Greedy signal space methods for incoherence and beyond

Raja Giryes*, Deanna Needell

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


Abstract Compressive sampling (CoSa) has provided many methods for signal recovery of signals compressible with respect to an orthonormal basis. However, modern applications have sparked the emergence of approaches for signals not sparse in an orthonormal basis but in some arbitrary, perhaps highly overcomplete, dictionary. Recently, several "signal-space" greedy methods have been proposed to address signal recovery in this setting. However, such methods inherently rely on the existence of fast and accurate projections which allow one to identify the most relevant atoms in a dictionary for any given signal, up to a very strict accuracy. When the dictionary is highly overcomplete, no such projections are currently known; the requirements on such projections do not even hold for incoherent or well-behaved dictionaries. In this work, we provide an alternate analysis for signal space greedy methods which enforce assumptions on these projections which hold in several settings including those when the dictionary is incoherent or structurally coherent. These results align more closely with traditional results in the standard CoSa literature and improve upon previous work in the signal space setting.

Original languageEnglish
Article number993
Pages (from-to)1-20
Number of pages20
JournalApplied and Computational Harmonic Analysis
Issue number1
StatePublished - 1 Jul 2015
Externally publishedYes


FundersFunder number
Simons Foundation Collaboration274305
Directorate for Mathematical and Physical Sciences1348721
Azrieli Foundation


    • Algorithms
    • Approximation
    • CoSaMP
    • Coherent dictionaries
    • Compressed Sensing
    • Restricted Isometry Property
    • Signal space methods
    • Sparse approximation
    • Sparse modeling


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