Traditional radar detection schemes are typically studied for single target scenarios and they can be non-optimal when there are multiple targets in the scene. In this paper, we develop a framework to discuss multi-target detection schemes with sparse reconstruction techniques that is based on the Neyman-Pearson criterion. We will describe an initial result in this framework concerning false alarm probability with LASSO as the sparse reconstruction technique. Then, several simulations validating this result will be discussed. Finally, we describe several research avenues to further pursue this framework.