紧框架域重加权L1范数正则化图像恢复模型

Reweighted L1 Norm Regularization Image Restoration Model of Compact Frame Domain

针对传统紧框架域L1范数模型忽略框架变换后分解系数与原始图像结构信息之间的联系,采用均匀惩罚的不足,提出一种新的重加权紧框架L1范数正则化稀疏模型.首先对待恢复图像进行紧框架分解,得到包含原始图像多层结构信息的框架系数;其次在L1范数稀疏正则化的基础上,引入框架系数模的图像先验信息作为权重函数,建立重加权L1范数的正则化能量泛函;最后结合恢复过程中权重因子的更新,采用多步交替优化算法求解模型.算法能有效克服传统恢复模型易导致边缘细节模糊的不足,获得更高的结构相似测度(SSIM)和峰值信噪比(PSNR).仿真实验表明,模型具有更强的边缘细节保护能力,大大提高图像恢复质量.

Aimed at the disadvantage ofthe traditional tight frame L1 norm model which neglected the connection of frame coefficientand the original image structure information after compact frame transformation and adopted uniform penalty,this paper proposes a re-weighted sparse restoration model. Firstly, it makes multi-level frame decomposition for the corrupted image in the tight frame do-main. And then on the account of the L1 norm sparse regularization item, this paper introduces a weighting factor related with imageprior information,and establishes reweighted energy functional regularization model. Finally,according to the update of weighted factorin the image restoration process, the model is solved by multi-stage alternating optimization algorithm. The proposed model is superiorto traditional restoration regularization model in terms of detail preservation,such as edge, and the proposed algorithm can achievehigherpeak signal-to-noise and structural similarity index measure than the traditional restoration models. Our numerical implementa-tions show that the proposed model has a better preservation of sharp edges and details, and can improve the quality of recovery imagegreatly.