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We address the problem of unconstrained face recognition from remotely acquired images. The main factors that make this problem challenging are image degradation due to blur, and appearance variations due to illumination and pose. In this paper, we address the problems of blur and illumination. We show that the set of all images obtained by blurring a given image forms a convex set. Based on this set-theoretic characterization, we propose a blur-robust algorithm whose main step involves solving simple convex optimization problems. We do not assume any parametric form for the blur kernels, however, if this information is available it can be easily incorporated into our algorithm. Furthermore, using the low-dimensional model for illumination variations, we show that the set of all images obtained from a face image by blurring it and by changing the illumination conditions forms a bi-convex set. Based on this characterization, we propose a blur and illumination-robust algorithm. Our experiments on a challenging real dataset obtained in uncontrolled settings illustrate the importance of jointly modeling blur and illumination.