Sparse MRI: The application of compressed sensing for rapid MR imaging

Citations Over TimeTop 1% of 2007 papers

Abstract

The sparsity which is implicit in MR images is exploited to significantly undersample k-space. Some MR images such as angiograms are already sparse in the pixel representation; other, more complicated images have a sparse representation in some transform domain-for example, in terms of spatial finite-differences or their wavelet coefficients. According to the recently developed mathematical theory of compressed-sensing, images with a sparse representation can be recovered from randomly undersampled k-space data, provided an appropriate nonlinear recovery scheme is used. Intuitively, artifacts due to random undersampling add as noise-like interference. In the sparse transform domain the significant coefficients stand out above the interference. A nonlinear thresholding scheme can recover the sparse coefficients, effectively recovering the image itself. In this article, practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference. Incoherence is introduced by pseudo-random variable-density undersampling of phase-encodes. The reconstruction is performed by minimizing the l(1) norm of a transformed image, subject to data fidelity constraints. Examples demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin-echo brain imaging and 3D contrast enhanced angiography.

Related Papers

• → Reducing acquisition time in clinical MRI by data undersampling and compressed sensing reconstruction(2015)238 cited
• → Spatio-temporal undersampling: Recovering ultrasonic guided wavefields from incomplete data with compressive sensing(2020)25 cited
• → High‐frequency subband compressed sensing MRI using quadruplet sampling(2012)22 cited
• → Joint reconstruction framework of compressed sensing and nonlinear parallel imaging for dynamic cardiac magnetic resonance imaging(2021)10 cited
• → Improved regularisation constraints for compressed sensing of multi-slice MRI(2014)6 cited