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收稿：2018-06-20，
修回：2018-8-20，
纸质出版：2019-02-16
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目的
2
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。为此根据图像分块平稳的特点提出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
2
该模型采用广义高斯分布（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
2
本文算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的条件下，经本文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0.04~2.96 dB和0.14~3.19 dB；在高噪声（加4%噪声）不同模糊核下，能分别提高0.19~4.50 dB和0.20~3.63 dB，同时本文算法相比2017年Pan等人提出的算法（加2%噪声）能提升0.15~0.36 dB。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
2
本文算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。
Objective
2
Natural images generally consist of smooth regions with sharp edges
which lead to a heavy-tailed gradient distribution. The gradient priors of these images are commonly used for image deblurring. However
previous results show that existing parameter estimation methods cannot tightly fit the texture change of different image patches. This study presents an image deblurring algorithm that uses a local adaptive sparse gradient model that is based on a blocky stationary distribution characteristic of a natural image.
Method
2
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
rather than assigning a single image gradient prior to an entire image. Third
an alternating minimization algorithm based on a variable-splitting technique is employed to solve the optimization problem of the deblurring model. This optimization problem is divided into two sub-problems
namely
latent image
$$\boldsymbol{u}$$
and auxiliaryvariable
$$\boldsymbol{\omega }$$
estimations. An alternating minimization strategy is adopted to solve the two sub-problems. Given a fixed
$$\boldsymbol{\omega }$$
$$\boldsymbol{u}$$
can be obtained by solving the first sub-problem
and given a fixed
$$\boldsymbol{u}$$
$$\boldsymbol{\omega }$$
can be acquired by solving the second sub-problem. A generalized shrinkage threshold algorithm is used to solve the second sub-problem. In addition
we initially deconvolve blurred image
$$\boldsymbol{g}$$
using standard Tikhonov regularization in the shape parameter estimation of a GGD to obtain an initial approximation image
$$\boldsymbol{u}_0$$
. Next
an edge-preserving smoothing filter is applied to obtain a new estimate image
$$\boldsymbol{u}_1$$
. Then
we divide the new estimate image
$$\boldsymbol{u}_1$$
into two regions
namely
textured and smooth regions. A globally convergent method is deployed to estimate the shape parameters of the GGD of the textured region
and a fixed parameter value is imposed to the smooth region.
Result
2
We evaluate the proposed method on different types of natural image. We also compare our method with 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. Moreover
our method exhibits good convergence and only requires 2
3 iterations. In comparison with other competing methods
we observe that textured regions are best restored by utilizing a content-aware image prior
which illustrates the benefit of the proposed method. We also compare our results with those reconstructed via other competing methods using signal-to-noise ratio (SNR) as quality metrics. We observe that our method can achieve a high SNR. Our method can achieve 0.04~2.96 dB and 0.14~3.19 dB SNR gains when the noise level is low (1%) compared with competing methods under blur kernel1 and kernel2
respectively. Our method can achieve 0.19~4.50 dB and 0.20~3.63 dB SNR gains when the noise level is high (4%) under blur kernel1 and kernel2
respectively. In addition
at a low noise level (2%)
the proposed method can achieve 0.15~0.36 dB and 0.33~0.89 dB SNR gains compared with Pan's (2017) and Cho's (2012) methods
respectively.
Conclusion
2
In comparison with state-of-the-art deblurring approaches
the proposed method not only efficient and effectively removes blurs and noise but also preserves salient edge structures and textured regions. Our method can be used for the deblurring of natural and low-illumination images and can be extended to image capture and video surveillance systems.
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