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We give the first computationally tractable and almost optimal solution to the problem of one-bit compressed sensing, showing how to accurately recover an s-sparse vector x in R^n from the signs of O(s log^2(n/s)) random linear measurements of x.
Random points, sets and tessellations on the surface of a sphere
Miles, R · 1971
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The volume of convex bodies and Banach space geometry
Pisier, G · 1989
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Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
Goemans, M. X., and Williamson, D. P · 1995
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The probabilistic method
Alon, N., and Spencer, J. H · 2000
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Error correction via linear programming
Candes, E., Rudelson, M., Vershynin, R., and Tao, T · 2005
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Threshold group testing
Damaschke, P · 2005
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Stable signal recovery from incomplete and inaccurate measurements
Candès, E. J., Romberg, J. K., and Tao, T · 2006
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Near-optimal signal recovery from random projections: Universal encoding strategies?
Candes, E. J., and Tao, T · 2006
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The Dantzig selector: Statistical estimation when p is much larger than n
Candes, E., and Tao, T · 2007
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1-Bit compressive sensing
Boufounos, P. T., and Baraniuk, R. G · 2008
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Bit precision analysis for compressed sensing
Ardestanizadeh, E., Cheraghchi, M., and Shokrollahi, A · 2009
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Simultaneous analysis of Lasso and Dantzig selector
Bickel, P. J., Ritov, Y., and Tsybakov, A. B · 2009
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Greedy sparse signal reconstruction from sign measurements
Boufounos, P. T · 2009
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A comparative study of quantized compressive sensing schemes
Dai, W., Pham, H. V., and Milenkovic, O · 2009
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Compressed sensing makes every pixel count
Mackenzie, D · 2009
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Reconstruction of sparse signals from distorted randomized measurements
Boufounos, P. T · 2010
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Sigma delta quantization for compressed sensing
Gunturk, C., Lammers, M., Powell, A., Saab, R., and Ylmaz, O · 2010
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Sample complexity for 1-bit compressed sensing and sparse classification
Gupta, A., Nowak, R., and Recht, B · 2010
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Trust, but verify: Fast and accurate signal recovery from 1-bit compressive measurements
Laska, J. N., Wen, Z., Yin, W., and Baraniuk, R. G · 2010
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Introduction to the non-asymptotic analysis of random matrices
Vershynin, R · 2010
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Compressed sensing with quantized measurements
Zymnis, A., Boyd, S., and Candes, E · 2010
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Sun, J., and Goyal, V · 2009
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Stability and instance optimality for Gaussian measurements in compressed sensing
Wojtaszczyk, P · 2009
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Sobolev duals for random frames and sigma-delta quantization of compressed sensing measurements
Gunturk, C., Lammers, M., Powell, A., Saab, R., and Ylmaz, O
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Robust 1-bit compressive sensing via binary stable embeddings of sparse vectors
Jacques, L., Laska, J. N., Boufounos, P. T., and Baraniuk, R. G
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Stochastic geometry and random tessellations
Møller, J., and Stoyan, D
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Dequantizing compressed sensing: When oversampling and non-gaussian constraints combine
Jacques, L., Hammond, D., and Fadili, J · 2011
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Democracy in action: Quantization, saturation, and compressive sensing
Laska, J. N., Boufounos, P. T., Davenport, M. A., and Baraniuk, R. G · 2011
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