Local reconstruction from localized projections attains importance in Computed Tomography (CT). Several researchers addressed the local recovery (or interior) problem in different frameworks. The recent sparsity based optimization techniques in Compressed Sensing (CS) are shown to be useful for CT reconstruction. The CS based methods provide hardware-friendly algorithms, while using lesser data compared to other methods. The interior reconstruction in CT, being ill-posed, in general admits several solutions. Consequently, a question arises pertaining to the presence of target (or interior-centric) pixels in the recovered solution. In this paper, we address this problem by posing the local CT problem in the prior support constrained CS framework. In particular, we provide certain analytical guarantees for the presence of intended pixels in the recovered solution, while demonstrating the efficacy of our method empirically. © 2022 Walter de Gruyter GmbH, Berlin/Boston 2022.