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.

**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, 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)

**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]

**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]

**References:**

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]

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)