A linearly constrained mathematical formulation is provided for the problem
of coherent radar imaging. In contrast to studies of field-aligned irregul
arities in the ionosphere, where the technique has previously been applied,
lower atmospheric imaging is complicated by the fact that the scattering s
tructures are not aligned along any single baseline. As a result, a two-dim
ensional generalization of the brightness distribution was required. It is
shown that Fourier-based imaging is a special case of this general formulat
ion. Furthermore, an imaging technique based on constrained optimization is
introduced and shown to exhibit higher resolution and resistance to interf
ering signals. These techniques were applied to data from the middle and up
per atmosphere radar in Shigaraki, Japan. The experiment was conducted duri
ng the Baiu season, which is characterized by significant precipitation eve
nts.