Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data

By Rick Chartrand. IEEE International Symposium on Biomedical Imaging, 2009

331 citations recorded by the source corpus.

Compressive sensing is the reconstruction of sparse images or signals from very few samples, by means of solving a tractable optimization problem. In the context of MRI, this can allow reconstruction from many fewer k-space samples, thereby reducing scanning time. Previous work has shown that nonconvex optimization reduces still further the number of samples required for reconstruction, while still being tractable. In this work, we extend recent Fourier-based algorithms for convex optimization to the nonconvex setting, and obtain methods that combine the reconstruction abilities of previous nonconvex approaches with the computational speed of state-of-the-art convex methods.

Subfields: Biomedical Engineering, Computational Mechanics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/3e55ea38a594f4410ddd3de49974fbb378a3420b

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In Biomedical Engineering

In Computational Mechanics

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data (2010, methodology): “In this section, we present MR image reconstruction results of RecPF and two other recently proposed algorithms: a two-step iterative shrinkage/thresholding algorithm (TwIST) [6] and an operator splitting-based algorithm that we call OS [35], both of which have been regarded fast for solving inverse”
DAGAN: Deep De-Aliasing Generative Adversarial Networks for Fast Compressed Sensing MRI Reconstruction (2018, background): “Finally, nonlinear optimisation algorithms ensure the achievement of efﬁcient, stable and accurate reconstruction [16], [18], [29], [30].”
MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning (2011, methodology): “Similarly to prior work on CSMRI [ 18 ]‐[20], [22], [58] the CS data acquisition was simulated by subsampling the 2D discrete Fourier transform of the MR images (except in Figs.”
Fast Image Deconvolution using Hyper-Laplacian Priors (2009, methodology): “approximation (see [1]) to the quasi-norm is used, allowing the derivation of a generalized shrinkage operator to solve the sub-problem efficiently.”
$L_{1/2}$ Regularization: A Thresholding Representation Theory and a Fast Solver (2012, unknown): “Different from those approaches, Krishnan and Fergus [16], Chartrand [17], [18] developed a closed-form-solutionbased approach.”
Accelerated dynamic MRI exploiting sparsity and low-rank structure: k-t SLR (2011, unknown): “Motivated by the recent results in the use of nonconvex penalties in compressed sensing [17], [18], we introduce novel nonconvex spectral penalties to minimize the number of measurements required to recover a low-rank matrix.”