Global sparse gradient guided variational Retinex model for image enhancement

In this paper, we propose a global sparse gradient guided variational Retinex model (GSG-VR) for image enhancement. Based on the Retinex theory, a new variational Retinex model is proposed to decompose an image into illumination layer and reflectance layer. The gradient of illumination layer is expected to approximate a guided gradient field which is estimated by a global sparse gradient model (GSG). To estimate the guided gradient at each pixel, GSG makes use of pixels within its neighborhood (even global image). And a sparse regularization is imposed on the whole gradient field. These two models, the new variational Retinex and GSG model, compose a complete system GSG-VR. To solve it, a proximal forward-backward splitting algorithm and an alternating minimization algorithm are developed. A few numerical examples are presented to illustrate the effectiveness of the proposed models and algorithms.