 

    Wakin, Michael; Donoho, David; Choi, Hyeokho; Baraniuk, Richard G. (2005-08-01)
    In this paper, we study families of images generated by varying a parameter that controls the appearance of the object/scene in each image. Each image is viewed as a point in high-dimensional space; the family of images ...
  • Multiscale Wedgelet Image Analysis: Fast Decompositions and Modeling 

    Romberg, Justin; Wakin, Michael; Baraniuk, Richard G. (2002-06-01)
    The most perceptually important features in images are geometrical, the most prevalent being the smooth contours ("edges") that separate different homogeneous regions and delineate distinct objects. Although wavelet based ...
  • Non-Redundant, Linear-Phase, Semi-Orthogonal, Directional Complex Wavelets 

    Fernandes, Felix; Wakin, Michael; Baraniuk, Richard G. (2004-05-01)
    The directionality and phase information provided by non-redundant complex wavelet transforms (NCWTs) provide significant potential benefits for image/video processing and compression applications. However, because existing ...
  • On The Problem of Simultaneous Encoding of Magnitude and Location Information 

    Castro, Rui; Wakin, Michael; Orchard, Michael (2002-11-20)
    Modern image coders balance bitrate used for encoding the location of signicant transform coefficients, and bitrate used for coding their values. The importance of balancing location and value information in practical ...
  • Phase and Magnitude Perceptual Sensitivities in Nonredundant Complex Wavelet Representations 

    Wakin, Michael; Orchard, Michael; Baraniuk, Richard G.; Chandrasekaran, Venkat (2003-11-01)
    The recent development of a nonredundant complex wavelet transform allows a novel framework for image analysis. Work on this representation has recognized that the phase and magnitude of complex coefficients can be related ...
  • Random Filters for Compressive Sampling and Reconstruction 

    Baraniuk, Richard G.; Wakin, Michael; Duarte, Marco F.; Tropp, Joel A.; Baron, Dror (2006-05-01)
    We propose and study a new technique for efficiently acquiring and reconstructing signals based on convolution with a fixed FIR filter having random taps. The method is designed for sparse and compressible signals, i.e., ...
  • Random Projections of Signal Manifolds 

    Wakin, Michael; Baraniuk, Richard G. (2006-05-01)
    Random projections have recently found a surprising niche in signal processing. The key revelation is that the relevant structure in a signal can be preserved when that signal is projected onto a small number of random ...
  • Random Projections of Smooth Manifolds 

    Baraniuk, Richard G.; Wakin, Michael (2006-10-01)
    Many types of data and information can be described by concise models that suggest each data vector (or signal) actually has â few degrees of freedomâ relative to its size N. This is the motivation for a variety of ...
  • Rate-Distortion Optimized Image Compression using Wedgelets 

    Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G. (2002-06-01)
    Most wavelet-based image coders fail to model the joint coherent behavior of wavelet coefficients near edges. Wedgelets offer a convenient parameterization for the edges in an image, but they have yet to yield a viable ...
  • Representation and Compression of Multi-Dimensional Piecewise Functions Using Surflets 

    Chandrasekaran, Venkat; Wakin, Michael; Baron, Dror; Baraniuk, Richard G. (2006-03-01)
    We study the representation, approximation, and compression of functions in M dimensions that consist of constant or smooth regions separated by smooth (M-1)-dimensional discontinuities. Examples include images containing ...
  • Surflets: A Sparse Representation for Multidimensional Functions Containing Smooth Discontinuities 

    Chandrasekaran, Venkat; Wakin, Michael; Baron, Dror; Baraniuk, Richard G. (2004-07-01)
    Discontinuities in data often provide vital information, and representing these discontinuities sparsely is an important goal for approximation and compression algorithms. Little work has been done on efficient representations ...
  • Universal Distributed Sensing via Random Projections 

    Wakin, Michael; Duarte, Marco F.; Baraniuk, Richard G.; Baron, Dror (2006-04-01)
    This paper develops a new framework for distributed coding and compression in sensor networks based on distributed compressed sensing (DCS). DCS exploits both intra-signal and inter-signal correlations through the concept ...
  • Wavelet-domain Approximation and Compression of Piecewise Smooth Images 

    Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G. (2005-01-15)
    The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to <i>piecewise ...
  • Wavelet-Domain Approximation and Compression of Piecewise Smooth Images 

    Wakin, Michael; Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G. (2006-05-01)
    The wavelet transform provides a sparse representation for smooth images, enabling efficient approximation and compression using techniques such as zerotrees. Unfortunately, this sparsity does not extend to piecewise smooth ...