Compressed sensing (CS) utilizes the sparsity of magnetic resonance (MR) images to enable accurate reconstruction from undersampled k-space data. Recent CS methods have employed analytical sparsifying transforms such as wavelets, curvelets, and finite differences. In this paper, we propose a novel framework for adaptively learning the sparsifying transform (dictionary), and reconstructing the image simultaneously from highly undersampled k-space data. The sparsity in this framework is enforced on overlapping image patches emphasizing local structure. Moreover, the dictionary is adapted to the particular image instance thereby favoring better sparsities and consequently much higher undersampling rates. The proposed alternating reconstruction algorithm learns the sparsifying dictionary, and uses it to remove aliasing and noise in one step, and subsequently restores and fills-in the k-space data in the other step. Numerical experiments are conducted on MR images and on real MR data of several anatomies with a variety of sampling schemes. The results demonstrate dramatic improvements on the order of 4-18 dB in reconstruction error and doubling of the acceptable undersampling factor using the proposed adaptive dictionary as compared to previous CS methods. These improvements persist over a wide range of practical data signal-to-noise ratios, without any parameter tuning.

MR Image Reconstruction From Highly Undersampled k-Space Data by Dictionary Learning

Compressive Sensing (CS) is an effective approach for fast Magnetic Resonance Imaging (MRI). It aims at reconstructing MR image from a small number of under-sampled data in k-space, and accelerating the data acquisition in MRI. To improve the current MRI system in reconstruction accuracy and computational speed, in this paper, we propose a novel deep architecture, dubbed ADMM-Net. ADMM-Net is defined over a data flow graph, which is derived from the iterative procedures in Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing a CS-based MRI model. In the training phase, all parameters of the net, e.g., image transforms, shrinkage functions, etc., are discriminatively trained end-to-end using L-BFGS algorithm. In the testing phase, it has computational overhead similar to ADMM but uses optimized parameters learned from the training data for CS-based reconstruction task. Experiments on MRI image reconstruction under different sampling ratios in k-space demonstrate that it significantly improves the baseline ADMM algorithm and achieves high reconstruction accuracies with fast computational speed.

https://proceedings.neurips.cc/paper/2016/file/1679091c5a880faf6fb5e6087eb1b2dc-Paper.pdf

Deep ADMM-Net for compressive sensing MRI

Compressed sensing magnetic resonance imaging (CS-MRI) enables fast acquisition, which is highly desirable for numerous clinical applications. This can not only reduce the scanning cost and ease patient burden, but also potentially reduce motion artefacts and the effect of contrast washout, thus yielding better image quality. Different from parallel imaging-based fast MRI, which utilizes multiple coils to simultaneously receive MR signals, CS-MRI breaks the Nyquist–Shannon sampling barrier to reconstruct MRI images with much less required raw data. This paper provides a deep learning-based strategy for reconstruction of CS-MRI, and bridges a substantial gap between conventional non-learning methods working only on data from a single image, and prior knowledge from large training data sets. In particular, a novel conditional Generative Adversarial Networks-based model (DAGAN)-based model is proposed to reconstruct CS-MRI. In our DAGAN architecture, we have designed a refinement learning method to stabilize our U-Net based generator, which provides an end-to-end network to reduce aliasing artefacts. To better preserve texture and edges in the reconstruction, we have coupled the adversarial loss with an innovative content loss. In addition, we incorporate frequency-domain information to enforce similarity in both the image and frequency domains. We have performed comprehensive comparison studies with both conventional CS-MRI reconstruction methods and newly investigated deep learning approaches. Compared with these methods, our DAGAN method provides superior reconstruction with preserved perceptual image details. Furthermore, each image is reconstructed in about 5 ms, which is suitable for real-time processing.

/pdf/dagan-deep-de-aliasing-generative-adversarial-networks-for-3u7cltdv1j.pdf

DAGAN: Deep De-Aliasing Generative Adversarial Networks for Fast Compressed Sensing MRI Reconstruction

Computational and Mathematical Methods in Medicine

Multi-focus image fusion with a deep convolutional neural network

Compressed sensing has shown great potential to speed up magnetic resonance imaging (MRI) assuming the image is sparse and compressible in a transform domain. Conventional methods typically use a pre-defined sparsifying transform such as wavelets or finite difference, which sometimes does not lead to a sufficient sparse representation. In this paper, we design a patch-based nonlocal operator (PANO) to model the sparsity between image patches. The linearity of PANO allows us to establish a general formulation to reconstruct magnetic resonance image from undersampled data and provides feasibility to incorporate prior information learnt from guide images. To demonstrate the feasibility and performance of PANO, learning similarities from multi-modal images are presented to significantly improve the reconstructed images over conventional redundant wavelets in terms of visual quality and reconstruction errors.

Magnetic resonance image reconstruction using similarities learnt from multi-modal images

OBJECTIVE
Multi-shot interleaved echo planer imaging (Ms-iEPI) can obtain diffusion-weighted images (DWI) with high spatial resolution and low distortion, but suffers from ghost artifacts introduced by phase variations between shots. In this work, we aim at solving the ms-iEPI DWI reconstructions under inter-shot motions and ultra-high b-values.


METHODS
An iteratively joint estimation model with paired phase and magnitude priors is proposed to regularize the reconstruction (PAIR). The former prior is low-rankness in the k-space domain. The latter explores similar edges among multi-b-value and multi-direction DWI with weighted total variation in the image domain. The weighted total variation transfers edge information from the high SNR images (b-value=0) to DWI reconstructions, achieving simultaneously noise suppression and image edges preservation.


RESULTS
Results on simulated and in vivo data show that PAIR can remove inter-shot motion artifacts very well (8 shots) and suppress the noise under the ultra-high b-value (4000 s/mm2) significantly.


CONCLUSION
The joint estimation model PAIR with complementary priors has a good performance on challenging reconstructions under inter-shot motions and a low signal-to-noise ratio.


SIGNIFICANCE
PAIR has potential in advanced clinical DWI applications and microstructure research.

A Paired Phase and Magnitude Reconstruction for Advanced Diffusion-Weighted Imaging.

Images are often corrupted by impulse noise. In this paper, an alternating direction minimization with continuation algorithm is modified and iteratively used to remove the impulse noise in images by exploring its self-similarity. A patch-based nonlocal operator and sparse representation are married in the - optimization model to be solved. Simulation results demonstrate that the proposed algorithm outperforms typical denoising methods in terms of preserving edges and textures for both salt-and-pepper noise and random-valued impulse noise. It can be also applied to suppress impulse noise-like artifacts in real mural images.

/pdf/a-modified-iterative-alternating-direction-minimization-3g0fu0j658.pdf

A Modified Iterative Alternating Direction Minimization Algorithm for Impulse Noise Removal in Images

Hypercomplex Low Rank Reconstruction for NMR Spectroscopy

https://chemistry-europe.onlinelibrary.wiley.com/doi/pdf/10.1002/chem.202084662

Di Guo

Papers

Magnetic resonance image reconstruction using similarities learnt from multi-modal images

A Paired Phase and Magnitude Reconstruction for Advanced Diffusion-Weighted Imaging.

A Modified Iterative Alternating Direction Minimization Algorithm for Impulse Noise Removal in Images

Hypercomplex Low Rank Reconstruction for NMR Spectroscopy

Frontispiece: Review and Prospect: Deep Learning in Nuclear Magnetic Resonance Spectroscopy