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b-bit Marginal Regression
Martin Slawski · Ping Li

Tue Dec 08 04:00 PM -- 08:59 PM (PST) @ 210 C #81
We consider the problem of sparse signal recovery from $m$ linear measurements quantized to $b$ bits. $b$-bit Marginal Regression is proposed as recovery algorithm. We study the question of choosing $b$ in the setting of a given budget of bits $B = m \cdot b$ and derive a single easy-to-compute expression characterizing the trade-off between $m$ and $b$. The choice $b = 1$ turns out to be optimal for estimating the unit vector corresponding to the signal for any level of additive Gaussian noise before quantization as well as for adversarial noise. For $b \geq 2$, we show that Lloyd-Max quantization constitutes an optimal quantization scheme and that the norm of the signal canbe estimated consistently by maximum likelihood.

Author Information

Martin Slawski (Rutgers University)
Ping Li (Rugters University)

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