Colorization of natural images via L1 optimization

Natural images in the colour space YUV have been observed to have a non-Gaussian, heavy tailed distribution (called `sparse') when the filter ¿(U)(r) = U(r) -
_s¿N(r)
¿ w(Y)rsU(s), is applied to the chromacity channel U (and equivalently to V), where w is a weighting function constructed from the intensity component Y. In this paper we develop Bayesian analysis of the colorization problem using the filter response as a regularization term to arrive at a non-convex optimization problem. This problem is convexified using L
¹
optimization which often gives the same results for sparse signals. It is observed that L
¹
optimization, in many cases, over-performs the colorization algorithm of Levin et al..