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      Sparsity order estimation for single snapshot compressed sensing

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      Author
      Romer, F.
      Lavrenko, A.
      Del Galdo, G.
      Hotz, T.
      Arıkan, Orhan
      Thoma, R. S.
      Date
      2015-11
      Source Title
      Conference Record - Asilomar Conference on Signals, Systems and Computers
      Print ISSN
      1058-6393
      Publisher
      IEEE
      Pages
      1220 - 1224
      Language
      English
      Type
      Conference Paper
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      Abstract
      In this paper we discuss the estimation of the spar-sity order for a Compressed Sensing scenario where only a single snapshot is available. We demonstrate that a specific design of the sensing matrix based on Khatri-Rao products enables us to transform this problem into the estimation of a matrix rank in the presence of additive noise. Thereby, we can apply existing model order selection algorithms to determine the sparsity order. The matrix is a rearranged version of the observation vector which can be constructed by concatenating a series of non-overlapping or overlapping blocks of the original observation vector. In both cases, a Khatri-Rao structured measurement matrix is required with the main difference that in the latter case, one of the factors must be a Vandermonde matrix. We discuss the choice of the parameters and show that an increasing amount of block overlap improves the sparsity order estimation but it increases the coherence of the sensing matrix. We also explain briefly that the proposed measurement matrix design introduces certain multilinear structures into the observations which enables us to apply tensor-based signal processing, e.g., for enhanced denoising or improved sparsity order estimation. © 2014 IEEE.
      Keywords
      Additive noise
      Product design
      Signal processing
      Signal reconstruction
      Khatri-Rao products
      Matrix rank
      Measurement matrix
      Model-order selection
      Observation vectors
      Order estimation
      Single snapshots
      Vandermonde matrix
      Compressed sensing
      Permalink
      http://hdl.handle.net/11693/28252
      Published Version (Please cite this version)
      http://dx.doi.org/10.1109/ACSSC.2014.7094653
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      • Department of Electrical and Electronics Engineering 3597
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