One-bit compressed sensing with non-Gaussian measurements

@article{Ai2012OnebitCS,
  title={One-bit compressed sensing with non-Gaussian measurements},
  author={Albert Ai and Alexander F. Lapanowski and Y. Plan and R. Vershynin},
  journal={ArXiv},
  year={2012},
  volume={abs/1208.6279}
}
Abstract In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples involving extremely sparse signals. We show that approximately sparse signals that are not extremely sparse can be accurately… Expand
124 Citations
Robust one-bit compressed sensing with non-Gaussian measurements
  • 7
Robust one-bit compressed sensing with partial circulant matrices
  • 10
  • PDF
One-bit Compressed Sensing with the k-Support Norm
  • 13
  • Highly Influenced
  • PDF
One-bit compressive sampling with time-varying thresholds for sparse parameter estimation
  • 36
One-Bit Compressed Sensing via One-Shot Hard Thresholding
  • Jie Shen
  • Computer Science, Mathematics
  • UAI
  • 2020
  • PDF
HISTORY: An Efficient and Robust Algorithm for Noisy 1-Bit Compressed Sensing
  • 5
  • PDF
Quantized Compressed Sensing: A Survey
  • 6
On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds
  • 8
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 16 REFERENCES
One-bit compressed sensing by linear programming
  • 347
  • PDF
1-Bit compressive sensing
  • 592
  • PDF
Sample complexity for 1-bit compressed sensing and sparse classification
  • 85
  • PDF
Robust 1-bit Compressed Sensing and Sparse Logistic Regression: A Convex Programming Approach
  • 376
  • PDF
Robust 1-Bit Compressive Sensing via Binary Stable Embeddings of Sparse Vectors
  • 515
  • PDF
Introduction to the non-asymptotic analysis of random matrices
  • R. Vershynin
  • Mathematics, Computer Science
  • Compressed Sensing
  • 2012
  • 2,224
  • PDF
Compressed Sensing: Theory and Applications
  • 1,026
  • PDF
Probability Theory, an Analytic View
  • 272
...
1
2
...