目的 图像的梯度分布被广泛应用在自然图像去模糊中，但研究结果显示先前的梯度参数估计方法不能很好地适应图像局部纹理变化。该文根据图像分块平稳的特点提出了一种采用局部自适应梯度稀疏模型的图像去模糊模型。方法 该模型采用广义高斯分布（Generalized Gaussian Distribution, GGD）来描述图像不同区域的梯度分布，在最大后验概率框架下建立自适应梯度稀疏模型，然后采用变量分裂交替优化算法来求解模型中的最小化问题。在GGD参数估计中，先对模糊图像进行预处理，并将预处理后的图像分成纹理区和平滑区，仅对纹理区采用全局收敛算法进行GGD参数估计，而对平滑区设置固定参数值。结果 提出的方法与近年来常用的去模糊去噪算法在不同类型的自然图像上进行了对比。实验结果表明本文的参数估计法能精确地表达图像局部纹理变化，当在低噪声（加1%噪声），分别加入模糊核1和2条件下，经提出算法去除模糊和噪声后的图像相较对比算法能分别提高信噪比值0.04dB~2.96dB和0.14dB~3.19dB；在高噪声（加4%噪声）不同模糊核下，能分别提高0.19dB~4.50dB和0.20dB~3.63dB，同时本文算法相比2017年Pan等的算法在加2%噪声下能提升0.15dB~0.36dB。此外，本文算法在主观视觉上能获得更清晰的纹理和边缘结构信息。结论 本方法在主客观评价上都表现出了良好的去模糊性能，可应用在自然图像和低照明图像等的去模糊领域。
Image Deblurring Using an Adaptive Sparse Gradient Model
杨 洁,周 洋,谢 菲,张 旭光(Faculty of communication, Hangzhou Dianzi University, Hangzhou 310018, China)
Objective In general, natural images consist of the smooth region with sharp edges, leading to a heavy-tailed gradient distribution. This image’s gradient priors are commonly used for image deblurring, but previous results show that the existing parameter estimation methods cannot tightly fit the texture change of different image patches. The paper proposes an image deblurring algorithm using a local adaptive sparse gradient model which is based on a blocky stationary distribution characteristic of a natural image.Method First, our method uses a generalized Gaussian distribution (GGD) to represent the image’s heavy-tailed gradient statistics. Second, an adaptive sparse gradient model is established to estimate a clean image via the maximization of posterior probability. In the model, different patches have different gradient statistics distribution even within a single image, instead of assigning a single image gradient prior to a whole image. Third, an alternating minimization algorithm based on the variable-splitting technique is employed to solve the optimization problem of the deblurring model. This optimization problem is divided into the two sub-problems: estimating latent image u and estimating auxiliary variable ω. An alternating minimization strategy is adopted to solve the two sub-problems. Given a fixed ω, u can be obtained by solving the sub-problem I, and then given a fixed u, ω can be acquired by solving the sub-problem II. A generalized shrinkage threshold algorithm is used to solve the sub-problem II. In addition, in the stage of the shape parameter estimation of a generalized Gaussian distribution, we first deconvolve the blurred image g using standard Tikhonov regularization to obtain an initial approximation image u0. Next, an edge-preserving smoothing filter is applied to obtain a new estimate image u1. Then we divide the new estimate image u1 into two regions, namely textured and smooth regions. A globally convergent method is deployed to estimate the shape parameters of the generalized Gaussian distribution of the textured region, whereas a fixed parameter value is imposed to the smooth region.Result We evaluate the proposed method on the different types of natural images, and compare our method with the state-of-the-art deblurring and denoising approaches. Experimental results demonstrate that the proposed parameter estimation method can accurately adapt to the local gradient statistics of an image patch. Meanwhile, our method exhibits good convergence and only need 2~3 iterations. Compared to the competing methods, we observe that textured regions are best be restored by exploiting the content-aware image prior, illustrating the benefit of the proposed methods. We also compare our results to those reconstructed via other competing methods, using signal-to-noise ratio (SNR) as quality metrics. We observe that our method can achieve a higher signal to noise ratio. When the noise level is low (1%)，our method can achieve 0.04dB~2.96dB and 0.14dB~3.19dB SNR gain, compared to the competing methods at giving the blur kernel1 and kernel2, respectively. When the noise level is high (4%), our method can achieve 0.19dB~4.50dB and 0.20dB~3.63dB SNR gain at giving the blur kernel1 and kernel2, respectively. Also, the proposed method can achieve 0.15dB~0.36dB and 0.33dB~0.89dB SNR gain compared with Pan’s method (2017) and Cho’s method (2012) at the noise level is low (2%), respectively.Conclusion Compared with the state-of-the-art deblurring approaches, the proposed method not only efficient and effective remove blur and noise but also preserve the salient edge structures and textured regions clearly. Our method can be used for the deblurring of the nature images and low-illumination images, and also can be further extended to image capture, video surveillance systems, etc.