自适应加权核范数最小化的图像去噪

Image Denoising with Adaptive Weighted Kernel Norm Minimization

摘要: 针对加权核范数最小化算法在图像去噪过程中存在难以分离低秩信息与噪声、参数选取过度依赖经验值的问题，提出了一种自适应加权核范数最小化的图像去噪算法。首先，利用图像非局部相似先验构建加权核范数最小化图像去噪模型，然后引入改进Gerschgorin理论从观测矩阵中准确估计出低秩矩阵的秩。在此基础上，结合秩估计方法提出自适应思想，通过奇异值分解与软阈值算子对自适应加权核范数最小化图像去噪模型进行求解，得到最终的去噪图像。实验结果表明，文章算法与现有的多种经典去噪算法相比具有更高的峰值信噪比值和结构相似性值，有效提高去噪性能的同时保持了图像的边缘纹理等细节信息，具有良好的鲁棒性和泛化性。

Abstract: Aiming at the problems that it is difficult to separate low-rank information from noise and over- dependence on empirical value in parameter selection in image denoising process of weighted ker-nel norm minimization algorithm, an adaptive weighted kernel norm minimization algorithm is proposed. Firstly, a weighted kernel norm minimization image denoising model is constructed us-ing image non-local similar priors, and then an improved Gerschgorin theory is introduced to accu-rately estimate the rank of the low-rank matrix from the observation matrix. On this basis, an adap-tive idea is proposed by combining rank estimation method, and the adaptive weighted kernel norm minimization image denoising model is solved by singular value decomposition and soft threshold operator, and the final denoising image is obtained. The experimental results show that the proposed algorithm has higher peak signal-to-noise ratio and structural similarity value com-pared with the existing classical denoising algorithms, which can effectively improve the denoising performance while preserving the image edge texture and other details, and has good robustness and generalization.