We consider the problem of identifying bad measurements in
compressive sensing. These bad measurements can be present due to
malicious attacks and system malfunction.
Since the linear system of equations in compressive sensing is
underconstrained, errors introduced by these bad measurements can
result in large changes in computed solutions. We describe a
separation-based method for identifying bad measurements. In this
method we separate out top non-zero variables by ranking, eliminate
these variables from the system of equations, and then solve the
reduced overconstrained problem to identify bad measurements.
Comparing to prior methods based on direct or joint l1-minimization,
the separation-based method can addresses challenging cases when
there are only a moderate number of samples. In developing the method
we introduce the notion of inversions which govern the separability
of the non-zero variables.
Tsung-Han Lin is a Ph.D. candidate in Computer Science of Harvard
University. He has received his B.S. and M.S. degree in the Department
of Electrical Engineering, National Taiwan University. His research
interests include wireless networks, compressive sensing, wireless
networking for unmanned aerial vehicles (UAVs), and wireless sensor