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Natural images in the colour space YUV have been observed to have anon-Gaussian, heavy tailed distribution (called 'sparse') when the filterG(U)(r) = U(r) - sum_{s \in N(r)} w{(Y)_{rs}} U(s), is applied to thechromacity channel U (and equivalently to V), where w is a weighting functionconstructed from the intensity component Y [1]. In this paper we developBayesian analysis of the colorization problem using the filter response as aregularization term to arrive at a non-convex optimization problem. Thisproblem is convexified using L1 optimization which often gives the same resultsfor sparse signals [2]. It is observed that L1 optimization, in many cases,over-performs the famous colorization algorithm by Levin et al [3].

Colorization of Natural Images via L1 Optimization