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 (CS) is a new jointly sampling and compression technology for remote sensing. In hyperspectral imaging, a typical CS method encodes the two-dimensional (2-D) spatial information of each spectral band or encodes the third spectral information simultaneously. However, encoding the spatial information is much easier than encoding the spectral information. Therefore, it is crucial to make use of the spectral information to improve the compression rate on 2-D CS data. We propose to encode the third spectral information with an adaptive Karhunen–Loeve transform. With a mathematical proof, we show that interspectral correlations are preserved among 2-D randomly encoded spatial information. This property means that one can compress 2-D CS data effectively with a Karhunen–Loeve transform. Experiments demonstrate that the proposed method can better reconstruct both spectral curves and spatial images than traditional compression methods at the bit rates 0 to 1.

Karhunen-Loève transform for compressive sampling hyperspectral images

An index signal de-noising method relates to a signal de-noising method, and is easy to operate and exhibits excellent effects. The method includes the step of modeling index signals: filling the index signals in a Hankel matrix according to a set sequence, establishing a Hankel matrix low-rank reconstruction model, and solving the model to de-noise the signals. The method is fast in speed and high in precision, and parameters can be set on the basis of measured noise variances. During practical applications, the optimized model can be adopted to de-noise signals such as time-domain signals of nuclear magnetic resonance wave spectrums and signals that accord with the index characteristics, so the sampling time is reduced and the spectra resolution is increased. The index signal de-noising method, provided by the invention, exhibits excellent effects and is easy to operate.

Index signal de-noising method

The invention discloses a high-dimensional nuclear magnetic resonance time-domain signal completion method, and relates to nuclear magnetic resonance high-dimensional spectrum signal processing. The high-dimensional nuclear magnetic resonance time-domain signal completion method comprises the following steps: firstly, confirming the position of a time-domain signal to be completed according to acquired data and the provided spectrum width and resolution of a nuclear magnetic resonance spectrum, and designing a template; further establishing a reestablished model by using the provided high-dimensional nuclear magnetic resonance time-domain signal completion method, and solving a complete high-dimensional nuclear magnetic resonance time-domain signal by using an optimal algorithm; and finally, performing Fourier transform on the completed time-domain signal, thereby obtaining the nuclear magnetic resonance spectrum. As the characteristics of the high-dimensional nuclear magnetic resonance signal self are utilized, any high-dimensional nuclear magnetic resonance time-domain signal can be completed, and the purposes of shortening the sampling time, increasing the signal to noise ratio and providing the spectrum width and the resolution of the nuclear magnetic resonance spectrum can be achieved.

High-dimensional nuclear magnetic resonance time-domain signal completion method

Accelerating patch-based directional wavelets with multicore parallel computing in compressed sensing MRI.

Multidimensional nuclear magnetic resonance (NMR) spectroscopy is one of the most crucial detection tools for molecular structure analysis and has been widely used in biomedicine and chemistry. However, the development of NMR spectroscopy is hampered by long data collection time. Non-uniform sampling empowers rapid signal acquisition by collecting a small subset of data. Since the sampling rate is lower than that of the Nyquist sampling ratio, undersampling artifacts arise in reconstructed spectra. To obtain a high-quality spectrum, it is necessary to apply reasonable prior constraints in spectrum reconstruction models. The self-learning subspace method has been shown to possess superior advantages than that of the state-of-the-art low-rank Hankel matrix method when adopting high acceleration in data sampling. However, the self-learning subspace method is time-consuming due to the singular value decomposition in iterations. In this paper, we propose a fast self-learning subspace method to enable fast and high-quality reconstructions. Aided by parallel computing, the experiment results show that the proposed method can reconstruct high-fidelity spectra but spend less than 10% of the time required by the non-parallel self-learning subspace method.

https://www.mdpi.com/2076-3417/10/11/3939/pdf

Di Guo

Papers

Karhunen-Loève transform for compressive sampling hyperspectral images

Index signal de-noising method

High-dimensional nuclear magnetic resonance time-domain signal completion method

Accelerating patch-based directional wavelets with multicore parallel computing in compressed sensing MRI.

A Fast Self-Learning Subspace Reconstruction Method for Non-Uniformly Sampled Nuclear Magnetic Resonance Spectroscopy