In this paper, we present a general optimization framework that leverages structured sparsity to achieve superior recovery results. The traditional method for solving the structured sparse objectives based on$\ell _{2,0}$-norm is to use the$\ell _{2,1}$-norm as a convex surrogate. However, such an approximation often yields a large performance gap. To tackle this issue, we first provide a framework that allows for a wide range of surrogate functions (including non-convex surrogates), which exhibits better performance in harnessing structured sparsity. Moreover, we develop a fixed point algorithm that solves a key underlying non-convex structured sparse recovery optimization problem to global optimality with a guaranteed super-linear convergence rate. Building on this, we consider three specific applications, i.e., outlier pursuit, supervised feature selection, and structured dictionary learning, which can benefit from the proposed structured sparsity optimization framework. In each application, how the optimization problem can be formulated and thus be relaxed under a generic surrogate function is explained in detail. We conduct extensive experiments on both synthetic and real-world data and demonstrate the effectiveness and efficiency of the proposed framework.

Single image haze removal, which is to recover the clear version of a hazy image, is a challenging task in computer vision. In this paper, an additive haze model is proposed to approximate the hazy image formation process. In contrast with the traditional optical model, it regards the haze as an additive layer to a clean image. The model thus avoids estimating the medium transmission rate and the global atmospherical light. In addition, based on a critical observation that haze changes gradually and smoothly across the image, a haze smoothness prior is proposed to constrain this model. This prior assumes that the haze layer is much smoother than the clear image. Benefiting from this prior, we can directly separate the clean image from a single hazy image. Experimental results and comparisons with synthetic images and real-world images demonstrate that the proposed method outperforms state-of-the-art single image haze removal algorithms.

In this paper, we focus on the multi-view clustering problem. A novel multi-view clustering framework, called multi-view subspace clustering based on tensor Schatten-p norm (MVSC-TSP), is proposed for clustering task. In our method, the tensor Schatten-p norm, which is based on tensor singular value decomposition, is utilized to explore the global low-rank structure of multi-view self-representations. Since 0<; p<; 1, using tensor Schatten-p norm to relax the tensor multi-rank is more effective than the commonly used tensor nuclear norm. Furthermore, we present a new generalized tensor soft thresholding algorithm to solve the tensor Schatten-p norm minimization problem. Based on this, the proposed non-convex optimal problem can be efficiently solved by the alternating direction method of multipliers. Experimental results on image clustering demonstrate that the proposed method is superior to the state-of-the-art methods in term of various evaluation metrics.

Recently, group sparse representation which is based on a hypothesis about correlation of coefficient variables has attracted much attention due to its effectiveness and robustness in dictionary learning. Traditional group sparse representation methods use ℓ2,1norm to enforce the estimation of models with joint sparsity patterns, which often leads to over-punishment phenomenon. To solve this issue, we replace ℓ2,1with non-convex surrogate of ℓ2,1, and give a general solver for the corresponding optimization algorithm. Experimental results confirm the effectiveness of our proposed method.

Single image haze removal is a challenging ill-posed problem in computer vision. Instead of leveraging the traditional model or handcrafted image priors, an end-to-end multi-scale convolutional neural network is proposed for single image haze removal task by directly mapping the hazy image to its corresponding haze-free image. To better retain the coarse and fine information, a multi-scale block is elaborated and embedded into the proposed architecture. This block can extract the feature at varying scales with a model size that is as small as possible. The global skip connection is adopted to promote the model performance. Extensive experiment results demonstrate that the proposed network outperforms the state-of-the-art single image haze removal algorithms on both synthetical and real-world images. In addition, the size of the model in this paper dominates among the high performance methods based on convolutional neural networks.

In this paper, we propose a new single-image dehazing method for synthetic and real-world hazy images. Based on the color attenuation prior, this proposed dehazing method improves it in two aspects. First, we estimate the atmospheric light with the haze-lines prior, which is based on the observation that pixel values of a hazy image can be modeled as lines in the RGB color space that intersects at the air-light. Second, the dynamic scattering coefficient, which is an exponential function of image depth, is proposed to replace the constant scattering coefficient. Experimental results demonstrate that the dehazed image of proposed algorithm is clearer and more natural than that of the color attenuation prior. The proposed algorithm can effectively improve the effect of dehazing.