报告题目：Blind Multilinear Identification

报告人：Lek-Heng Lim (UniversityofChicago)

时间：2014年6月19日（星期四）16:00-17:00

地点：理科楼数学系A304

摘要：We discuss a technique that allows blind recovery of signals or blind identification of mixtures in instances where such recovery or identification were previously thought to be impossible: (i) closely located or highly correlated sources in antenna array processing, (ii) highly correlated spreading codes in CDMA radio communication, (iii) nearly dependent spectra in fluorescent spectroscopy. This has important implications — in the case of antenna array processing, it allows for joint localization and extraction of multiple sources from the measurement of a noisy mixture recorded on multiple sensors in an entirely deterministic manner. In the case of CDMA, it allows the possibility of having a number of users larger than the spreading gain. In the case of fluorescent spectroscopy, it allows for detection of nearly identical chemical constituents. The proposed technique involves the solution of a bounded coherence low-rank multilinear approximation problem. We show that bounded coherence allows us to establish existence and uniqueness of the recovered solution. We will provide some statistical motivation for the approximation problem and discuss greedy approximation bounds. To provide the theoretical underpinnings for this technique, we develop a corresponding theory of sparse separable decompositions of functions, including notions of rank and nuclear norm that specialize to the usual ones for matrices and operators but apply to also hypermatrices and tensors.

报告人简介：Prof Lek-Heng Lim（林力行教授）是芝加哥大学统计系的助理教授，主要研究方向是代数几何种的算法和复杂性，致力于张量计算和应用研究。其研究领域广泛，涉及到应用和计算代数，微分几何，数值线性代数，优化，机器学习等领域，特别感兴趣霍奇拉普拉斯算子和几何子空间。林力行教授在斯坦福获得博士学位，剑桥和康奈尔大学获得硕士学位，新加坡国立大学获得学士学位。现任"Linear Algebra and its Applications" and "Linear and Multilinear Algebra"的编委。曾获得奖项：AFOSR Young Investigator Award and an NSF Early Career Award

联系人：张立平