One-bit compressive sensing with norm estimation
COPYRIGHT 2014
Karin Knudson , UT Austin
Rayan Saab , UCSD
Rachel Ward , UT Austin
Based on the algorithms described in
K. Knudson, R. Saab, R. Ward, One-bit compressive sensing with norm estimation,
Preprint, 2014.
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Files included:
normEstEDF.m
Matlab function file for estimating the l2 norm of x given binary measurements of the form sign( - tau),for random Gaussian a, using the empirical distribution function.
See Theorems 10,11, K. Knudson, R. Saab, R. Ward, One-bit compressive sensing with norm estimation, Preprint, 2014.
normEstPV.m
Matlab function file for estimating the norm of an N-dimensional signal x given binary measurements y1 of the form sign(a_i x - t_i) (a_i,j ~N(0,1) and t_i~N(0,tau) for nonzero tau) by augmenting x and applying the algorithm from Plan and Vershynin. "One-bit compressed sensing by linear programming." 2013
See Theorem 4, K. Knudson, R. Saab, R. Ward, One-bit compressive sensing with norm estimation, Preprint, 2014.
normEstPV_Alternate.m
Matlab function file for estimating the norm of an N-dimensional signal x given binary measurements y1 of the form sign(a_i x - t_i) (a_i,j ~N(0,1) and t_i~N(0,tau) for nonzero tau) by augmenting x and applying the algorithm from Plan and Vershynin. "Robust 1-bit compressive sensing and sparse logistic regression" 2012
See Remark 7, K. Knudson, R. Saab, R. Ward, One-bit compressive sensing with norm estimation, Preprint, 2014.
normRecoveryExample.m
Matlab script to generate an example sparse signal and measurement matrix, and recover the signalâ€™s norm (and the signal itself, if applicable) from one-bit measurements using the methods above. User should run this file to call the functions normEstEDF, normEstPV and normEstPV_Alternate.
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Other requirements:
normEstPV.m and normEstPV_Alternate.m make use of the cvx package for convex optimization, (Michael Grant and Stephen Boyd. CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx, September 2013). CVX is available for download here: http://cvxr.com/cvx/download/.