Timezone: »

 
Poster
b-bit Marginal Regression
Martin Slawski · Ping Li

Tue Dec 08 04:00 PM -- 08:59 PM (PST) @ 210 C #81 #None
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)

More from the Same Authors