Framelet regularization for uneven intensity correction of color images with illumination and reflectance estimation

To solve the problem of simultaneously estimating the illumination and reflectance (IR) from a single image based on the Retinex theory, an effective way is utilizing a Maximum-a-Posterior (MAP) distribution as an approximation. However, the current MAP-based image enhancement methods fail to fully utilize the property of the reflectance, which leads to the loss of detailed structures of images. Through a large number of observations, it is found that the properties of reflectance can be effectively extracted by a powerful operator called framelet transform. Therefore, we propose a novel image enhancement scheme with framelet regularization on the reflectance, which is able to simultaneously estimate the IR while keeping image details. To be specific, a MAP distribution is adopted where a framelet regularization is proposed as a prior to exploiting the multi-scale edge information and sparsity of reflectance. Then the MAP problem is converted to a minimization of an energy function, which can be efficiently solved by an alternating direction method of multipliers with split Bregman iteration (ADMM-SBI). Furthermore, an adaptive Gamma correction operator is proposed to avoid over-enhancement of the illumination. Experiments show that the proposed approach outperforms the state-of-the-arts in terms of brightness improvement, contrast enhancement and details preservation.