Accelerated Regularized Estimation of MR Coil Sensitivities Using Augmented Lagrangian Methods

Abstract

Several magnetic resonance (MR) parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM–Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method (PCG) over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.

Sensitivity Encoding for Aligned Multishot Magnetic Resonance Reconstruction

“…In order to replicate the expected anatomical features contained in a real image, a motion-free T 2 neonatal brain axial image is selected from a fast spin echo sequence with acquired pixel resolution 0.8 × 0.8 mm, 1.6 mm slice thickness, echo time T E = 145 ms, repetition time T R = 12 s and flip angle α = 90 • using a head coil array with C = 32 channels on a 3 T PHILIPS ACHIEVA TX. Coil sensitivity maps were estimated from a separate reference scan using [16], which has been selected taking into account its robustness when extrapolating the sensitivities outside the calibrated region. The image has been reconstructed without zero filling, so that the resolution is maintained, and subsequently cropped to a 128×128 matrix so that the brain almost completely fills the FOV.…”

“…Acquisition parameters are selected as T R = 11 ms, T E = 4.6 ms, inversion time T I = 1.4 s, α = 9 • , and shot interval 2.075 s. The proposed reconstruction procedure is applied to a dataset of 207 babies with gestational ages ranging from 35 + 1 to 42 + 2 weeks, scanned using a 3 T PHILIPS ACHIEVA TX with a dedicated C = 32-channel neonatal head coil (RAPID BIOMEDICAL) and patient handling system [19]. As a preprocessing step of our method, coil sensitivity maps are estimated from a separate reference scan [16].…”

Constrained Source Space MR Spectroscopy: Multiple Voxels, No Gradient Readout

“…The C matrices can be estimated by various approaches, [18][19][20] though previous CSS work has shown that a simple procedure is sufficient for proof-of-concept implementation. 14 Two sets of fast gradient-echo images were acquired with the same pulse sequence parameters (TE, 1.3 milliseconds; TR, 34 milliseconds; flip angle, 5°; field of view, 30 cm; 64 ϫ 64 acquisition matrix; section thickness, 5 mm): 1 set with the body coil and 1 set with the multichannel head coil receiver.…”

Fast Parallel MR Image Reconstruction via B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithms (BARISTA)

“…The data matrix size was 256 × 144 × 128 uniformly spaced samples. Sensitivity maps were estimated using a quadratic regularized least squares routine [14]. The data were retrospectively undersampled in the Fourier domain using a Poisson disk sampling scheme [20] with a fully sampled center (32-by-32 block), which has been demonstrated to be useful in compressed sensing MRI applications [21].…”

“…We will use this property in the following sections. Furthermore, D f is easy to compute once one has determined the coil sensitivities, and with the recent development of fast algorithms for SENSE map estimation it is quickly available in online settings [14]. …”