基于联合正则化的稀疏磁共振图像重构

Reconstruction of sparse MRI based on compound regularizers

基于压缩感知的MRI图像重构是利用图像稀疏性,从数量非常有限的观测数据集合中重构出图像,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,重构效果不理想,而且在一些图像重构的应用中,单一正则项的作用有限并不能很好地完成复原任务。针对此问题,引入待重构图像的L1/2范数作为新正则项,与TV范数构成联合正则项,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,联合正则项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。

Magnetic resonance images can be reconstructed close to the original in which way that we use the compressed sensing from a very limited number of observation data set. Usually the L1 norm can produce a sparse solution, but it is different from the true sparse solution （L0 solution）, and result in the inferior reconstruction, what＇s more, in the application of some image reconstruction, a single reguiarization is limited and can＇t complete the task of recovery. Aiming at this problem, the method is introduced the L1/2 norm as a new regular of the reconstructed images, combined with the TV regular to reconstruct the image. 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 compared to the traditional model can have excellent stability and get a higher signal-to-noise ratio.