Dataset Information

Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories.

ABSTRACT:

Purpose

Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories.

Theory

PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in ? 1 and ? 2 -norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques.

Methods

In this article we construct such a preconditioner by approximating the system matrix of the linear system, which comprises the data fidelity and includes total variation and wavelet regularization, by a matrix that is block circulant with circulant blocks. Due to this structure, the preconditioner can be constructed quickly and its inverse can be evaluated fast using only two fast Fourier transformations. We test the performance of the preconditioner for the conjugate gradient method as the linear solver, integrated into the well-established Split Bregman algorithm.

Results

The designed circulant preconditioner reduces the number of iterations required in the conjugate gradient method by almost a factor of 5. The speed up results in a total acceleration factor of approximately 2.5 for the entire reconstruction algorithm when implemented in MATLAB, while the initialization time of the preconditioner is negligible.

Conclusion

The proposed preconditioner reduces the reconstruction time for PI and CS in a Split Bregman implementation without compromising reconstruction stability and can easily handle large systems since it is Fourier-based, allowing for efficient computations.

SUBMITTER: Koolstra K

PROVIDER: S-EPMC6283050 | biostudies-literature | 2019 Jan

REPOSITORIES: biostudies-literature

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Publications

Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories.

Koolstra Kirsten K van Gemert Jeroen J Börnert Peter P Webb Andrew A Remis Rob R

Magnetic resonance in medicine 20180807 1

<h4>Purpose</h4>Design of a preconditioner for fast and efficient parallel imaging (PI) and compressed sensing (CS) reconstructions for Cartesian trajectories.<h4>Theory</h4>PI and CS reconstructions become time consuming when the problem size or the number of coils is large, due to the large linear system of equations that has to be solved in ℓ1 and ℓ2 -norm based reconstruction algorithms. Such linear systems can be solved efficiently using effective preconditioning techniques.<h4>Methods</h4> ...[more]

PMID: 30084505

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Project description:Objective. Model based deep learning (MBDL) has been challenging to apply to the reconstruction of 3D non-Cartesian MRI due to GPU memory demand because the entire volume is needed for data-consistency steps embedded in the model. This requirement makes holding even a single unroll in GPU memory difficult meaning memory efficient techniques used to increase unroll number like gradient checkpointing and deep equilibrium learning will not work well for high spatial resolution 3D non-Cartesian reconstructions without modification. Here we develop a memory efficient method called block-wise learning that combines gradient checkpointing with patch-wise training to overcome this obstacle and allow for fast and high-quality 3D non-Cartesian reconstructions using MBDL.Approach. Block-wise learning applied to a single unroll decomposes the input volume into smaller patches, gradient checkpoints each patch, passes each patch iteratively through a neural network regularizer, and then rebuilds the full volume from these output patches for data-consistency. This method is applied across unrolls during training. Block-wise learning significantly reduces memory requirements by tying GPU memory for a single unroll to user selected patch size instead of the full volume. This algorithm was used to train a MBDL architecture to reconstruct highly undersampled, 1.25 mm isotropic, pulmonary magnetic resonance angiography volumes with matrix sizes varying from 300-450 × 200-300 × 300-450 on a single GPU. We compared block-wise learning reconstructions against L1 wavelet compressed reconstructions and proxy ground truth images.Main results. MBDL with block-wise learning significantly improved image quality relative to L1 wavelet compressed sensing while simultaneously reducing average reconstruction time 38x.Significance. Block-wise learning allows for MBDL to be applied to high spatial resolution, 3D non-Cartesian datasets with improved image quality and significant reductions in reconstruction time relative to traditional iterative methods.

Dataset Information

Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories.

Purpose

Theory

Methods

Results

Conclusion

Publications

Accelerating compressed sensing in parallel imaging reconstructions using an efficient circulant preconditioner for cartesian trajectories.

Similar Datasets

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