Noise power spectrum in compressed sensing magnetic resonance imaging

Compressed sensing magnetic resonance imaging (CS-MRI) uses random undersampling and nonlinear iterative reconstruction. This study was conducted to clarify the noise power spectrum (NPS) characteristics of CS-MRI. We measured two-dimensional (2D) NPS of CS-MRI with various acceleration factors (AF) and denoising factors (DF) and compared their appearance to those of conventional parallel MR images. Results showed that the 2D NPS of CS-MRI exhibited the following characteristics: (1) local decrease in the low-frequency region, (2) gradual decrease in the high-frequency region, and (3) a stripe pattern aligned at unequal intervals in the phase-encoding direction. Specifically, the 2D NPS of CS-MRI reflects the random undersampling pattern of k-space data. Additionally, 2D NPS allowed visualization of AF-dependent noise characteristics of CS-MRI. Furthermore, 1D NPS graph shapes clarified the CS-MRI noise characteristic dependence on AF and DF.