小波框架中改进的l_0平滑算法的图像复原

Image restoration study based on smoothed l_0 algorithm in wavelet frame

传统的小波变换无法对图像提供最优的稀疏表示,不能取得好的复原效果。为此,人们提出了一种基于平滑的图像复原算法。但由于当优化模型中存在基于范数的约束项时,会使得求解方法较为复杂,且时间复杂度较高。针对这一问题,通过光滑高斯函数近似代替范数,提出了改进的平滑的图像复原模型。通过牛顿迭代法使小波系数到达最小。实验结果表明,与PD和MDAL算法相比,提出的改进模型能够明显改善图像的视觉效果,且具有较高的峰值信噪比(PSNR)。

Traditional wavelet transform can not provide optimal sparse representation to image, so can not get a better restoration effects. Thus, an algorithm of image restoration based on smoothed l0 norm was proposed. But when a constraint based on 10 norm exists in optional model, it may lead to a complicated solving method and a high computational cost. The problem was solved through a smooth Gaussian function substitute l0 norm approximately, modified smoothed l0 algorithm applied in wavelet frame was proposed. By using Newton method to update it, the wavelet coefficients obtain the minimum. Compared with the PD method and the MDAL method, the experimental results demonstrate that the modified approach has a better visual effect and a high Peak Signal-to-Noise Ratio （ PSNR）.