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We present a simple, accurate, and flexible method to calibrate intrinsic parameters of a camera together with (possibly significant) lens distortion. This new method can work under a wide range of practical scenarios: using multiple images of a known pattern, multiple images of an unknown pattern, single or multiple image(s) of multiple patterns, etc. Moreover, this new method does not rely on extracting any low-level features such as corners or edges. It can tolerate considerably large lens distortion, noise, error, illumination and viewpoint change, and still obtain accurate estimation of the camera parameters. The new method leverages on the recent breakthroughs in powerful high-dimensional convex optimization tools, especially those for matrix rank minimization and sparse signal recovery. We will show how the camera calibration problem can be formulated as an important extension to principal component pursuit, and solved by similar techniques. We characterize to exactly what extent the parameters can be recovered in case of ambiguity. We verify the efficacy and accuracy of the proposed algorithm with extensive experiments on real images.