We in this paper propose a realizable framework TECU, which embeds task-specific strategies into update schemes of coordinate descent, for optimizing multivariate non-convex problems with coupled objective functions. On one hand, TECU is capable of improving algorithm efficiencies through embedding productive numerical algorithms, for optimizing univariate sub-problems with nice properties. From the other side, it also augments probabilities to receive desired results, by embedding advanced techniques in optimizations of realistic tasks. Integrating both numerical algorithms and advanced techniques together, TECU is proposed in a unified framework for solving a class of non-convex problems. Although the task embedded strategies bring inaccuracies in sub-problem optimizations, we provide a realizable criterion to control the errors, meanwhile, to ensure robust performances with rigid theoretical analyses. By respectively embedding ADMM and a residual-type CNN in our algorithm framework, the experimental results verify both efficiency and effectiveness of embedding task-oriented strategies in coordinate descent for solving practical problems.
 In this paper, we propose to introduce intrinsic image decomposition priors into decomposition models for contrast enhancement. Since image decomposition is a highly ill-posed problem, we introduce constraints on both reflectance and illumination layers to yield a highly reliable solution. We regularize the reflectance layer to be piecewise constant by introducing a weighted @math norm constraint on neighboring pixels according to the color similarity, so that the decomposed reflectance would not be affected much by the illumination information. The illumination layer is regularized by a piecewise smoothness constraint. The proposed model is effectively solved by the Split Bregman algorithm. Then, by adjusting the illumination layer, we obtain the enhancement result. To avoid potential color artifacts introduced by illumination adjusting and reduce computing complexity, the proposed decomposition model is performed on the value channel in HSV space. Experiment results demonstrate that the proposed method performs well for a wide variety of images, and achieves better or comparable subjective and objective quality compared with the state-of-the-art methods. Images captured under water are usually degraded due to the effects of absorption and scattering. Degraded underwater images show some limitations when they are used for display and analysis. For example, underwater images with low contrast and color cast decrease the accuracy rate of underwater object detection and marine biology recognition. To overcome those limitations, a systematic underwater image enhancement method, which includes an underwater image dehazing algorithm and a contrast enhancement algorithm, is proposed. Built on a minimum information loss principle, an effective underwater image dehazing algorithm is proposed to restore the visibility, color, and natural appearance of underwater images. A simple yet effective contrast enhancement algorithm is proposed based on a kind of histogram distribution prior, which increases the contrast and brightness of underwater images. The proposed method can yield two versions of enhanced output. One version with relatively genuine color and natural appearance is suitable for display. The other version with high contrast and brightness can be used for extracting more valuable information and unveiling more details. Simulation experiment, qualitative and quantitative comparisons, as well as color accuracy and application tests are conducted to evaluate the performance of the proposed method. Extensive experiments demonstrate that the proposed method achieves better visual quality, more valuable information, and more accurate color restoration than several state-of-the-art methods, even for underwater images taken under several challenging scenes. This paper addresses extracting two layers from an image where one layer is smoother than the other. This problem arises most notably in intrinsic image decomposition and reflection interference removal. Layer decomposition from a single-image is inherently ill-posed and solutions require additional constraints to be enforced. We introduce a novel strategy that regularizes the gradients of the two layers such that one has a long tail distribution and the other a short tail distribution. While imposing the long tail distribution is a common practice, our introduction of the short tail distribution on the second layer is unique. We formulate our problem in a probabilistic framework and describe an optimization scheme to solve this regularization with only a few iterations. We apply our approach to the intrinsic image and reflection removal problems and demonstrate high quality layer separation on par with other techniques but being significantly faster than prevailing methods.