  It is well-known that subspace migration is stable and effective
non-iterative imaging technique in inverse scattering problem. But, for a
proper application, geometric features of unknown targets must be considered
beforehand. Without this consideration, one cannot retrieve good results via
subspace migration. In this paper, we identify the mathematical structure of
single- and multi-frequency subspace migration without any geometric
consideration of unknown targets and explore its certain properties. This is
based on the fact that elements of so-called Multi-Static Response (MSR) matrix
can be represented as an asymptotic expansion formula. Furthermore, based on
the examined structure, we improve subspace migration and consider the
multi-frequency subspace migration. Various results of numerical simulation
with noisy data support our investigation.
