arXiv subjects

Justin P. Haldar

Publications and source records attributed to Justin P. Haldar.

21 records · Page 2Linked to original sources

arXiv2018

Optimal Experiment Design for Magnetic Resonance Fingerprinting: Cramér-Rao Bound Meets Spin Dynamics

Magnetic resonance (MR) fingerprinting is a new quantitative imaging paradigm, which simultaneously acquires multiple MR tissue parameter maps in a single experiment. In this paper, we present an estimation-theoretic framework to perform experiment design for MR fingerprinting. Specifically, we describe a discrete-time dynamic system to model spin dynamics, and derive an estimation-theoretic bound, i.e., the Cramer-Rao bound (CRB), to characterize the signal-to-noise ratio (SNR) efficiency of an MR fingerprinting experiment. We then formulate an optimal experiment design problem, which determines a sequence of acquisition parameters to encode MR tissue parameters with the maximal SNR efficiency, while respecting the physical constraints and other constraints from the image decoding/reconstruction process. We evaluate the performance of the proposed approach with numerical simulations, phantom experiments, and in vivo experiments. We demonstrate that the optimized experiments substantially reduce data acquisition time and/or improve parameter estimation. For example, the optimized experiments achieve about a factor of two improvement in the accuracy of $T_2$ maps, while keeping similar or slightly better accuracy of $T_1$ maps. Finally, as a remarkable observation, we find that the sequence of optimized acquisition parameters appears to be highly structured rather than randomly/pseudo-randomly varying as is prescribed in the conventional MR fingerprinting experiments.

eess.SP↗

arXiv2018

Accelerated Wirtinger Flow: A fast algorithm for ptychography

This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger gradient descent. Theoretical results enable prespecification of all AWF algorithm parameters, with no need for computationally-expensive line searches and no need for manual parameter tuning. AWF is evaluated in the context of simulated X-ray ptychography, where we demonstrate fast convergence and low per-iteration computational complexity. We also show examples where AWF reaches higher image quality with less computation than classical algorithms. AWF is also shown to have robustness to noise and probe misalignment.

eess.IV↗

arXiv2018

Navigator-free EPI Ghost Correction with Structured Low-Rank Matrix Models: New Theory and Methods

Structured low-rank matrix models have previously been introduced to enable calibrationless MR image reconstruction from sub-Nyquist data, and such ideas have recently been extended to enable navigator-free echo-planar imaging (EPI) ghost correction. This paper presents novel theoretical analysis which shows that, because of uniform subsampling, the structured low-rank matrix optimization problems for EPI data will always have either undesirable or non-unique solutions in the absence of additional constraints. This theory leads us to recommend and investigate problem formulations for navigator-free EPI that incorporate side information from either image-domain or k-space domain parallel imaging methods. The importance of using nonconvex low-rank matrix regularization is also identified. We demonstrate using phantom and \emph{in vivo} data that the proposed methods are able to eliminate ghost artifacts for several navigator-free EPI acquisition schemes, obtaining better performance in comparison to state-of-the-art methods across a range of different scenarios. Results are shown for both single-channel acquisition and highly accelerated multi-channel acquisition.

cs.CV↗