Uniform recovery from subgaussian multi-sensor measurements

Parallel acquisition systems are employed successfully in a variety of different sensing applications when a single sensor cannot provide enough measurements for a high-quality reconstruction. In this paper, we consider compressed sensing (CS) for parallel acquisition systems when the individual sensors use subgaussian random sampling. Our main results are a series of uniform recovery guarantees which relate the number of measurements required to the basis in which the solution is sparse and certain characteristics of the multi-sensor system, known as sensor profile matrices. In particular, we derive sufficient conditions for optimal recovery, in the sense that the number of measurements required per sensor decreases linearly with the total number of sensors, and demonstrate explicit examples of multi-sensor systems for which this holds. We establish these results by proving the so-called Asymmetric Restricted Isometry Property (ARIP) for the sensing system and use this to derive both nonuniversal and universal recovery guarantees. Compared to existing work, our results not only lead to better stability and robustness estimates but also provide simpler and sharper constants in the measurement conditions. Finally, we show how the problem of CS with block-diagonal sensing matrices can be viewed as a particular case of our multi-sensor framework. Specializing our results to this setting leads to a recovery guarantee that is at least as good as existing results.     

一种适用于微弱信号提取的盲源分离算法

本文首次提出了适用于微弱信号提取的盲源分离算法,这种方法是在常用的自然梯度串行更新算法基础上采用了有监督的机制。通过观察两个信号互相关的程度自动判别激活函数的种类,实现了超高斯亚高斯强弱信号混合下的盲源分离。信号仿真表明,有监督的盲源分离技术收敛速度较快,精度较高。     

Stability Properties of Neighbourly Random Polytopes

We introduce a quantitative parameter measuring m-neighbourliness of symmetric convex polytopes in ℝ ^k . We discuss this parameter for random polytopes generated by subgaussian vectors and show its stability properties. Research of P. Mankiewicz was partially supported by KBN Grant no. 1 P03A 015 27. N. Tomczak-Jaegermann holds the Canada Research Chair in Geometric Analysis.