A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Jin, Kyong Hwan; Lee, Dong‐Wook; Ye, Jong Chul

doi:10.1109/tci.2016.2601296

Cited by 220 publications

(327 citation statements)

References 43 publications

Supporting

Mentioning

327

Contrasting

Order By: Relevance

“…A SLRA model assumes some property of the signal data is equivalent to the low-rank property of a matrix constructed from the data. This paper is motivated by recent convolutional SLRA models in MRI reconstruction [2], [4]–[8], [28], and related inverse problems in imaging [6], [29], [30]. In this setting, various spatial domain properties of the image (e.g., limited support, smooth phase, piecewise constant, etc.)…”

Section: Signal Reconstruction By Convolutional Structured Low-ramentioning

confidence: 99%

“…The linear dependencies between the Fourier coefficients exploited the in structured low-rank matrix priors result from a variety of assumptions, including continuous domain analogs of sparsity [3], [6], [8], [9], correlations in the locations of the sparse coefficients in space [8], [9], multi-channel sampling [2], [10], [11], or smoothly varying complex phase [4]. For example, the LORAKS framework [4] capitalized on the sparsity and smooth phase of the continuous domain image using structured low-rank priors, which offers improved reconstructions over conventional ℓ 1 recovery.…”

Section: Introductionmentioning

confidence: 99%

“…This model, which exploits the smooth structure of the discontinuities along with sparsity, can lead to significant improvement in reconstruction quality over traditional methods such as total variation (TV) minimization; see [8], [9] for more details. Similarly, the ALOHA framework [6] reformulates the recovery of a transform sparse signal as a structured low-rank matrix recovery problem, e.g., images that are sparse under the undecimated Harr wavelet transform. Inspired by auto-calibration techniques in parallel MRI [12]–[15], the extension to recovery of parallel MRI from undersampled measurements is formulated as a structured low-rank matrix recovery problem in [2], [10].…”

Section: Introductionmentioning

confidence: 99%

“…Despite improvements in empirical and statistical recovery performance over traditional methods as seen from [2]–[4], [6], [8], [16], these structured low-rank matrix recovery schemes are associated with a dramatic increase in computational complexity and memory demand; this restricts their direct extension to multi-dimensional imaging applications, such as dynamic MRI reconstruction. In particular, these algorithms involve the recovery of a large-scale Toeplitz-like matrix whose combined dimensions are several orders of magnitude larger than those of the image.…”

Section: Introductionmentioning

confidence: 99%

“…Several strategies have been introduced to minimize or avoid SVD’s in these algorithms. For example, the algorithms derived in [4], [6] replace the full SVD’s with more efficient truncated SVD’s or matrix inversions by assuming the matrix to be recovered is low-rank, or well approximated as such. However, even with these low-rank modifications, the algorithms in [4], [6] still have considerable memory demand, since they require storing a variable having dimensions of the large-scale matrix.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Ongie

Jacob

2017

IEEE Trans. Comput. Imaging

View full text Add to dashboard Cite

Fourier domain structured low-rank matrix priors are emerging as powerful alternatives to traditional image recovery methods such as total variation (TV) and wavelet regularization. These priors specify that a convolutional structured matrix, i.e., Toeplitz, Hankel, or their multi-level generalizations, built from Fourier data of the image should be low-rank. The main challenge in applying these schemes to large-scale problems is the computational complexity and memory demand resulting from a lifting the image data to a large scale matrix. We introduce a fast and memory efficient approach called the Generic Iterative Reweighted Annihilation Filter (GIRAF) algorithm that exploits the convolutional structure of the lifted matrix to work in the original un-lifted domain, thus considerably reducing the complexity. Our experiments on the recovery of images from undersampled Fourier measurements show that the resulting algorithm is considerably faster than previously proposed algorithms, and can accommodate much larger problem sizes than previously studied.

show abstract

Section: Signal Reconstruction By Convolutional Structured Low-ramentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Ongie

Jacob

2017

IEEE Trans. Comput. Imaging

View full text Add to dashboard Cite

show abstract

Spatial orthogonal attention generative adversarial network for MRI reconstruction

Zhou

Mei

et al. 2020

Medical Physics

View full text Add to dashboard Cite

Purpose: Recent studies have witnessed that self-attention modules can better solve the vision understanding problems by capturing long-range dependencies. However, there are very few works designing a lightweight self-attention module to improve the quality of MRI reconstruction. Furthermore, it can be observed that several important self-attention modules (e.g., the non-local block) cause high computational complexity and need a huge number of GPU memory when the size of the input feature is large. The purpose of this study is to design a lightweight yet effective spatial orthogonal attention module (SOAM) to capture long-range dependencies, and develop a novel spatial orthogonal attention generative adversarial network, termed as SOGAN, to achieve more accurate MRI reconstruction. Methods: We first develop a lightweight SOAM, which can generate two small attention maps to effectively aggregate the long-range contextual information in vertical and horizontal directions, respectively. Then, we embed the proposed SOAMs into the concatenated convolutional autoencoders to form the generator of the proposed SOGAN. Results: The experimental results demonstrate that the proposed SOAMs improve the quality of the reconstructed MR images effectively by capturing long-range dependencies. Besides, compared with state-of-the-art deep learning-based CS-MRI methods, the proposed SOGAN reconstructs MR images more accurately, but with fewer model parameters. Conclusions: The proposed SOAM is a lightweight yet effective self-attention module to capture long-range dependencies, thus, can improve the quality of MRI reconstruction to a large extent. Besides, with the help of SOAMs, the proposed SOGAN outperforms the state-of-the-art deep learning-based CS-MRI methods.

show abstract

Deep neural networks for magnetic resonance elastography acceleration in thermal‐ablation monitoring

Shan

Yang

et al. 2022

Medical Physics

View full text Add to dashboard Cite

Purpose To develop a deep neural network for accelerating magnetic resonance elastography (MRE) acquisition, to validate the ability to generate reliable MRE results with the down‐sampled k‐space data, and to demonstrate the feasibility of the proposed method in monitoring the stiffness changes during thermal ablation in a phantom study. Materials and methods MRE scans were performed with 60 Hz excitation on porcine ex‐vivo liver gel phantoms in a 0.36T MRI scanner to generate the training dataset. The acquisition protocol was based on a spin‐echo MRE pulse sequence with tailored motion‐sensitive gradients to reduce echo time (TE). A U‐Net based deep neural network was developed and trained to interpolate the missing data from down‐sampled k‐space. We calculated the errors of 80 sets magnitude/phase images reconstructed from the zero‐filled, compressive sensing (CS) and deep learning (DL) method for comparison. The peak signal‐to‐noise rate (PSNR) and structural similarity index (SSIM) of the magnitude/phase images were also calculated for comparison. The stiffness changes were recorded before, during, and after ablation. The mean stiffness values over the region of interest (ROI) were compared between the elastograms reconstructed from the fully sampled k‐space and interpolated k‐space after thermal ablation. Results The mean absolute error (MAE), PSNR, and SSIM of the proposed DL approach were significantly better than the results from the zero‐filled method (p < 0.0001) and CS (p < 0.0001). The stiffness changes before and after thermal ablation assessed by the proposed approach (before: 7.7±1.1 kPa, after: 11.9±4.0 kPa, 4.2‐kPa increase) gave close agreement with the values calculated from the fully sampled data (before: 8.0±1.0 kPa, after: 12.6±4.2 kPa, 4.6‐kPa increase). In contrast, the stiffness changes computed from the zero‐filled method (before: 4.9±1.4 kPa, after: 5.6±2.8 kPa, 0.7‐kPa increase) were substantially underestimated. Conclusion This study demonstrated the capability of the proposed DL method for rapid MRE acquisition and provided a promising solution for monitoring the MRI‐guided thermal ablation.

show abstract

A General Framework for Compressed Sensing and Parallel MRI Using Annihilating Filter Based Low-Rank Hankel Matrix

Cited by 220 publications

References 43 publications

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

A Fast Algorithm for Convolutional Structured Low-Rank Matrix Recovery

Spatial orthogonal attention generative adversarial network for MRI reconstruction

Deep neural networks for magnetic resonance elastography acceleration in thermal‐ablation monitoring

Contact Info

Product

Resources

About