Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using priors to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve the related WPM. Numerical experiments demonstrate the effectiveness and efficiency of CQNPM.
Purpose: Arterial Spin Labeling (ASL) is a quantitative, non-invasive alternative to perfusion imaging with contrast agents. Fixing values of certain model parameters in traditional ASL, which actually vary from region to region, may introduce bias in perfusion estimates. Adopting Magnetic Resonance Fingerprinting (MRF) for ASL is an alternative where these parameters are estimated alongside perfusion, but multiparametric estimation can degrade precision. We aim to improve the sensitivity of ASL-MRF signals to underlying parameters to counter this problem, and provide precise estimates. We also propose a regression based estimation framework for MRF-ASL. Methods: To improve the sensitivity of MRF-ASL signals to underlying parameters, we optimize ASL labeling durations using the Cramer-Rao Lower Bound (CRLB). This paper also proposes a neural network regression based estimation framework trained using noisy synthetic signals generated from our ASL signal model. Results: We test our methods in silico and in vivo, and compare with multiple post labeling delay (multi-PLD) ASL and unoptimized MRF-ASL. We present comparisons of estimated maps for six parameters accounted for in our signal model. Conclusions: The scan design process facilitates precise estimates of multiple hemodynamic parameters and tissue properties from a single scan, in regions of gray and white matter, as well as regions with anomalous perfusion activity in the brain. The regression based estimation approach provides perfusion estimates rapidly, and bypasses problems with quantization error. Keywords: Arterial Spin Labeling, Magnetic Resonance Fingerprinting, Optimization, Cramer-Rao Bound, Scan Design, Regression, Neural Networks, Deep Learning, Precision, Estimation, Brain Hemodynamics.