A Convex Optimization Model Based Retinex For Image Enhancement

Image enhancement technology is one of the basic problems of computer vision and digital image processing. Its purpose is to improve the visual ability of the human beings and increase the readability of images. We can analysis and process the contents contained in the images. Retinex is a theory of image enhancement based on scientific experiments and scientific analysis. This theory is simulating and explaining how human visual system perceives colors under different illumination conditions. Retinex theory thinks that the color of the object is determined by the reflectance of the object.The essence of the theory is removing the light affects of the image in order to obtain the reflection components of the object. That is to say, we can get the original appearance of the object by this way. Compared with other traditional methods of image enhancement, the enhancement methods based on Retinex theory have enhanced edge,color constancy, large dynamic range compression and so on. This method can keep color fidelity and restore the original appearance of the images.This article focuses on studying the Retinex theory. Then based on the Retinex theory, we analysis several classical of image enhancement methods. The main contribution of this paper is to present a new convex optimization model and algorithm for Retinex. Retinex methods can be classified into random walk methods, recursive methods, center/surround methods, PDE-based methods, and variational methods. The random walk need to regulate many parameters and has high computational complexity.The recursive methods are difficult to know how much iteration is executed in the process. The methods based on PDE need to calculate a lot of partial differential equations and Poisson equations. But these methods have serious modeling errors. The most popular methods are variational methods, but these methods are transformed into a logarithmic domain. The motivation behind is that we have noticed that once the input image is converted to the logarithmic domain, the small differences and little texture feature between image pixels tend to be ignored.Different from existing methods, the main idea is to rewrite a multiplicative form such that the illumination variable and the reflection variable are decoupled in spatial domain to get rid of disadvantages of traditional methods. The resulting objective function involves three terms including the Tikhonov regularization of the illuminationcomponent, the total variation regularization of the reciprocal of the reflection component, and the data-fitting term among the input image, the illumination component, and the reciprocal of the reflection component. We develop an alternating direction method of multipliers(ADMM) to solve the convex optimization model.ADMM transforms functional minimization problem with constraints to unconstrained minimization problem. Numerical experiments demonstrate the effectiveness of the proposed model which can decompose an image into the illumination and the reflection components quite well to enhance the nature image and the medical image.