Today I read a paper titled “Colorization of Natural Images via L1 Optimization”
The abstract is:
Natural images in the colour space YUV have been observed to have a non-Gaussian, heavy tailed distribution (called ‘sparse’) when the filter G(U)(r) = U(r) – sum_{s \in N(r)} w{(Y)_{rs}} U(s), is applied to the chromacity channel U (and equivalently to V), where w is a weighting function constructed from the intensity component Y [1].
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 L1 optimization which often gives the same results for sparse signals [2].
It is observed that L1 optimization, in many cases, over-performs the famous colorization algorithm by Levin et al [3].