Low Quality Image Improvement Based On Variational Regularization And Statistical Learning

Vision is the most advanced sense for human perception of the outside world. Therefore, images play an important role in human visual perception. The aim of image processing is to make the output satisfy further analysis and application of human and computer vision. High quality image is pleasing to the eyes of viewer due to its natural colors, clear details and structures. It is also more suitable than low quality image for feature extraction and high level pattern recognition. Therefore, how to obtain high quality image is a common concerned problem. However, affectted by some inevitable and unfavorable factors in imaging procedure, such as camera shake, nonuniform lighting, and bad weather, imaging device usually produces low quality image having bad visual effects, for example, the objects in images are blurry, and structures are difficult to see. Thus, low quality image improvement, including image denoising, image deblurring, image enhancement, image dehazing, image super-resolution, becomes the enduring research topic in image processing.In order to solve the low quality image improvement problem, in this paper we focus on four kinds of low quality image, and study new methods in image processing based on variational regularization and statistical learning. The main achievements and innovations are as follows:(1) To solve the image restoration problem, we study the variational regularization method which is commonly used for solving ill-posed inverse problems. Since we aim at preserving sharp edges, local structures and details in image, we analyze advantages and disadvantages of the classical total vatiation (TV) regularization and the sparsity priori based regularization, and then propose a new image restoration method based on a compound regularization model associated with the weighted anisotropic total variation (WATV) and the tetrolets-based sparsity. In the proposed variational model, the WATV is used to recover four directional sharp edges. Because the tetrolet transform is able to adapt its basis to the local image structures, we also use the tetrolets to model a tetrolets-based sparse regularization. Then the proposed model can preserve details such as textures and edges in the processing of image restoration by combining the WATV with the tetrolets-based sparsity. Finally, we present an alternate iterative scheme which consists of the variable splitting method and the operator splitting method to solve the proposed minimization problem. Experimental results demonstrate the efficiency of our image restoration method for preserving the structure details and the sharp edges of both grayscale images and color images.(2) In the perceptually inspired variational framework for color enhancement, the contrast energy term cannot adapt local contrast enhancement to the brightness of images, and the entropic dispersion energy term does not care about the relative positions of the pixels in images when measure the difference between two images. In order to overcome these drawbacks, we propose a local brightness adaptive variational model using Wasserstein distance for color image enhancement under the perceptually inspired variational framework. The average brightness of image local patch is used as a local brightness indicator in the contrast energy term. With this indicator, the proposed model is adapted to the local brightness and the details in both dark and bright areas can be recovered efficiently. We also propose a new dispersion energy term by using Wasserstein distance which is a more natural and efficient distance to measure the statistical similarity between two images. Thus, the proposed model is able to maintain the statistical relations between pixels and restore image true colors. The minimization problem of the proposed energy functional is solved by a gradient descent algorithm. Experimental results demonstrate the efficiency of the proposed model for removing color cast, enhancing contrast, and equalizing low key images.(3) Based on the traditional Retinex theory, we propose a variational Bayesian method for Retinex to simulate and interpret how the human vision system perceives color and illumination. We first study the properties of pixel intensity, reflectance, and illumination of image. Then by assuming that the reflection function is piecewise continuous and illumination function is spatially smooth, we define the energy functions in the Gibbs distribution as a TV function and a smooth function for the reflectance function and the illumination function, respectively. With the hierarchical Bayesian paradigm, a statistical estimation freamwork is constructed to simultaneously estimate model parameters along with the unknown illumination image and reflectance image, and does not require parameters tuning. Theoretical analysis and experimental results demonstrate the flexibility and the efficiency of the proposed method for designing different Retinex methods given different image priors, and providing competitive performance without additional information about the unknown parameters, and when prior information is added the proposed method outperforms the non-Bayesian-based Retinex methods we compared.(4) Based on the haze optical model and the example based learning, we propose an image dehazing method using 2D canonical correlation analysis (CCA). By assuming that the intensities of small local patches in hazy-free image are smooth and approximated to constant, we deduce a linear correlation between the observed hazy image patches and corresponding transmission patches. In order to take full advantage of the relationship between the hazy image and corresponding transmission,2D CCA is utilized for learning a subspace in which this correlation is maximized and the reconstruction of the estimated transmission map is more meaningful and reliable. Then given a test hazy image, the estimated transmission map is reconstructed by the nearest neighbor algorithm in the subspace. To refine the estimated coarse transmission map, we propose a local mean adaptive guided filter in which the regularization parameter is adaptively adjusted by the local mean of the estimated transmission map. Thus, the distant hazy structures are able to be preserved and the nearby details are able to be smoothed out. The final hazy-free image is obtained by using the dichromatic atmospheric model. Experimental results demonstrate the efficiency of the proposed method for single image dehazing.