Retinex based on exponent-type total variation scheme

Abstract

Retinex theory deals with compensation for illumination effects in images, which has a number of applications including Retinex illusion, medical image intensity inhomogeneity and color image shadow effect etc.. Such ill-posed problem has been studied by researchers for decades. However, most exiting methods paid little attention to the noises contained in the images and lost effectiveness when the noises increase. The main aim of this paper is to present a general Retinex model to effectively and robustly restore images degenerated by both illusion and noises. We propose a novel variational model by incorporating appropriate regularization technique for the reflectance component and illumination component accordingly. Although the proposed model is non-convex, we prove the existence of the minimizers theoretically. Furthermore, we design a fast and efficient alternating minimization algorithm for the proposed model, where all subproblems have the closed-form solutions. Applications of the algorithm to various gray images and color images with noises of different distributions yield promising results.

Image retinex based on the nonconvex TV-type regularization

“…To demonstrate the performance of our proposed model ( 8), this section presents a series of numerical implementations to remove the different illusions and noisy levels of the different kind of the images. To this end, we choose some state-of-the art models such as the TVH1 [42], the HOTVL1 [34], the L0MS [12] and the ETV [32] compared with our proposed model (8).…”

“…We remark the difference between the ETV used in [32] and the proposed model (8). It is obvious that the model ( 8) is the ETV if setting p = q = 1.…”

“…Furthermore, these existing models due to the lacking of the efficient penalty for the noise prior are not robust when the image contains some noises. In order to overcome these drawbacks, Liu et al [32] established a new TV-based model (called the ETV), where the data-fitting term uses the exponent transform to replace the log-transform and one of the regularization terms is used to describe the noise prior and their proposed model can enhance the image details. Aiming to extend this work, this paper employs the non-convex p -quasi-norm for improving the ETV and the main contributions are summarized as follows.…”

Simultaneous Image Enhancement and Restoration with Non-convex Total Variation

“…[57] focused on intrinsic image decomposition and introduced constraints on both reflectance and illumination layers, but they did not consider noise in the decomposition process. Recently, Liu et al [34] proposed an integrated model to recover a noise-free image and decompose it into reflectance and illumination parts, which was capable of dealing with different types of noises. Moreover, the authors in [30,31,47] and [48] proposed decomposition models based on the original Retinex model.…”

A parallel operator splitting algorithm for solving constrained total-variation retinex

“…It is well-known that the AM method can be convergent for strongly convex optimization, which is a possible reason for introducing the dummy regularizer µ 2 l 2 in (6a). The interested reader is referred to [31] for retinex with noise and [7] for retinex by learned dictionary. In this paper, we are interested in the constrained version of the retinex model (6), and devise a tailor-made algorithm by making use of inherent traits of regularizers and constraints.…”