For large scale monitoring of the environment, the number of possible pollution sources can be larger than the number of sensors. For optimal sensor placement under various wind fields in source inversion problems, this paper proposes a framework under non-Gaussian priors for the detection and inversion estimate of emission rates. The optimization framework with non-Gaussian prior utilizes a bi-level optimization expression with inner quadratic programming. The proposed truncated Gaussian prior is to incorporate non-negativity of emission rates, but it poses a challenge in optimization. We preliminarily investigate the bi-level optimization with a Gaussian plume model example. The Karush-Kuhn-Tucker conditions of the inner quadratic programming are considered for solving the bi-level optimization. The efficiency of the proposed optimization framework is demonstrated by numerical results to optimally place sensors and quantify emission rates.