Catadioptric omnidirectional cameras offer a 360 \(^\circ \) horizontal field of view but suffer from low image resolution. Image super-resolution (SR) techniques provide an effective solution to enhance image quality without upgrading hardware. This paper proposes a general framework based on deep learning to address the SR of catadioptric omnidirectional images. We first design a cylindrical projection model to transform the data structure of catadioptric images, enabling precise pixel-level projection. Based on this model, we generate two datasets: one for standard training (COCP-SR) and another for distortion correction training (SIM-SR). We then propose a dedicated SR network, COSISR, incorporating a Distortion Feature Extraction Block and two latitude-adaptive modules. COSISR learns multidimensional distortion features and achieves state-of-the-art SR performance. Here, we show that COSISR outperforms existing SR algorithms, with gains of over 1 dB in PSNR for \(\times \) 2 SR and over 0.45 dB for \(\times \) 4 SR. This work significantly improves the resolution and visual fidelity of catadioptric omnidirectional images, broadening their application in fields such as 3D scene reconstruction and visual navigation. The relevant data and code are published in https://github.com/Flower-h/COSISR.