Content

  • About Me
  • Real-time MRI
  • Image Reconstruction
  • Software
  • Publications
  • 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 in k-space can be expressed as approximation in this space. This novel formulation yields insights about sampling in k-space which go beyond what is possible with the traditional g-factor 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 show 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.

    References:

    Vivek Athalye, Michael Lustig, and Martin Uecker. Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space, submitted (2013) arXiv:1310.7489 [physics.med-ph]

    Autocalibrated Parallel MRI with ESPIRiT

    ESPIRiT is a new algorithm for autocalibrated parallel MRI, which combines the robustness of GRAPPA with the speed and flexibility of a SENSE-based reconstruction. Implementations of ESPIRiT calibration and reconstruction are available in our reconstruction toolbox. The algorithm is related to multi-channel multi-variate spectral estimation.

    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.

    References:

    Martin Uecker, Patrick Virtue, Frank Ong, Mark J. Murphy, Marcus T. Alley, Shreyas S. Vasanawala, Michael Lustig, Software Toolbox and Programming Library for Compressed Sensing and Parallel Imaging, ISMRM Workshop on Data Sampling and Image Reconstruction, Sedona 2013.

    Martin Uecker, Patrick Virtue, Shreyas S Vasanawala, and Michael Lustig. ESPIRiT Reconstruction Using Soft SENSE. Annual Meeting ISMRM, Salt Lake City 2013, In Proc. Intl. Soc. Mag. Reson. Med 21; 127 (2013)

    Martin Uecker, Peng Lai, Mark J. Murphy, Patrick Virtue, Michael Elad, John M. Pauly, Shreyas S. Vasanawala, and Michael Lustig. ESPIRiT - An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE meets GRAPPA. Magnetic Resonance in Medicine, 71:990-1001 (2014)

    Autocalibrated 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 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.

    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).

    Reference:

    Martin Uecker, Thorsten Hohage, Kai Tobias Block, and Jens Frahm, Image Reconstruction by Regularized Nonlinear Inversion - Joint Estimation of Coil Sensitivities and Image Content, Magnetic Resonance in Medicine 60 (3): 674-682 (2008) [source code]

    Florian Knoll, Christian Clason, Martin Uecker, and Rudolf Stollberger, Improved Reconstruction in Non-Cartesian Parallel Imaging by Regularized Nonlinear Inversion, Annual Meeting ISMRM Honolulu 2009, In Proc. Intl. Soc. Mag. Reson. Med. 17: 2721 (2009)

    Martin Uecker, Shuo Zhang, and Jens Frahm, Nonlinear Inverse Reconstruction for Real-time MRI of the Human Heart Using Undersampled Radial FLASH, Magnetic Resonance in Medicine 63 (6): 1456-1462 (2010) [source code]

    Florian Knoll, Christian Clason, Kristian Bredies, Martin Uecker, and Rudolf Stollberger, Parallel Imaging with Nonlinear Reconstruction using Variational Penalties, Magnetic Resonance in Medicine 67:34-41 (2012) [source code]

    (Non-Cartesian) Parallel MRI with Compressed Sensing

    Compressed sensing is a new technique, which can be used to accelerate MRI by exploiting the redundancy of the acquired images. Parallel MRI and compressed sensing can be combined to achieve even higher acceleration. This can be formulated as a linear inverse problem with non-linear penalties.

    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.

    References:

    Kai Tobias Block, Martin Uecker, and Jens Frahm, Undersampled Radial MRI with Multiple Coils. Iterative Image Reconstruction Using a Total Variation Constraint, Magnetic Resonance in Medicine 57 (6): 1086-1098 (2007)

    Martin Uecker, Kai Tobias Block, and Jens Frahm, Nonlinear Inversion with L1-Wavelet Regularization - Application to Autocalibrated Parallel Imaging, ISMRM Annual Meeting, Toronto 2008, In Proc. Intl. Soc. Mag. Reson. Med. 16: 1479 (2008)

    Florian Knoll, Christian Clason, Kristian Bredies, Martin Uecker, and Rudolf Stollberger, Parallel Imaging with Nonlinear Reconstruction using Variational Penalties, Magnetic Resonance in Medicine 67:34-41 (2012) [source code]

    Martin Uecker, Peng Lai, Mark J. Murphy, Patrick Virtue, Michael Elad, John M. Pauly, Shreyas S. Vasanawala, and Michael Lustig. ESPIRiT - An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE meets GRAPPA. Magnetic Resonance in Medicine, 71:990-1001 (2014) [source code]

    Model-based Reconstruction

    Model-based reconstruction methods formulate reconstruction as parameter estimation in domain-specific physical models. This leads improved quantitative MRI and can also be used to obtain multiple images with different contrast from a single scan.

    References:

    Kai Tobias Block, Martin Uecker, and Jens Frahm, Iterative Reconstruction for R2 Mapping Based on Radial Fast Spin-Echo MRI, ISMRM Annual Meeting, Toronto 2008, In Proc. Intl. Soc. Mag. Reson. Med. 16: 1432 (2008)

    Kai Tobias Block, Martin Uecker, and Jens Frahm, Model-based Iterative Reconstruction for Radial Fast Spin-Echo MRI, IEEE Transactions on Medical Imaging 28:1759-1769 (2009)

    Tilman J Sumpf, Martin Uecker, Susann Boretius, and Jens Frahm, Model-based Nonlinear Inverse Reconstruction for T2 Mapping Using Highly Undersampled Spin-Echo MRI, Journal of Magnetic Resonance Imaging, 34:420-428 (2011) [source code]

    Tilman J. Sumpf, Amir Moussavi, Martin Uecker, Susann Boretius, and Jens Frahm, Effects of Phase Alternations in Nonlinear Inverse T2 Reconstructions from Undersampled Data, Annual Meeting ISMRM, Melbourne 2012, In Proc. Intl. Soc. Mag. Reson. Med 20: 2400 (2012)

    Tilman J. Sumpf, Andreas Petrovic, Martin Uecker, Florian Knoll, and Jens Frahm. Fast T2 Mapping with Improved Accuracy Using Undersampled Spin-echo MRI and Model-based Reconstructions with a Generating Function, IEEE Transactions on Medical Imaging, Epub (2014) arxiv:1405:3574 [physics.med-ph]