  This paper presents two new greedy sensor placement algorithms, named minimum
nonzero eigenvalue pursuit (MNEP) and maximal projection on minimum eigenspace
(MPME), for linear inverse problems, with greater emphasis on the MPME
algorithm for performance comparison with existing approaches. We select the
sensing locations one-by-one. In this way, the least number of required sensors
can be determined by checking whether the estimation accuracy is satisfied
after each sensing location is determined. The minimum eigenspace is defined as
the eigenspace associated with the minimum eigenvalue of the dual observation
matrix. For each sensing location, the projection of its observation vector
onto the minimum eigenspace is shown to be monotonically decreasing w.r.t. the
worst case error variance (WCEV) of the estimated parameters. We select the
sensing location whose observation vector has the maximum projection onto the
minimum eigenspace of the current dual observation matrix. The proposed MPME is
shown to be one of the most computationally efficient algorithms. Our
Monte-Carlo simulations showed that MPME outperforms the convex relaxation
method [1], the SparSenSe method [2], and the FrameSense method [3] in terms of
WCEV and the mean square error (MSE) of the estimated parameters, especially
when the number of available sensor nodes is very limited.
