Abstract
The recent work [17] developed a 1-bit compressed sensing (CS) algorithm based on α-stable random projections. Although it was shown in [17] that the method is a strong competitor to other existing 1-bit CS algorithms, the procedure requires knowing K, the sparsity, which is the l0 norm of the signal. Other existing 1-bit CS algorithms require the l2 norm of the signal. In this paper, we develop an estimation procedure for the lα norm of the signal, where 0 < α ≤ 2 from binary or multi-bit measurements. We demonstrate that using a simple closed-form estimator with merely 1-bit information does not result in a significant loss of accuracy if the parameter is chosen appropriately. Theoretical tail bounds are also provided. Using 2 or more bits per measurement reduces the variance and importantly, stabilizes the estimate so that the variance is not too sensitive to chosen parameters.
Original language | American English |
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State | Published - Jan 1 2017 |
Event | 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017 - Fort Lauderdale, United States Duration: Apr 20 2017 → Apr 22 2017 |
Conference
Conference | 20th International Conference on Artificial Intelligence and Statistics, AISTATS 2017 |
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Country/Territory | United States |
City | Fort Lauderdale |
Period | 4/20/17 → 4/22/17 |
ASJC Scopus subject areas
- Artificial Intelligence
- Statistics and Probability