• Corpus ID: 117808340

A Convex Optimization Approach to pMRI Reconstruction

  title={A Convex Optimization Approach to pMRI Reconstruction},
  author={Cisheng Zhang and Ifat-Al Baqee},
  journal={arXiv: Medical Physics},
In parallel magnetic resonance imaging (pMRI) reconstruction without using estimation of coil sensitivity functions, one group of algorithms reconstruct sensitivity encoded images of the coils first followed by the magnitude only image reconstruction, e.g. GRAPPA, and another group of algorithms jointly compute the image and sensitivity functions by regularized optimization which is a non-convex problem with local only solutions. For the magnitude only image reconstruction, this paper derives a… 

Figures and Tables from this paper



Fast Algorithms for Image Reconstruction with Application to Partially Parallel MR Imaging

This paper presents two fast algorithms for total variation-based image reconstruction in a magnetic resonance imaging technique known as partially parallel imaging (PPI), where the inversion matrix

Image reconstruction by regularized nonlinear inversion—Joint estimation of coil sensitivities and image content

A respective algorithm based on a Newton‐type method with appropriate regularization terms is demonstrated to improve the performance of autocalibrating parallel MRI—mainly due to a better estimation of the coil sensitivity profiles.

Joint image reconstruction and sensitivity estimation in SENSE (JSENSE)

The problem of error propagation in the sequential procedure of sensitivity estimation followed by image reconstruction in existing methods, such as sensitivity encoding (SENSE) and simultaneous acquisition of spatial harmonics (SMASH), is considered and reformulates the image reconstruction problem as a joint estimation of the coil sensitivities and the desired image, which is solved by an iterative optimization algorithm.

Parallel imaging reconstruction for arbitrary trajectories using k‐space sparse matrices (kSPA)

The kSPA algorithm is noniterative and the computed sparse approximate inverse can be applied repetitively to reconstruct all subsequent images, therefore, this algorithm is particularly suitable for the aforementioned applications.

An algorithm for sparse MRI reconstruction by Schatten p-norm minimization.

Nuclear norm-regularized SENSE reconstruction.

Ambiguity and regularization in parallel MRI

  • D. GolL. Potter
  • Mathematics
    2011 Annual International Conference of the IEEE Engineering in Medicine and Biology Society
  • 2011
It is proposed that the analysis of the subsampled blind deconvolution task provides insight into both the multiply determined nature of the pMRI task and possible design strategies for sampling and reconstruction.

Generalized autocalibrating partially parallel acquisitions (GRAPPA)

This technique, GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) is an extension of both the PILS and VD‐AUTO‐SMASH reconstruction techniques and provides unaliased images from each component coil prior to image combination.

SENSE: Sensitivity encoding for fast MRI

The problem of image reconstruction from sensitivity encoded data is formulated in a general fashion and solved for arbitrary coil configurations and k‐space sampling patterns and special attention is given to the currently most practical case, namely, sampling a common Cartesian grid with reduced density.

Sparsity-Promoting Calibration for GRAPPA Accelerated Parallel MRI Reconstruction

This work proposes a sparsity-promoting regularized calibration method that finds a GRAPPA kernel consistent with the ACS fit equations that yields jointly sparse reconstructed coil channel images and can increase the total achievable acceleration while reducing degradation of the reconstructed image better than existingregularized calibration methods.