图像恢复问题的梯度稀疏化正则方法

Gradient sparse based regularization model for image restoration

针对图像恢复中边缘损坏及细节丢失等问题,从分析梯度直方图的分布特征及梯度稀疏性最佳表示出发,提出了一种基于梯度稀疏性的正则方法,建立了具有梯度先验信息的图像恢复模型。该模型不仅能够增强图像的细节特征,而且能够在去除模糊及噪声与保持图像边缘之间取得很好的平衡。设计了一种新的优化算法对模型进行求解。实验结果表明,新算法快速有效且收敛性好,新模型能够在很好地去除模糊和噪声的同时,有效保留图像边缘及纹理等信息。

In order to alleviate the defects in image restoration, e.g. , the damage of the edges and the loss of the details, a new gradient sparsity regularization model is derived based on the analysis of the gradient histogram and the best penalty in sparse representation. The proposed model can not only highlight the image detail effectively but also achieve a good balance between blur and noise removal and edge preservation. A new optimization algorithm is designed to solve the new model. Simulation experiments on image denoising and deblurring confirm that the numerical method is fast and efficient, the proposed regularization model can well preserve the significant edges and textures when effectively removing the blur and noise.