Solving inverse problems using data-driven models

Arridge, Simon R.; Maaß, Peter; Öktem, Ozan; Schönlieb, Carola-Bibiane

doi:10.1017/s0962492919000059

Cited by 499 publications

(421 citation statements)

References 463 publications

(769 reference statements)

Supporting

Mentioning

417

Contrasting

Unclassified

Order By: Relevance

“…However, when inverse problems are extremely ill-conditioned, the MBIR approach using handcrafted regularizers g(x) has limitations in recovering signals. Alternatively, there has been a growing trend in learning sparsifying regularizers (e.g., convolutional regularizers [16], [17], [32], [34], [35]) from training datasets and applying the learned regularizers to the following MBIR problem [33]:…”

Section: Backgrounds: Mbir Using Learned Regularizersmentioning

confidence: 99%

“…The downside of applying solution (33) is that it would require additional memory to store the corresponding extrapolated points -{ź (i+1) l,k } -and the memory grows with N , L, and K. Considering the sharpness of the majorizer in (30), i.e., M Z = I N , and the memory issue, it is reasonable to consider the solution (33) with no extrapolation, i.e., {E . While having these benefits, empirically (31) has equivalent convergence rates as (33) using {λ Z = 1 + }; see Fig.…”

Section: B Sparse Code Update: {Z Lk }-Block Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

Convolutional Analysis Operator Learning: Acceleration and Convergence

Chun

Fessler

2020

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations when learning kernels from large datasetsparticularly with multi-layered structures, e.g., convolutional neural networks -or when applying the learned kernels to highdimensional signal recovery problems. The so-called convolution approach does not store many overlapping patches, and thus overcomes the memory problems particularly with careful algorithmic designs; it has been studied within the "synthesis" signal model, e.g., convolutional dictionary learning. This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, with sharp majorizers, BPEG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art block proximal gradient (BPG) method. Numerical experiments for sparse-view computational tomography show that a convolutional sparsifying regularizer learned via CAOL significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Using more and wider kernels in a learned regularizer better preserves edges in reconstructed images.

show abstract

Section: Backgrounds: Mbir Using Learned Regularizersmentioning

confidence: 99%

Section: B Sparse Code Update: {Z Lk }-Block Optimizationmentioning

confidence: 99%

Convolutional Analysis Operator Learning: Acceleration and Convergence

Chun

Fessler

2020

IEEE Trans. on Image Process.

View full text Add to dashboard Cite

show abstract

“…The standard approach to overcome the ill-posedness is to incorporate a priori information, an approach that is known as regularization. There are plenty of regularization methods for computed tomography ranging from established model-based methods [5,16,48], to more recent end-to-end data-driven approaches, for the latter see the survey in [3]. Additionally, the sparsity of the solution under the shearlet representation [8] or the adjoint operator [1] can be used for regularization.…”

Section: Higher-order Wavefront Set Extraction and Inverse Problemsmentioning

confidence: 99%

Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks

Andrade-Loarca¹,

Kutyniok²,

Öktem³

et al. 2019

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct extraction of those. In this paper, we introduce the first algorithmic approach to extract the wavefront set of images, which combines data-based and model-based methods. Based on a celebrated property of the shearlet transform to unravel information on the wavefront set, we extract the wavefront set of an image by first applying a discrete shearlet transform and then feeding local patches of this transform to a deep convolutional neural network trained on labeled data. The resulting algorithm outperforms all competing algorithms in edge-orientation and ramp-orientation detection.

show abstract

“…The relationship between k-space data and MR image can be described, using the well-known MRI encoding matrix in an equality constraint [1,11]. With such computationally scalable and tractable prior model, the maximum a posterior can serve as an effective estimator [8] for the high dimensional image reconstruction problem tackled in this study. To summarize, the Bayesian inference for MRI reconstruction had two separate models: the k-space likelihood model that was used to encourage data consistency and the image prior model that was used to exploit knowledge learned from an MRI database.…”

Section: Introductionmentioning

confidence: 99%

MRI reconstruction using deep Bayesian estimation

Luo

Zhao

Jiang

et al. 2020

Magnetic Resonance in Med

View full text Add to dashboard Cite

Purpose: To develop a deep learning-based Bayesian inference for MRI reconstruction.Methods: We modeled the MRI reconstruction problem with Bayes's theorem, following the recently proposed PixelCNN++ method. The image reconstruction from incomplete k-space measurement was obtained by maximizing the posterior possibility. A generative network was utilized as the image prior, which was computationally tractable, and the k-space data fidelity was enforced by using an equality constraint. The stochastic backpropagation was utilized to calculate the descent gradient in the process of maximum a posterior, and a projected subgradient method was used to impose the equality constraint. In contrast to the other deep learning reconstruction methods, the proposed one used the likelihood of prior as the training loss and the objective function in reconstruction to improve the image quality.Results: The proposed method showed an improved performance in preserving image details and reducing aliasing artifacts, compared with GRAPPA, 1 -ESPRiT, and MODL, a state-of-the-art deep learning reconstruction method. The proposed method generally achieved more than 5 dB peak signal-to-noise ratio improvement for compressed sensing and parallel imaging reconstructions compared with the other methods. Conclusion:The Bayesian inference significantly improved the reconstruction performance, compared with the conventional 1 -sparsity prior in compressed sensing reconstruction tasks. More importantly, the proposed reconstruction framework can be generalized for most MRI reconstruction scenarios.

show abstract

Solving inverse problems using data-driven models

Cited by 499 publications

References 463 publications

Convolutional Analysis Operator Learning: Acceleration and Convergence

Convolutional Analysis Operator Learning: Acceleration and Convergence

Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks

MRI reconstruction using deep Bayesian estimation

Contact Info

Product

Resources

About