In this work, we address the challenge of accurately obtaining channel state information at the transmitter (CSIT) for frequency division duplexing (FDD) multiple input multiple output systems. Although CSIT is vital for maximizing spatial multiplexing gains, traditional CSIT estimation methods often suffer from impracticality due to the substantial training and feedback overhead they require. To address this challenge, we leverage two sources of prior information simultaneously: the presence of limited local scatterers at the base station (BS) and the time-varying characteristics of the channel. The former results in a redundant angular sparsity of users' channels exceeding the spatial dimension (i.e., the number of BS antennas), while the latter provides a prior non-uniform distribution in the angular domain. We propose a weighted optimization framework that simultaneously reflects both of these features. The optimal weights are then obtained by minimizing the expected recovery error of the optimization problem. This establishes an analytical closed-form relationship between the optimal weights and the angular domain characteristics. Numerical experiments verify the effectiveness of our proposed approach in reducing the recovery error and consequently resulting in decreased training and feedback overhead.