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Omnidirectional images have attracted significant attention in recent years due to the rapid development of virtual reality technologies. Equirectangular projection (ERP), a naive form to store and transfer omnidirectional images, however, is challenging for existing two-dimensional (2D) image super-resolution (SR) methods due to its inhomogeneous distributed sampling density and distortion across latitude. In this paper, we make one of the first attempts to design a spherical pseudo-cylindrical representation, which not only allows pixels at different latitudes to adaptively adopt the best distinct sampling density but also is model-agnostic to most off-the-shelf SR methods, enhancing their performances. Specifically, we start by upsampling each latitude of the input ERP image and design a computationally tractable optimization algorithm to adaptively obtain a (sub)-optimal sampling density for each latitude of the ERP image. Addressing the distortion of ERP, we introduce a new viewport-based training loss based on the original 3D sphere format of the omnidirectional image, which inherently lacks distortion. Finally, we present a simple yet effective recursive progressive omnidirectional SR network to showcase the feasibility of our idea. The experimental results on public datasets demonstrate the effectiveness of the proposed method as well as the consistently superior performance of our method over most state-of-the-art methods both quantitatively and qualitatively.