A linearly constrained mathematical formulation is provided for the problem of coherent radar imaging. In contrast to studies of field-aligned irregularities in the ionosphere, where the technique has previously been applied, lower atmospheric imaging is complicated by the fact that the scattering structures are not aligned along any single baseline. As a result, a two-dimensional generalization of the brightness distribution was required. It is shown that Fourier-based imaging is a special case of this general formulation. Furthermore, an imaging technique based on constrained optimization is introduced and shown to exhibit higher resolution and resistance to interfering signals. These techniques were applied to data from the middle and upper atmosphere radar in Shigaraki, Japan. The experiment was conducted during the Baiu season, which is characterized by significant precipitation events.