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  1. DETERMINISTIC MATRICES MATCHING THE COMPRESSED SENSING PHASE TRANSITIONS OF GAUSSIAN RANDOM MATRICES

    Monajemi, Hatef
    Stanford, California : Department of Statistics, STANFORD UNIVERSITY, 2012.

    Online statistics.stanford.edu

  2. Code and Data supplement to "Incoherence of Partial Component Sampling in multidimensional NMR"

    Monajemi, Hatef
    2016

    The data and code provided here are supplementary information for the paper “Incoherence of Partial Component Sampling in multidimensional NMR" by H. Monajemi, D.L. Donoho, J.C. Hoch, and A.D. Schuyler. Please read INSTRUCTION.TXT for reproducing the results of the article. Abstract of the article: In NMR spectroscopy, random undersampling in the indirect dimensions causes reconstruction artifacts whose size can be bounded using the so-called {\it coherence}. In experiments with multiple indirect dimensions, new undersampling approaches were recently proposed: random phase detection (RPD) \cite{Maciejewski11} and its generalization, partial component sampling (PCS) \cite{Schuyler13}. The new approaches are fully aware of the fact that high-dimensional experiments generate hypercomplex-valued free induction decays; they randomly acquire only certain low-dimensional components of each high-dimensional hypercomplex entry. We provide a classification of various hypercomplex-aware undersampling schemes, and define a hypercomplex-aware coherence appropriate for such undersampling schemes; we then use it to quantify undersampling artifacts of RPD and various PCS schemes.

  3. Code and data supplement for "Sparsity/Undersampling Tradeoffs in Anisotropic Undersampling, with Applications in MR Imaging/Spectroscopy"

    Monajemi, Hatef
    2013 - 2016

    The data and code provided here are supplementary material for the Information and Inference paper “Sparsity/Undersampling Tradeoffs in Anisotropic Undersampling, with Applications in MR Imaging/Spectroscopy" by H. Monajemi, and D.L. Donoho. Please read README file for reproducing the results of the article. Abstract of the article: We study anisotropic undersampling schemes like those used in multi-dimensional NMR spectroscopy and MR imaging, which sample exhaustively in certain time dimensions and randomly in others. Our analysis shows that anisotropic undersampling schemes are equivalent to certain block-diagonal measurement systems. We develop novel exact formulas for the sparsity/undersampling tradeoffs in such measurement systems. Our formulas predict finite-N phase transition behavior differing substantially from the well known asymptotic phase transitions for classical dense undersampling. Extensive empirical work shows that our formulas accurately describe observed finite-N behavior, while the usual asymptotic predictions based on universality are substantially inaccurate. We also vary the anisotropy, keeping the total number of samples fixed, and for each variation we determine the precise sparsity/undersampling tradeoff (phase transition). We show that, other things being equal, the ability to recover a sparse spectrum decreases with an increasing number of exhaustively-sampled dimensions.

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