Sparse Recovery Over Networks
Speaker: A. Kevin Tang, Cornell University
Department: Electrical Engineering
Location: Engineering Quadrangle B 205
Date/Time: Thursday, March 8, 2012, 4:30 p.m. - 5:30 p.m.
Given that large scale networks such as the Internet and power grids have become ever more crucial for our society, it is critical to keep monitoring states of such networks to avoid possible system failure and to optimize performance. The scale and complexity of such systems raise the need to quickly infer component characteristics from a relatively small number of indirect aggregate measurements.
Motivated by tomography problems in information networks, we first discuss sparse recovery with graph constraints in the sense that we can take additive measurements over nodes only if they induce a connected subgraph. We provide explicit measurement constructions for several special graphs including line, 2-D grid and tree. A general measurement construction algorithm is also proposed and evaluated. For any given graph G with n nodes, we derive order optimal upper bounds of the minimum number of measurements needed to recover any k-sparse vector over G.
Second, to deal with bad data detection in power grids, an iterative mixed L1 and L2 convex programming is used to estimate the true state by locally linearizing the nonlinear measurements. We give conditions under which the solution of the iterative algorithm converges to the true state. We also numerically evaluate our solution to perform bad data detections in nonlinear electrical power networks problems.
Besides their clear applications, both formulations significantly generalize the current compressive sensing framework: from complete graph to arbitrary graph (first part of the talk) and from additive linear measurements to nonlinear measurements (second part of the talk).