Regularized image reconstruction for PS model-based cardiovascular MRI

Real-time cardiovascular MRI is a useful and challenging dynamic imaging application. The partial separability (PS) model enables reconstruction of dynamic cardiac images from highly undersampled (k, t)-space data. However, the underlying PS model-based reconstruction problem is ill-conditioned, so regularization is often necessary to stabilize its solution. It has been shown that ℓ
₁
regularization is useful for finding sparse solutions, and ℓ
₂
regularization is widely used to incorporate anatomical constraints. An important practical question is which regularization scheme to use for PS model-based cardiovascular imaging. We address this problem by implementing both schemes and evaluating their performances in terms of reconstruction error, image artifacts, image noise, computation time, and performance characterizability. The ℓ
₁
-regularized results exhibit lower reconstruction error, artifact energy, and noise variance, while ℓ
₂
regularization is much faster and produces predictable reconstruction results. This study indicates that the ℓ
₁
scheme is preferable when image quality is the main concern.