Rice Univesrity Logo
    • FAQ
    • Deposit your work
    • Login
    View Item 
    •   Rice Scholarship Home
    • Faculty & Staff Research
    • George R. Brown School of Engineering
    • Electrical and Computer Engineering
    • ECE Publications
    • View Item
    •   Rice Scholarship Home
    • Faculty & Staff Research
    • George R. Brown School of Engineering
    • Electrical and Computer Engineering
    • ECE Publications
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Random Projections of Signal Manifolds

    Thumbnail
    Name:
    Wak2006Mar5RandomProj.PDF
    Size:
    518.0Kb
    Format:
    PDF
    View/Open
    Author
    Wakin, Michael; Baraniuk, Richard G.
    Date
    2006-01-01
    Abstract
    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 basis functions. Recent work has exploited this fact under the rubric of Compressed Sensing (CS): signals that are sparse in some basis can be recovered from small numbers of random linear projections. In many cases, however, we may have a more specific low-dimensional model for signals in which the signal class forms a nonlinear manifold in R^N. This paper provides preliminary theoretical and experimental evidence that manifold-based signal structure can be preserved using small numbers of random projections. The key theoretical motivation comes from Whitneyâ s Embedding Theorem, which states that a K-dimensional manifold can be embedded in R^{2K+1}. We examine the potential applications of this fact. In particular, we consider the task of recovering a manifold-modeled signal from a small number of random projections. Thanks to our (more specific) model, the ability to recover the signal can be far superior to existing techniques in CS.
    Description
    Conference Paper
    Citation
    M. Wakin and R. G. Baraniuk, "Random Projections of Signal Manifolds," vol. 5, 2006.
    Published Version
    http://dx.doi.org/10.1109/ICASSP.2006.1661432
    Keyword
    random projections; signal manifolds; Multiscale geometry processing; random projections; signal manifolds
    Type
    Conference paper
    Citable link to this page
    https://hdl.handle.net/1911/20434
    Metadata
    Show full item record
    Collections
    • DSP Publications [508]
    • ECE Publications [1468]

    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map

     

    Searching scope

    Browse

    Entire ArchiveCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsTypeThis CollectionBy Issue DateAuthorsTitlesSubjectsType

    My Account

    Login

    Statistics

    View Usage Statistics

    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map