A Fast Fixed Point Algorithm for Total Variation Deblurring and Segmentation

In this paper, we propose a fast fixed point algorithm and apply it to total variation (TV) deblurring and segmentation. The TV-based models can be written in the form of a general minimization problem. The novel method is derived from the idea of establishing the relation between solutions of the general minimization problem and new variables, which can be obtained by a fixed point algorithm efficiently. Under gentle conditions it provides a platform to develop efficient numerical algorithms for various image processing tasks. We then specialize this fixed point methodology to the TV-based image deblurring and segmentation models, and the resulting algorithms are compared with the split Bregman method, which is a strong contender for the state-of-the-art algorithms. Numerical experiments demonstrate that the algorithm proposed here performs favorably.     

Domain Decomposition Methods for Nonlocal Total Variation Image Restoration

Nonlocal total variation (TV) regularization (Gilboa and Osher in Multiscale Model Simulat 7(3): 1005–1028, 2008; Zhou and Schölkopf in Pattern recognition, proceedings of the 27th DAGM symposium. Springer, Berlin, pp 361–368, 2005) has been widely used for the natural image processing, since it is able to preserve repetitive textures and details of images. However, its applications have been limited in practice, due to the high computational cost for large scale problems. In this paper, we apply domain decomposition methods (DDMs) (Xu et al. in Inverse Probl Imag 4(3):523–545, 2010) to the nonlocal TV image restoration. By DDMs, the original problem is decomposed into much smaller subproblems defined on subdomains. Each subproblem can be efficiently solved by the split Bregman algorithm and Bregmanized operator splitting algorithm in Zhang et al. (SIAM J Imaging Sci 3(3):253–276, 2010). Furthermore, by using coloring technique on the domain decomposition, all subproblems defined on subdomains with same colors can be computed in parallel. Our numerical examples demonstrate that the proposed methods can efficiently solve the nonlocal TV based image restoration problems, such as denoising, deblurring and inpainting. It can be computed in parallel with a considerable speedup ratio and speedup efficiency.     

Local motion deblurring using an effective image prior based on both the first- and second-order gradients

Local motion deblurring is a highly challenging problem as both the blurred region and the blur kernel are unknown. Most existing methods for local deblurring require a specialized hardware, an alpha matte, or user annotation of the blurred region. In this paper, an automatic method is proposed for local motion deblurring in which a segmentation step is performed to extract the blurred region. Then, for blind deblurring, i.e., simultaneously estimating both the blur kernel and the latent image, an optimization problem in the form of maximum-a-posteriori (MAP) is introduced. An effective image prior is used in the MAP based on both the first- and second-order gradients of the image. This prior assists to well reconstruct salient edges, providing reliable edge information for kernel estimation, in the intermediate latent image. We examined the proposed method for both global and local deblurring. The efficiency of the proposed method for global deblurring is demonstrated by performing several quantitative and qualitative comparisons with the state-of-the-art methods, on both a benchmark image dataset and real-world motion blurred images. In addition, in order to demonstrate the efficiency in local motion deblurring, the proposed method is examined to deblur some real-world locally linear motion blurred images. The qualitative results show the efficiency of the proposed method for local deblurring at various blur levels.     

基于广义规范化稀疏模型的图像盲去模糊算法

针对基于规范化稀疏先验的图像盲去模糊方法估计精度低、计算速度慢、参数选择敏感等问题,提出一种Tikhonov正则增强的广义规范化稀疏模型,且将其作为中间清晰图像和运动模糊核的共同先验约束。随后,利用算子分裂、交替方向乘子法以及快速傅立叶变换,最小化关于中间清晰图像与运动模糊核的目标函数,导出一种快速图像盲去模糊算法。在标准测试集以及实际彩色模糊图像上的实验结果验证了提出方法的有效性和鲁棒性。此外,在同等条件下与近期文献中的盲去模糊方法进行比较,显示了本文方法在估计精度和估计效率上的双重优势。     

A Hybrid Motion Deblurring Strategy Using Patch Based Edge Restoration and Bilateral Filter

Motion blur is a common problem in digital photography. In the dim light, a long exposure time is needed to acquire a satisfactory photograph, and if the camera shakes during exposure, a motion blur is captured. Image deblurring has become a crucial image-processing challenge, because of the increased popularity of handheld cameras. Traditional motion deblurring methods assume that the blur degradation is shift-invariant; therefore, the deblurring problem can be reduced to a deconvolution problem. Edge-specific motion deblurring sharpened the strong edges of the image and then used them to estimate the blur kernel. However, this also enhanced noise and narrow edges, which cause ambiguity and ringing artifacts. We propose a hybrid-based single image motion deblurring algorithm to solve these problems. First, we separated the blurred image into strong edge parts and smooth parts. We applied the improved patch-based sharpening method to enhance the strong edge for kernel estimation, but for the smooth part, we used the bilateral filter to remove the narrow edge and the noise for avoiding the generation of ringing artifacts. Experimental results show that the proposed method is efficient at deblurring for a variety of images and can produce images of a quality comparable to other state-of-the-art techniques.     

基于辐照度的运动模糊图像去模糊

目的 已有的图像运动去模糊研究没有考虑模糊实际上发生在辐照度图像中的问题,也缺少自动检测成块饱和像素的方法。针对这两个问题,提出基于辐照度的运动模糊图像去模糊方法。方法 提出能量累积形成模糊的运动过程与摄像机响应函数相结合的摄像机响应函数求解方法,以及基于块的饱和像素自动检测算法并在此基础上,对辐照度图去除运动模糊和亮度还原,实现清晰原图恢复。结果 对单幅图像的定性去模糊取得了比直接去模糊等前人方法更小的振铃,较好的噪声抑制和清晰图像还原效果;采用信噪比的定量对比也取得较前人方法更高的数值。结论 基于辐照度的方法对图像运动去模糊效率有提升作用。     

Bilevel Parameter Learning for Nonlocal Image Denoising Models

We propose a bilevel optimization approach for the estimation of parameters in nonlocal image denoising models. The parameters we consider are both the fidelity weight and weights within the kernel of the nonlocal operator. In both cases, we investigate the differentiability of the solution operator in function spaces and derive a first-order optimality system that characterizes local minima. For the numerical solution of the problems, we use a second-order trust-region algorithm in combination with a finite element discretization of the nonlocal denoising models and introduce a computational strategy for the solution of the resulting dense linear systems. Several experiments illustrate the applicability and effectiveness of our approach.

     

A fast implementation algorithm of TV inpainting model based on operator splitting method

In this paper, we propose a fast algorithm to solve the well known total variation (TV) inpainting model. Classically, the Euler-Lagrange equation deduced from TV inpainting model is solved by the gradient descent method and discretized by an explicit scheme, which produces a slow inpainting process. Sometimes an implicit scheme is also used to tackle the problem. Although the implicit scheme is several times faster than the explicit one, it is still too slow in many practical applications. In this paper, we propose to use an operator splitting method by adding new variables in the Euler-Lagrange equation of TV inpainting model such that the equation is split into a few very simple subproblems. Then we solve these subproblems by an alternate iteration. Numerically, the proposed algorithm is very easy to implement. In the numerical experiments, we mainly compare our algorithm with the existing implicit TV inpainting algorithms. It is shown that our algorithm is about ten to twenty times faster than the implicit TV inpainting algorithms with similar inpainting quality. The comparison of our algorithm with harmonic inpainting algorithm also shows some advantages and disadvantages of the TV inpainting model.     

基于Gauss-Markov随机场的贝叶斯盲复原

针对图像盲复原中图像细节恢复的同时块效应放大的问题,提出了一种贝叶斯盲复原算法。首先使用贝叶斯框架模式,对原始图像、观察图像、点扩散函数(PSF)及模型参数分别建立先验模型,并将能有效描述图像局部统计特征的带有高斯特性的Markov(Gauss-Markov)随机场模型作为原始图像的先验模型;然后利用贝叶斯公式推导出原始图像及点扩散函数的迭代公式。实验结果表明,与总变分(TV)先验模型的恢复图像相比,所提算法的恢复图像块效应明显减少,并且视觉效果更好;在点扩散函数的大小已知和未知的情况下,相比TV先验模型,所提算法的改善信噪比(ISNR)能提高1dB左右。     

Efficient video denoising based on dynamic nonlocal means

A video denoising algorithm, which is based on dynamic nonlocal means (DNLM), is developed. Firstly, the standard nonlocal means and Kalman filtering are reviewed briefly. Then, using the idea of nonlocal means and linear minimum variance fusion, a weighted translational motion model without the explicit motion estimation and a weighted translational observation model are proposed to modify the state transition and observation equations. Finally, the overall dynamic denoising algorithm under the Kalman filter framework is presented. The main contribution of our work is a dynamic nonlocal means algorithm that is developed for video denoising under the Kalman filtering framework. In this algorithm, all computations are pixel-wise and it is easy to realize an efficient recursive algorithm for real-time processing. Experimental results for different test videos demonstrate the power of proposed method based on peak signal-to-noise-ratio (PSNR), structural similarity (SSIM) and motion-based video integrity evaluation index (MOVIE). The proposed method performs better than SNLM with the average PSNR gain of 2.33 dB, and outperforms SEQWT, 3DWTF and IFSM with the average SSIM gains of 0.033, 0.0087 and 0.049. It has competitive performance with STA, WRSTF and 3DSWDCT, but needs lower computational cost. Though the proposed DNLM is not competitive with several state-of-the-art video denoising algorithms such as VBM3D, K-SVD, 3D-Patch, and ST-GSM, it may be anyway valuable to readers working in this field as a source of inspiration for their further researches.