Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Chambolle, Antonin; Ehrhardt, Matthias J.; Richtárik, Peter; Schönlieb, Carola-Bibiane

doi:10.1137/17m1134834

Cited by 144 publications

(230 citation statements)

References 42 publications

Supporting

Mentioning

227

Contrasting

Order By: Relevance

“…A stochastic primal-dual hybrid gradient algorithm (SPDHG) [14] was proposed to optimize the following problem:…”

Section: Stochastic Primal-dual Hybrid Gradient Algorithmmentioning

confidence: 99%

“…This means that each iteration requires both A i and A * i to be evaluated only for each selected index i ∈ S (k+1) . With a mild condition on the stepsizes τ and ρ i , the algorithm converges to an optimal solution of (2) almost surely in the sense of the Bregman distance (see [14,Theorem 4.3] for details).…”

Section: Stochastic Primal-dual Hybrid Gradient Algorithmmentioning

confidence: 99%

“…Recently, stochastic primal-dual splitting algorithms have been intensively studied for stochastic optimization [11][12][13][14]. Roughly speaking, at each iteration, the algorithms activate only the operations associated with randomly chosen variables, so that the said costs are significantly reduced.…”

Section: Introductionmentioning

confidence: 99%

“…Roughly speaking, at each iteration, the algorithms activate only the operations associated with randomly chosen variables, so that the said costs are significantly reduced. Actually, several studies show the utility of such block-coodinatewise randomization in image restoration [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

“…We focus on the ℓ 2 data-fidelity constraint, and introduce its equivalent expression via certain epigraphs, which enables us to deal with the constrained formulation by stochastic proximal splitting algorithms with randomized epigraphical projection. Specifically, we develop a randomized solver for the problem based on a stochastic primal-dual hybrid gradient algorithm [14]. The efficiency of our method is demonstrated on CT image reconstruction.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Ono

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated.

show abstract

“…A stochastic primal-dual hybrid gradient algorithm (SPDHG) [14] was proposed to optimize the following problem:…”

Section: Stochastic Primal-dual Hybrid Gradient Algorithmmentioning

confidence: 99%

Section: Stochastic Primal-dual Hybrid Gradient Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Ono

2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

View full text Add to dashboard Cite

show abstract

Coil sketching for computationally efficient MR iterative reconstruction

Oscanoa,

Ong,

Iyer

et al. 2023

Magnetic Resonance in Med

View full text Add to dashboard Cite

PurposeParallel imaging and compressed sensing reconstructions of large MRI datasets often have a prohibitive computational cost that bottlenecks clinical deployment, especially for three‐dimensional (3D) non‐Cartesian acquisitions. One common approach is to reduce the number of coil channels actively used during reconstruction as in coil compression. While effective for Cartesian imaging, coil compression inherently loses signal energy, producing shading artifacts that compromise image quality for 3D non‐Cartesian imaging. We propose coil sketching, a general and versatile method for computationally‐efficient iterative MR image reconstruction.Theory and MethodsWe based our method on randomized sketching algorithms, a type of large‐scale optimization algorithms well established in the fields of machine learning and big data analysis. We adapt the sketching theory to the MRI reconstruction problem via a structured sketching matrix that, similar to coil compression, considers high‐energy virtual coils obtained from principal component analysis. But, unlike coil compression, it also considers random linear combinations of the remaining low‐energy coils, effectively leveraging information from all coils.ResultsFirst, we performed ablation experiments to validate the sketching matrix design on both Cartesian and non‐Cartesian datasets. The resulting design yielded both improved computatioanal efficiency and preserved signal‐to‐noise ratio (SNR) as measured by the inverse g‐factor. Then, we verified the efficacy of our approach on high‐dimensional non‐Cartesian 3D cones datasets, where coil sketching yielded up to three‐fold faster reconstructions with equivalent image quality.ConclusionCoil sketching is a general and versatile reconstruction framework for computationally fast and memory‐efficient reconstruction.

show abstract

Resolution enhancement, noise suppression, and joint T2* decay estimation in dual‐echo sodium‐23 MR imaging using anatomically guided reconstruction

Schramm,

Filipovic,

Qian

et al. 2023

Magnetic Resonance in Med

View full text Add to dashboard Cite

PurposeSodium MRI is challenging because of the low tissue concentration of the 23Na nucleus and its extremely fast biexponential transverse relaxation rate. In this article, we present an iterative reconstruction framework using dual‐echo 23Na data and exploiting anatomical prior information (AGR) from high‐resolution, low‐noise, 1H MR images. This framework enables the estimation and modeling of the spatially varying signal decay due to transverse relaxation during readout (AGRdm), which leads to images of better resolution and reduced noise resulting in improved quantification of the reconstructed 23Na images.MethodsThe proposed framework was evaluated using reconstructions of 30 noise realizations of realistic simulations of dual echo twisted projection imaging (TPI) 23Na data. Moreover, three dual echo 23Na TPI brain datasets of healthy controls acquired on a 3T Siemens Prisma system were reconstructed using conventional reconstruction, AGR and AGRdm.ResultsOur simulations show that compared to conventional reconstructions, AGR and AGRdm show improved bias‐noise characteristics in several regions of the brain. Moreover, AGR and AGRdm images show more anatomical detail and less noise in the reconstructions of the experimental data sets. Compared to AGR and the conventional reconstruction, AGRdm shows higher contrast in the sodium concentration ratio between gray and white matter and between gray matter and the brain stem.ConclusionAGR and AGRdm generate 23Na images with high resolution, high levels of anatomical detail, and low levels of noise, potentially enabling high‐quality 23Na MR imaging at 3T.

show abstract

Stochastic Primal-Dual Hybrid Gradient Algorithm with Arbitrary Sampling and Imaging Applications

Cited by 144 publications

References 42 publications

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

Coil sketching for computationally efficient MR iterative reconstruction

Resolution enhancement, noise suppression, and joint T2* decay estimation in dual‐echo sodium‐23 MR imaging using anatomically guided reconstruction

Contact Info

Product

Resources

About