Jon Fredrik Nielsen

Regularization Parameter Selection for Nonlinear Iterative Image Restoration and MRI Reconstruction Using GCV and SURE-Based Methods

Regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values. We focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive (possibly complex) Gaussian noise. Generalized cross-validation (GCV) and (weighted) mean-squared error (MSE) approaches [based on Steins unbiased risk estimate (SURE)] need the Jacobian matrix of the nonlinear reconstruction operator (representative of the iterative algorithm) with respect to the data. We derive the desired Jacobian matrix for two types of nonlinear iterative algorithms: a fast variant of the standard iterative reweighted least-squares method and the contemporary split-Bregman algorithm, both of which can accommodate a wide variety of analysis- and synthesis-type regularizers. The proposed approach iteratively computes two weighted SURE-type measures: predicted-SURE and projected-SURE (which require knowledge of noise variance σ2), and GCV (which does not need σ2) for these algorithms. We apply the methods to image restoration and to magnetic resonance image (MRI) reconstruction using total variation and an analysis-type ℓ1-regularization. We demonstrate through simulations and experiments with real data that minimizing predicted-SURE and projected-SURE consistently lead to near-MSE-optimal reconstructions. We also observe that minimizing GCV yields reconstruction results that are near-MSE-optimal for image restoration and slightly suboptimal for MRI. Theoretical derivations in this paper related to Jacobian matrix evaluations can be extended, in principle, to other types of regularizers and reconstruction algorithms.

Separate Magnitude and Phase Regularization via Compressed Sensing

Compressed sensing (CS) has been used for accelerating magnetic resonance imaging acquisitions, but its use in applications with rapid spatial phase variations is challenging, e.g., proton resonance frequency shift (PRF-shift) thermometry and velocity mapping. Previously, an iterative MRI reconstruction with separate magnitude and phase regularization was proposed for applications where magnitude and phase maps are both of interest, but it requires fully sampled data and unwrapped phase maps. In this paper, CS is combined into this framework to reconstruct magnitude and phase images accurately from undersampled data. Moreover, new phase regularization terms are proposed to accommodate phase wrapping and to reconstruct images with encoded phase variations, e.g., PRF-shift thermometry and velocity mapping. The proposed method is demonstrated with simulated thermometry data and in vivo velocity mapping data and compared to conventional phase corrected CS.

Cardiovascular magnetic resonance phase contrast imaging

Cardiovascular magnetic resonance (CMR) phase contrast imaging has undergone a wide range of changes with the development and availability of improved calibration procedures, visualization tools, and analysis methods. This article provides a comprehensive review of the current state-of-the-art in CMR phase contrast imaging methodology, clinical applications including summaries of past clinical performance, and emerging research and clinical applications that utilize today’s latest technology.

Automatic correction of echo‐planar imaging (EPI) ghosting artifacts in real‐time interactive cardiac MRI using sensitivity encoding

To develop a method that automatically corrects ghosting artifacts due to echo‐misalignment in interleaved gradient‐echo echo‐planar imaging (EPI) in arbitrary oblique or double‐oblique scan planes.

Feasibility of in vivo measurement of carotid wall shear rate using spiral fourier velocity encoded MRI

Arterial wall shear stress is widely believed to influence the formation and growth of atherosclerotic plaque; however, there is currently no gold standard for its in vivo measurement. The use of phase contrast MRI has proved to be challenging due to partial‐volume effects and inadequate signal‐to‐noise ratio at the high spatial resolutions that are required. This work evaluates the use of spiral Fourier velocity encoded MRI as a rapid method for assessing wall shear rate in the carotid arteries. Wall shear rate is calculated from velocity histograms in voxels spanning the blood/vessel wall interface, using a method developed by Frayne and Rutt (Magn Reson Med 1995;34:378–387). This study (i) demonstrates the accuracy of the velocity histograms measured by spiral Fourier velocity encoding in a pulsatile carotid flow phantom compared with high‐resolution two‐dimensional Fourier transform phase contrast, (ii) demonstrates the accuracy of Fourier velocity encoding–based shear rate measurements in a numerical phantom designed using a computational fluid dynamics simulation of carotid flow, and (iii) demonstrates in vivo measurement of regional wall shear rate and oscillatory shear index in the carotid arteries of healthy volunteers at 3 T. Magn Reson Med 63:1537–1547, 2010.

Functional perfusion imaging using pseudocontinuous arterial spin labeling with low-flip-angle segmented 3D spiral readouts.

Arterial spin labeling (ASL) provides quantitative and reproducible measurements of regional cerebral blood flow, and is therefore an attractive method for functional MRI. However, most existing ASL functional MRI protocols are based on either two‐dimensional (2D) multislice or 3D spin‐echo and suffer from very low image signal‐to‐noise ratio or through‐plane blurring. 3D ASL with multishot (segmented) readouts can improve the signal‐to‐noise ratio efficiency relative to 2D multislice and does not suffer from T2‐blurring. However, segmented readouts require lower imaging flip‐angles and may increase the susceptibility to temporal signal fluctuations (e.g., due to physiology) relative to 2D multislice. In this article, we characterize the temporal signal‐to‐noise ratio of a segmented 3D spiral ASL sequence, and investigate the effects of radiofrequency phase cycling scheme and flip‐angle schedule on image properties. We show that radiofrequency‐spoiling is essential in segmented 3D spiral ASL, and that 3D ASL can improve temporal signal‐to‐noise ratio 2‐fold relative to 2D multislice when using a simple polynomial (cubic) flip‐angle schedule. Functional MRI results using the proposed optimized segmented 3D spiral ASL protocol show excellent activation in the visual cortex. Magn Reson Med, 2013.

Referenceless phase velocity mapping using balanced SSFP

Phase contrast MRI (PC‐MRI) is an established technique for measuring blood flow velocities in vivo. Although spoiled gradient recalled echo (GRE) PC‐MRI is the most widely used pulse sequence today, balanced steady state free precession (SSFP) PC‐MRI has been shown to produce accurate velocity estimates with superior SNR efficiency. We propose a referenceless approach to flow imaging that exploits the intrinsic refocusing property of balanced SSFP, and achieves up to a 50% reduction in total scan time. With the echo time set to exactly one half of the sequence repetition time (TE = TR/2), we show that non‐flow‐related image phase tends to vary smoothly across the field‐of‐view, and can be estimated from static tissue regions to produce a phase reference for nearby voxels containing flowing blood. This approach produces accurate in vivo one‐dimensional velocity estimates in half the scan time compared with conventional balanced SSFP phase‐contrast methods. We also demonstrate the feasibility of referenceless time‐resolved 3D flow imaging (called “7D” flow) in the carotid bifurcation from just three acquisitions. Magn Reson Med, 2009.

Molecular, dynamic, and structural origin of inhomogeneous magnetization transfer in lipid membranes.

To elucidate the dynamic, structural, and molecular properties that create inhomogeneous magnetization transfer (ihMT) contrast.

Interleaved balanced SSFP imaging: Artifact reduction using gradient waveform grouping

To analyze steady‐state signal distortions in interleaved balanced steady‐state free precession (bSSFP) caused by slightly unbalanced eddy‐current fields and develop a general strategy for mitigating these artifacts.

Monte Carlo SURE-Based Parameter Selection for Parallel Magnetic Resonance Imaging Reconstruction

Regularizing parallel magnetic resonance imaging (MRI) reconstruction significantly improves image quality but requires tuning parameter selection. We propose a Monte Carlo method for automatic parameter selection based on Steins unbiased risk estimate that minimizes the multichannel k‐space mean squared error (MSE). We automatically tune parameters for image reconstruction methods that preserve the undersampled acquired data, which cannot be accomplished using existing techniques.