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Panoramic Annular Lens (PAL) composed of few lenses has great potential in panoramic surrounding sensing tasks for mobile and wearable devices because of its tiny size and large Field of View (FoV). However, the image quality of tiny-volume PAL confines to optical limit due to the lack of lenses for aberration correction. In this paper, we propose an Annular Computational Imaging (ACI) framework to break the optical limit of light-weight PAL design. To facilitate learning-based image restoration, we introduce a wave-based simulation pipeline for panoramic imaging and tackle the synthetic-to-real gap through multiple data distributions. The proposed pipeline can be easily adapted to any PAL with design parameters and is suitable for loose-tolerance designs. Furthermore, we design the Physics Informed Image Restoration Network (PI2RNet) considering the physical priors of panoramic imaging and single-pass physics-informed engine. At the dataset level, we create the DIVPano dataset and the extensive experiments on it illustrate that our proposed network sets the new state of the art in the panoramic image restoration under spatially-variant degradation. In addition, the evaluation of the proposed ACI on a simple PAL with only 3 spherical lenses reveals the delicate balance between high-quality panoramic imaging and compact design. To the best of our knowledge, we are the first to explore Computational Imaging (CI) in PAL. Code and datasets are publicly available at https://github.com/zju-jiangqi/ACI-PI2RNet.