基于混合梯度与稀疏先验的图像复原算法

Image Restoration Algorithm Based on Mixed Gradient and Sparse Priors

摘要: 针对泊松噪声下的图像的复原问题，本文设计一种基于混合梯度与稀疏先验的复原算法。该算法模型采用Kullback-Leibler散度作为数据保真项，可以有效地抑制泊松噪声；在正则项上，采用重叠组稀疏正则化约束图像的一阶梯度，采用L₁和L_P范数联合约束图像的二阶梯度；使用交替方向乘子法、最小化方法和迭代加权最小二乘法对算法模型进行求解。将本文复原算法与FOTV、HTVp-OGS、P-HONOGSTV三种算法进行实验对比。实验结果表明，综合主观视觉和客观评价指标峰值信噪比和结构相似性上，本文算法优于以上几种对比算法。

Abstract: To address the problem of image restoration under Poisson noise, this paper designs a restoration algorithm based on mixed gradients and sparse priors. The algorithm model employs the Kullback-Leibler divergence as the data fidelity term, effectively suppressing Poisson noise. On the regularization term, overlapping group sparse regularization is used to constrain the first-order gradient of the image and L1 and LP norms are used to jointly constrain the second-order gradient of the image; the algorithm model is solved using alternating direction method of multipliers, minimization method, and iteratively reweighted least squares algorithm. Experimental comparisons are conducted between our restoration algorithm and three algorithms: FOTV, HTVp-OGS, and P-HONOGSTV through experiments. The experimental results show that our algorithm outperforms the above compared algorithms in terms of subjective visual and objective evaluation indicators such as peak signal-to-noise ratio and structural similarity.