High Order Total Variational Denoising Algorithm Based on l_0 Overlapping Combination Sparse

For addressing impulse noise in images, this paper proposes a denoising algorithm for non-convex impulse noise images based on the l_(0) norm fidelity term. Since the total variation of the l_(0) norm has a better denoising effect on the pulse noise, it is chosen as the model fidelity term, and the overlapping group sparse term combined with non-convex higher term is used as the regularization term of the model to protect the image edge texture and suppress the staircase effect. At the same time, the alternating direction method of multipliers, the majorization–minimization method and the mathematical program with equilibrium constraints were used to solve the model. Experimental results show that the proposed model can effectively suppress the staircase effect in smooth regions, protect the image edge details, and perform better in terms of the peak signal-to-noise ratio and the structural similarity index measure.

基于L_(p)范数联合全变分的磁共振成像重构方法

局部k空间邻域模型是最近提出的一种k空间低秩约束重构模型,其利用图像的线性位移不变性将图像的k空间数据映射到高维矩阵中,可以解决图像重构的问题。在并行磁共振成像重构的过程中,使用欠采样技术来提高成像速度会导致重构图像的质量下降,为此提出一种基于交替方向乘子法求解的L_(p)范数联合全变分正则项局部k空间邻域建模算法,将所提算法与其他算法在人体的脑部和膝盖数据集上进行实验。实验结果表明,相比于其他算法,所提算法能够减少重构图像的伪影,更好地保留重构图像的边缘轮廓信息,重构效果更好。