Another advantage is to use either of the two tanks in case of any one of the tanks becomes out of order and using another tank as stand alone in a single weighing compromising bit measurement uncertainty.
Our analysis shows that when the number of one-bit measurements is sufficiently large, with a high probability the sparse signal can be recovered with an error decaying linearly with the ℓ2-norm of the difference between the quantization thresholds and the original unquantized measurements.
We introduce an optimization model for reconstruction of sparse signals from 1-bit measurements.
We demonstrated the performance of the algorithm for reconstruction from 1-bit measurements.
As pointed out in [3, 4], quantization to 1-bit measurements is appealing in practical applications.
One-bit measurements is a more restricted case in which only the sign information of the random measurements is preserved.
Using matrix notation, the 1-bit measurements in (2) can be equivalently expressed as YPhi x ge 0, (3).
Binary iterative hard thresholding (BIHT) algorithms were recently introduced for reconstruction of sparse signals from 1-bit measurements in [4].
In [6], a convex minimization problem is formulated for reconstruction of sparse signals from 1-bit measurements and is solved by linear programming.
For consistent reconstruction from 1-bit measurements, the measurements are treated as sign constraints that are enforced in the reconstruction to recover the signal.
This algorithm exploits the prior statistical information on the signal for estimating the minimum-mean-squared error solution from 1-bit measurements.
