Compressed sensing MRI based on nonsubsampled contourlet transform

How to reduce acquisition time is very important in magnetic resonance imaging (MRI). Compressed sensing MRI emerges recently to suppress the aliasing when undersampling k-space data is employed. However, typical sparse transform for compressed sensing MRI ever used is wavelet, which only captures limited directional information with decay rate M
¹
. In this paper, we introduce contourlet into compressed sensing to obtain a sparse expansion for smooth contours with decay rate C(logM)
³
M
²
and employ nonsubsampled contourlet to increase the redundancy of basis for magnetic resonance images. We propose compressed sensing MRI based on nonsubsampled contourlet transform (NSCT). Experimental results demonstrate that NSCT outperforms wavelet on suppressing the aliasing and improves the visual appearance of magnetic resonance images.