Kawin Setsompop^1,2, Borjan A Gagoski³, Johnathan Polimeni^1,2, and Lawrence L Wald^1,4
1Radiology, A. A. Martinos Center for Biomedical Imaging, MGH, Charlestown, MA, United States, ²Harvard Medical School, Boston, MA, United States, ³Department of Electrical Engineering and Computer Science, MIT, cambridge, ma, United States, ⁴Harvard-MIT Division of Health Sciences and Technology, MIT, cambridge, ma, United States

Recent modifications to standard rectilinear 3D k-space sampling trajectories have provided more robust parallel imaging based reconstructions of highly undersampled datasets. Here, we introduce wave-CAIPIRINHA acquisition which combines 2D-CAIPIRINHA with BPE in two PE directions, and demonstrated its associated low g-factor penalty for highly accelerated acquisitions (Gmax=1.25 for an R=3x3 acquisition). For the reconstruction, we propose an algorithm based on generalized SENSE but perform in a pseudo-image domain (without gridding). This technique can be thought of as a way to sparsify the encoding matrix of wave-CAIPIRINHA to allow it to be divided into many small decoupled systems.

Michael Lustig¹, Peng Lai², Mark Murphy¹, Shreyas Mark Vasanawala³, Michael Elad⁴, Jian Zhang^5,6, and John Pauly^6
1Electrical Engineering and Computer Science, University of California Berkeley, Berkeley, CA, United States, ²ASL West, GE Healthcare, Menlo Park, CA, United States,³Radiology, Stanford University, Stanford, CA, United States, ⁴Computer Science, Technion IIT, Haifa, Israel, ⁵GE Healthcare, ⁶Electrical Engineering, Stanford University, Stanford, CA, United States

Parallel imaging techniques can be categorized roughly into two families: explicit sensitivity based methods like SENSE and autocalibrating methods (acPI) like GRAPPA. In this work we finally bridge the gap between these approaches. We present a new way to compute the explicit sensitivity maps that are (implicitly) used by acPI methods. These are found by Eigen-vector analysis of the k-space filtering in acPI algorithms. Our Eigen approach performs like other acPI methods when the prescribed FOV is smaller than the object, i.e., is not susceptible as SENSE to FOV limitations. At the same time, the reconstruction performs optimal calibration and optimal reconstruction, as SENSE. Our approach can be used to find the explicit sensitivity maps of any acPI method from its k-space kernels.

Fa-Hsuan Lin^1,2, Thomas Witzel², Aapo Nummenmaa^2,3, Panu Vesanen³, Risto J. Ilmoniemi³, and John W. Belliveau^2
1National Taiwan University, Taipei, Taiwan, ²Martinos Center, Massachusetts General Hospital, Charlestown, MA, United States, ³Department of Biomedical Engineering and Computational Science (BECS), Aalto University, Espoo, Finland

We propose the multi-dimensional encoded (MDE) MRI using over-complete spatial bases to achieve efficient encoding and image reconstructions. Different from traditional MRI using n-dimensional k-space to encode an n-dimensional object, MDE suggests encoding an n-dimensional object by a p-dimensional encoding space (p > n) using spatial bases generated by the combination of different spatial encoding magnetic fields and RF sensitivity profiles. Preliminary results using simultaneous multipolar SEMs in the PatLoc system and the O-space imaging with different center placements (CPs) indicates the potential of further optimizing MRI bases for a higher spatiotemporal resolution.

Gerrit Schultz¹, Daniel Gallichan¹, Hans Weber¹, Walter Witschey¹, Matthias Honal¹, Jürgen Hennig¹, and Maxim Zaitsev^1
1University Medical Center Freiburg, Freiburg, Germany

In parallel imaging, acquisition is usually accelerated by omitting k-space lines resulting in aliased images. A similar effect occurs when ambiguous encoding fields are applied instead of the standard linear gradient fields. Highly aliased images are produced when ambiguous field encoding is combined with k-space acceleration. In this case, calibration lines can only be acquired to partially unfold the image. Whereas in SENSE the aliasing artifacts from field ambiguities and from undersampling cannot be treated separately, we show that this is fundamentally different with k-space based methods like GRAPPA. This interesting property of GRAPPA is essential for k-space based image reconstructions from acquisitions based on ambiguous field encoding.

Kelvin Layton^1,2, Mark Morelande¹, Peter Mark Farrell¹, Bill Moran¹, and Leigh Andrea Johnston^1,3
1Electrical and Electronic Engineering, The University of Melbourne, Melbourne, Australia, ²NICTA Victorian Research Laboratory, Melbourne, Australia, ³Howard Florey Institute, Australia

Magnetic fields that varying nonlinearly across the field-of-view have recently been employed in parallel imaging to develop novel encoding schemes such as PatLoc and O-Space. A result of nonlinear encoding is that the quality of the image will vary across pixels. Since PatLoc satisfies certain properties, an expression for the spatially varying SNR can be derived analytically. However, no such expression is available for other schemes that are fundamentally different to PatLoc, such as O-Space imaging. In this work, we develop a simple metric to quantify the spatially varying performance, which is computationally efficient and applicable to arbitrary encoding schemes.

Michael Lustig^1
1Electrical Engineering and Computer Science, University of California Berkeley, Berkeley, CA, United States

An autocalibrating post-Cartesian parallel imaging method is presented. It is based on structured, low-rank matrix completion which is an extension of compressed sensing to Matrices. The method does not require a fully sampled autocalibration area in k-space. Instead it jointly calibrates and reconstructs the signal from the undersampled data alone. Results using spiral sampling are demonstrated showing similarly good reconstruction compared to method that use explicit calibration data.

Wei Lin¹, Peter Börnert², Feng Huang¹, George R Duensing¹, and Arne Reykowski^1
1Invivo Corporation, Philips Healthcare, Gainesville, FL, United States, ²Philips Research Europe, Hamburg, Germany

A rapid and self-calibrated parallel imaging reconstruction method is proposed for undersampled variable density spiral datasets. A set of Generalized GRAPPA for wider readout line (GROWL) operators are used to expand each acquired spiral line into a wider spiral band, therefore fulfilling Nyquist sampling criterion throughout the k-space. The calibration of GROWL operators is performed using the fully sampled central k-space region. In vivo brain scans demonstrate that the technique can be used either to achieve a significant acceleration and/or to reduce off-resonance artifacts due to shortened readout duration.

Florian Knoll¹, Christian Clason², Kristian Bredies², Martin Uecker³, and Rudolf Stollberger^1
1Institute of Medical Engineering, Graz University of Technology, Graz, Austria, ²Institute for Mathematics and Scientific Computing, University of Graz, Graz, Austria,³Biomedizinische NMR Forschungs GmbH, Max-Planck-Institut fuer biophysikalische Chemie, Goettingen, Germany

Nonlinear inversion was recently proposed for autocalibrated parallel imaging and shown to yield improved reconstruction quality. In addition, it has been shown that the aliasing arising from certain undersampled trajectories can be removed when using additional prior knowledge about the structure of the solution. Nonlinear inversion can be applied to arbitrary sampling trajectories, but the latter option was not yet exploited for this algorithm. In this work, it is demonstrated that nonlinear inversion can be extended with regularization terms that make use of such prior knowledge. The presented algorithms make use of the iteratively regularized Gauss-Newton method with additional variational constraints of total variation and total generalized variation type. Experimental results are presented for phantom and in-vivo measurements of undersampled radial and pseudorandom trajectories. The proposed approach yields results with reduced noise and undersampling artifacts in all cases when compared to conventional reconstruction with nonlinear inversion employing standard quadratic constraints.

Tsung-Min Huang¹, Thomas Witzel², Wen-Jui Kuo³, and Fa-Hsuan Lin^1,2
1Institute of Biomedical Engineering, National Taiwan University, Taipei, Taiwan, ²Martinos Center, Massachusetts General Hospital, Charlestown, MA, United States,³Institute of Neuroscience, National Yang-Ming University, Taipei, Taiwan

Dynamic magnetic resonance inverse imaging offers an unpredicted temporal resolution for BOLD fMRI by trading off the spatial resolution. Previously, we found that k-space InI (K-InI) reconstruction provides a higher spatial resolution compared with the image domain method based on the GRAPPA formulation. Here we hypothesize that the using SPIRiT (iterative self-consistent parallel imaging reconstruction) reconstruction can further improve K-InI reconstruction by adding a constraint to ensure data consistency in k-space. Preliminary results show that SPIRiT InI has a higher spatial resolution and comparable detection power to K-InI in BOLD fMRI measurements.

Jun Shen^1
1NIMH, Bethesda, Maryland, United States

A novel relationship between the partial derivatives of k space signal acquired using multichannel receive coils is described. It was found that the partial derivatives of the k space signal from one coil with respect to one direction can be expressed as a sum of partial derivatives of signals from multiple coils with respect to the perpendicular k space direction(s). Applications of this partial derivatives relationship to parallel imaging reconstruction in both k space and image domains are demonstrated.