Noise behavior of MR brain reconstructions using compressed sensing

Compressed sensing (CS) has demonstrated great potential to reconstruct high quality MR images from undersampled k-space data. However, successful application of CS in clinic is still limited by many factors. One of the key factors is that the noise behavior in CS reconstructions remains largely unexplored. The main objective of this work is to analyze the noise behavior of MR reconstructions using CS method with different reduction factors. Our work focuses on brain CS-MRI reconstructions using non-linear conjugate gradient (NLCG) solvers. After reconstruction, the noise behavior is characterized using the MP-Law method. The results show that the spatial noise distributed non-uniformly, and the noise variance from CS reconstruction increases with reduction factors. A kind of fitting model is given, which can be used to predict the noise behavior parameter for different reduction factors, and the noise amplification factor maps are shown to prove the denoising capability of CS reconstruction. The results provide a qualitative and quantitative understanding of the noise behavior in CS-MRI with different reduction factors.