Tuesday, July 10, 2012

One-Bit Measurements with Adaptive Thresholds

Ulugbek Kamilov just sent me the following:

Hi Igor,

I hope you are doing good and enjoying the summer. I just wanted to let you know about our recent paper on 1-bit compressive sensing that will soon appear in Letters. Maybe it will be helpful for other colleagues in the field.

- Ulugbek

We introduce a new method for adaptive one-bit quantization of linear measurements and propose an algorithm for the recovery of signals based on generalized approximate message passing (GAMP). Our method exploits the prior statistical information on the signal for estimating the minimummean-squared error solution from one-bit measurements. Our approach allows the one-bit quantizer to use thresholds on the real line. Given the previous measurements, each new threshold is selected so as to partition the consistent region along its centroid computed by GAMP. We demonstrate that the proposed adaptive-quantization scheme with GAMP reconstruction greatly improves the performance of signal and image recovery from one-bit measurements.
The GAMP toolbox and the BIHT algorithm are here.

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