Our group develops new methods for (Cardiovascular) Magnetic Resonance Imaging (MRI) with the goal of faster, more robust, and quantitative imaging. Our research interests extend from the development of fundamentally new measurement techniques to the translation of new methods into clinical use. A long-term aim is to replace all traditional methods in MRI which currently still rely on repeated breathholds and synchronization to an ECG with fast free-breathing techniques. A major step towards this goal was the development of a new method that allows two-dimensional imaging in real-time. Methodologically, we mostly focus on computational imaging methods that combine advanced numerical algorithms for image reconstruction with jointly designed data acquisition techniques.

(True) Real-time MRI

Continuous advances in hardware and software have made it possible to image dynamic processes in the human body in real-time with good quality using MRI. Our method is based on a new formulation of parallel MRI as a non-linear inverse problem (see below). The method is fast enough to observe turbulence after stirring in a water beaker, visualize swallowing and speaking, and to acquire images of the human heart without synchronization to an ECG. As one of many important applications we are working on interventional MRI procedures under real-time MRI guidance.

Figure: Real-time MRI of a human heart at a resolution of 50 ms.
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High-Dimensional (Cardiac) MRI

Using the combination of compressed sensing and parallel imaging (more) and the ESPIRIT algorithm as implemented in our BART toolbox, we develop highly accelerated methods for MRI in collaboration with researchers from UC Berkeley, Stanford University, and Harvard Medical School. These methods are under clinical evaluation in the Lucile Packard Children's Hospital and Boston Children's Hospital.

Figure: l1-ESPIRiT reconstruction of a human abdomen acquired with a variable-density Poisson-disc sampling at an acceleration rate of seven.
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Model-based Reconstruction for Quantitative MRI

Model-based reconstruction methods formulate quantitative reconstruction as parameter estimation in domain-specific physical models. This enables the development of fundamentally methods for quantitative MRI with short scan times.

Figure: Spin-density and color-coded T2 maps of the human brain obtained by GF-MARTINI reconstructions with validity mask and constant undersampling factors of 1, 2, 6, and 12. The corresponding measurement times were 12:54, 6:27, 2:09, and 1:05 min.
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High-Perfomance Computing

Iterative algorithms are computationally demanding. Early on, we started to look at graphical processing units for acceleration. In our work from 2010, we describe Toeplitz embedding for highly accelerated image reconstruction on Graphical Processing Units (GPUs) for non-Cartesian MRI - an implementation technique we used for real-time MRI using multi-GPU systems and that we later also reused when implementing the nuFFT in our BART toolbox.

Figure: Multi-GPU system for real-time image reconstruction. Picture: hzg/schmidt.
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(Non-Cartesian) Parallel MRI with Compressed Sensing

Compressed sensing is a new technique that can be used to accelerate measurements by exploiting the redundancy (compressibility) of the acquired data. Our publication from 2007 is one of the first examples where this method is used in an imaging application. For more information about compressed sensing in MRI, see this page from Michael Lustig at UC Berkeley who pioneered the use of this technique in MRI. Parallel MRI and compressed sensing can be combined to achieve even higher acceleration for MRI, which is the basis for most advanced image reconstruction methods in MRI. The 2007 paper is the first work to use this important combination.

Figure: Reconstruction of a human brain from 96, 48, and 24 radial spokes. (Top) Conventional gridding reconstruction (Bottom) Combination of linear non-Cartesian parallel imaging (generalized SENSE) and compressed sensing using a total-variation penalty.
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Parallel Imaging as Approximation in a Reproducing Kernel Hilbert Space

The space of ideal signals in parallel magnetic resonance imaging is a Reproducing Kernel Hilbert Space (RKHS) of vector-valued functions which is characterized by a kernel derived from the receive sensitivities. Parallel imaging using multiple receivers can be expressed as approximation in this space. This mathematical formulation yields insights about sampling which go beyond what is possible with the traditional analysis.

Figure: Human brain image reconstructed from randomly distributed samples using parallel imaging. Theoretical error bounds (power function) and noise amplification maps in k-space quantifiy how well missing samples can be recovered with parallel imaging from acquired samples (black dots). In this example, better results can be obtained with Cartesian or Poisson-disc sampling.
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Calibrationless Parallel MRI with ENLIVE

ENLIVE is our new algorithm for efficient and robust calibrationless parallel MRI. ENLIVE is based on NLINV but also integrates an important feature inspired by ESPIRiT: The classical SENSE model is relaxed to make the algorithm more robust to model violations.

Figure: A comparison of ENLIVE vs SAKE as another calibrationless parallel imaging method which is based on structured low-rank matrix completion. Reconstruction time when using a single core was 22 seconds for ENLIVE and 6.3 hours using SAKE.
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Autocalibrated Parallel MRI with ESPIRiT

ESPIRiT is an algorithm for autocalibrated parallel MRI, which combines the robustness of the GRAPPA method with the speed and flexibility of a SENSE-based reconstruction methods. The corresponding publication with Peng Lai (GE Healthcare), Michael Lustig (UC Berkeley) and colleagues is the highest-cited research paper published in the year 2014 (after two years) in Magnetic Resonance in Medicine, the leading jounral in MR methodology. Implementations of ESPIRiT calibration and reconstruction are available in our reconstruction toolbox.

Figure: Images of a human brain acquired with a small FOV. While the SENSE reconstruction has an artifact in the center, GRAPPA is free from this problem. Using multiple set of maps estimated with the ESPIRiT calibration method, a SENSE-based ESPIRiT reconstruction is able to produce an artifact-free image similar to GRAPPA.
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Calibrationless Parallel MRI with Nonlinear Inverse Reconstruction

Hiqh quality reconstruction in parallel MRI requires exact knowledge of the sensitivity profiles of the receive coils. In nonlinear inverse reconstruction, image content and coil sensitivities are estimated jointly, which avoids an explicit calibration step and improves reconstruction quality especially if the amount of calibration data is small. The problem leads to a blind-deconvolution problem (although the roles of frequency and time are switched in MRI). Because the technique can be applied directly to non-Cartesian data, it is ideal for real-time MRI with radial data acquisition. In fact, our method for real-time MRI is based on this algorithm.

Figure: 3D FLASH MRI with 2D acceleration of 4 = 2x2 and 16x16 reference lines. Comparison between GRAPPA, SENSE with coil sensitivities obtained from the fully sampled k-space center, and nonlinear inverse reconstruction (Inv).
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