中文摘要：

磁共振图像可以利用压缩感知从数量非常有限的观测数据集合中重构出,然而为了能够做到这一点,必须要解决定义在大量数据集合上的非光滑函数的最小化这一困难问题.通常L1范数能够产生稀疏解,但它往往与真实稀疏解（L0的解）差距甚大.针对该问题,研究一种基于变量分裂的图像重构模型,引入待重构图像的L1/2范数作为新正则项,采用交替增广拉格朗日乘子法进行求解.为考察方法的稳定性和重构效果,结合不同参数等评价标准与现有的图像重构模型进行比较.实验结果表明,L1/2范数作为正则子的图像重构模型相对于原有模型,图像重构结果稳定性好,可以获得更高的信噪比.

英文摘要：

Magnetic resonance images can be reconstructed close to the original in which we use the compressed sensing from a very limited number of observation data set.However,to achieve this,we must solve a problem：the nonsmooth functions that definition in the data set to minimize.Usually the norm can produce a sparse solution,but it is different from the true sparse solution（solution）.To solve the problem,a method is proposed based on variable splitting image reconstruction model.The method is introduced the norm as a new regular of the reconstructed images,which was solved by alternating the augmented Lagrange multiplier method.Finally,to verify the stability and reconstruction effect,selecting different parameters and evaluation standard are compared with existing models of image reconstruction.The experiments indicate that the improved model has excellent stability and gets a higher signal-to-noise ratio.