Coupled Dictionary Learning for Multi-Contrast MRI Reconstruction

Fourier Domain Robust Denoising Decomposition and Adaptive Patch MRI Reconstruction

The sparsity of the Fourier transform domain has been applied to magnetic resonance imaging (MRI) reconstruction in k -space. Although unsupervised adaptive patch optimization methods have shown promise compared to data-driven-based supervised methods, the following challenges exist in MRI reconstruction: 1) in previous k -space MRI reconstruction tasks, MRI with noise interference in the acquisition process is rarely considered. 2) Differences in transform domains should be resolved to achieve the high-quality reconstruction of low undersampled MRI data. 3) Robust patch dictionary learning problems are usually nonconvex and NP-hard, and alternate minimization methods are often computationally expensive. In this article, we propose a method for Fourier domain robust denoising decomposition and adaptive patch MRI reconstruction (DDAPR). DDAPR is a two-step optimization method for MRI reconstruction in the presence of noise and low undersampled data. It includes the low-rank and sparse denoising reconstruction model (LSDRM) and the robust dictionary learning reconstruction model (RDLRM). In the first step, we propose LSDRM for different domains. For the optimization solution, the proximal gradient method is used to optimize LSDRM by singular value decomposition and soft threshold algorithms. In the second step, we propose RDLRM, which is an effective adaptive patch method by introducing a low-rank and sparse penalty adaptive patch dictionary and using a sparse rank-one matrix to approximate the undersampled data. Then, the block coordinate descent (BCD) method is used to optimize the variables. The BCD optimization process involves valid closed-form solutions. Extensive numerical experiments show that the proposed method has a better performance than previous methods in image reconstruction based on compressed sensing or deep learning.

Quantitative MR Image Reconstruction Using Parameter-Specific Dictionary Learning With Adaptive Dictionary-Size and Sparsity-Level Choice

OBJECTIVE

We propose a method for the reconstruction of parameter-maps in Quantitative Magnetic Resonance Imaging (QMRI).

METHODS

Because different quantitative parameter-maps differ from each other in terms of local features, we propose a method where the employed dictionary learning (DL) and sparse coding (SC) algorithms automatically estimate the optimal dictionary-size and sparsity level separately for each parameter-map. We evaluated the method on a T1-mapping QMRI problem in the brain using the BrainWeb data as well as in-vivo brain images acquired on an ultra-high field 7 T scanner. We compared it to a model-based acceleration for parameter mapping (MAP) approach, other sparsity-based methods using total variation (TV), Wavelets (Wl), and Shearlets (Sh) to a method which uses DL and SC to reconstruct qualitative images, followed by a non-linear (DL+Fit).

RESULTS

Our algorithm surpasses MAP, TV, Wl, and Sh in terms of RMSE and PSNR. It yields better or comparable results to DL+Fit by additionally significantly accelerating the reconstruction by a factor of approximately seven.

CONCLUSION

The proposed method outperforms the reported methods of comparison and yields accurate T1-maps. Although presented for T1-mapping in the brain, our method's structure is general and thus most probably also applicable for the the reconstruction of other quantitative parameters in other organs.

SIGNIFICANCE

From a clinical perspective, the obtained T1-maps could be utilized to differentiate between healthy subjects and patients with Alzheimer's disease. From a technical perspective, the proposed unsupervised method could be employed to obtain ground-truth data for the development of data-driven methods based on supervised learning.

Systematic Review on Learning-based Spectral CT

Spectral computed tomography (CT) has recently emerged as an advanced version of medical CT and significantly improves conventional (single-energy) CT. Spectral CT has two main forms: dual-energy computed tomography (DECT) and photon-counting computed tomography (PCCT), which offer image improvement, material decomposition, and feature quantification relative to conventional CT. However, the inherent challenges of spectral CT, evidenced by data and image artifacts, remain a bottleneck for clinical applications. To address these problems, machine learning techniques have been widely applied to spectral CT. In this review, we present the state-of-the-art data-driven techniques for spectral CT.

Noise2Recon: Enabling SNR-robust MRI reconstruction with semi-supervised and self-supervised learning

PURPOSE

To develop a method for building MRI reconstruction neural networks robust to changes in signal-to-noise ratio (SNR) and trainable with a limited number of fully sampled scans.

METHODS

We propose Noise2Recon, a consistency training method for SNR-robust accelerated MRI reconstruction that can use both fully sampled (labeled) and undersampled (unlabeled) scans. Noise2Recon uses unlabeled data by enforcing consistency between model reconstructions of undersampled scans and their noise-augmented counterparts. Noise2Recon was compared to compressed sensing and both supervised and self-supervised deep learning baselines. Experiments were conducted using retrospectively accelerated data from the mridata three-dimensional fast-spin-echo knee and two-dimensional fastMRI brain datasets. All methods were evaluated in label-limited settings and among out-of-distribution (OOD) shifts, including changes in SNR, acceleration factors, and datasets. An extensive ablation study was conducted to characterize the sensitivity of Noise2Recon to hyperparameter choices.

RESULTS

In label-limited settings, Noise2Recon achieved better structural similarity, peak signal-to-noise ratio, and normalized-RMS error than all baselines and matched performance of supervised models, which were trained with14 × $$ 14\times $$ more fully sampled scans. Noise2Recon outperformed all baselines, including state-of-the-art fine-tuning and augmentation techniques, among low-SNR scans and when generalizing to OOD acceleration factors. Augmentation extent and loss weighting hyperparameters had negligible impact on Noise2Recon compared to supervised methods, which may indicate increased training stability.

CONCLUSION

Noise2Recon is a label-efficient reconstruction method that is robust to distribution shifts, such as changes in SNR, acceleration factors, and others, with limited or no fully sampled training data.

A novel data-driven method for the analysis and reconstruction of cardiac cine MRI

Cardiac cine magnetic resonance imaging (MRI) can be considered the optimal criterion for measuring cardiac function. This imaging technique can provide us with detailed information about cardiac structure, tissue composition and even blood flow, which makes it highly used in medical science. But due to the image time acquisition and several other factors the MRI sequences can easily get corrupted, causing radiologists to misdiagnose 40 million people worldwide each and every single year. Hence, the urge to decrease these numbers, researchers from different fields have been introducing novel tools and methods in the medical field. Aiming to the same target, we consider in this work the application of the higher order dynamic mode decomposition (HODMD) technique. The HODMD algorithm is a linear method, which was originally introduced in the fluid dynamics domain, for the analysis of complex systems. Nevertheless, the proposed method has extended its applicability to numerous domains, including medicine. In this work, HODMD in used to analyze sets of MR images of a heart, with the ultimate goal of identifying the main patterns and frequencies driving the heart dynamics. Furthermore, a novel interpolation algorithm based on singular value decomposition combined with HODMD is introduced, providing a three-dimensional reconstruction of the heart. This algorithm is applied (i) to reconstruct corrupted or missing images, and (ii) to build a reduced order model of the heart dynamics.

Multimodal MRI Reconstruction Assisted With Spatial Alignment Network

In clinical practice, multi-modal magnetic resonance imaging (MRI) with different contrasts is usually acquired in a single study to assess different properties of the same region of interest in the human body. The whole acquisition process can be accelerated by having one or more modalities under-sampled in the k -space. Recent research has shown that, considering the redundancy between different modalities, a target MRI modality under-sampled in the k -space can be more efficiently reconstructed with a fully-sampled reference MRI modality. However, we find that the performance of the aforementioned multi-modal reconstruction can be negatively affected by subtle spatial misalignment between different modalities, which is actually common in clinical practice. In this paper, we improve the quality of multi-modal reconstruction by compensating for such spatial misalignment with a spatial alignment network. First, our spatial alignment network estimates the displacement between the fully-sampled reference and the under-sampled target images, and warps the reference image accordingly. Then, the aligned fully-sampled reference image joins the multi-modal reconstruction of the under-sampled target image. Also, considering the contrast difference between the target and reference images, we have designed a cross-modality-synthesis-based registration loss in combination with the reconstruction loss, to jointly train the spatial alignment network and the reconstruction network. The experiments on both clinical MRI and multi-coil k -space raw data demonstrate the superiority and robustness of the multi-modal MRI reconstruction empowered with our spatial alignment network. Our code is publicly available at https://github.com/woxuankai/SpatialAlignmentNetwork.

Multi-channel convolutional analysis operator learning for dual-energy CT reconstruction

Objective. Dual-energy computed tomography (DECT) has the potential to improve contrast and reduce artifacts and the ability to perform material decomposition in advanced imaging applications. The increased number of measurements results in a higher radiation dose, and it is therefore essential to reduce either the number of projections for each energy or the source x-ray intensity, but this makes tomographic reconstruction more ill-posed. Approach. We developed the multi-channel convolutional analysis operator learning (MCAOL) method to exploit common spatial features within attenuation images at different energies and we propose an optimization method which jointly reconstructs the attenuation images at low and high energies with mixed norm regularization on the sparse features obtained by pre-trained convolutional filters through the convolutional analysis operator learning (CAOL) algorithm. Main results. Extensive experiments with simulated and real computed tomography data were performed to validate the effectiveness of the proposed methods, and we report increased reconstruction accuracy compared with CAOL and iterative methods with single and joint total variation regularization. Significance. Qualitative and quantitative results on sparse views and low-dose DECT demonstrate that the proposed MCAOL method outperforms both CAOL applied on each energy independently and several existing state-of-the-art model-based iterative reconstruction techniques, thus paving the way for dose reduction.

Combining convolutional sparse coding with total variation for sparse-view CT reconstruction

Conventional dictionary-learning-based computed tomography (CT) reconstruction methods extract patches from an original image to train, ignoring the consistency of pixels in overlapping patches. To address the problem, this paper proposes a method combining convolutional sparse coding (CSC) with total variation (TV) for sparse-view CT reconstruction. The proposed method inherits the advantages of CSC by directly processing the whole image without dividing it into overlapping patches, which preserves more details and reduces artifacts caused by patch aggregation. By introducing a TV regularization term to enhance the constraint of the image domain, the noise can be effectively further suppressed. The alternating direction method of multipliers algorithm is employed to solve the objective function. Numerous experiments are conducted to validate the performance of the proposed method in different views. Qualitative and quantitative results show the superiority of the proposed method in terms of noise suppression, artifact reduction, and image details recovery.

Dictionary Learning-Based Ultrasound Image Combined with Gastroscope for Diagnosis of Helicobacter pylori-Caused Gastrointestinal Bleeding

The study is aimed at evaluating the application value of ultrasound combined with gastroscopy in diagnosing gastrointestinal bleeding (GIB) caused by Helicobacter pylori (HP). An ultrasound combined with a gastroscopy diagnostic model based on improved K-means Singular Value Decomposition (N-KSVD) was proposed first. 86 patients with Peptic ulcer (PU) and GIB admitted to our Hospital were selected and defined as the test group, and 86 PU patients free of GIB during the same period were selected as the control group. The two groups were observed for clinical manifestations and HP detection results. The results showed that when the noise ρ was 10, 30, 50, and 70, the Peak Signal to Noise Ratio (PSNR) values of N-KSVD dictionary after denoising were 35.55, 30.47, 27.91, and 26.08, respectively, and the structure similarity index measure (SSIM) values were 0.91, 0.827, 0.763, and 0.709, respectively. Those were greater than those of DCT dictionary and Global dictionary and showed statistically significant differences versus the DCT dictionary (P < 0.05). In the test group, there were 60 HP-positives and 26 HP-negatives, and there was significant difference in the numbers of HP-positives and HP-negatives (P < 0.05), but no significant difference in gender and age (P > 0.05). Of the subjects with abdominal pain, HP-positives accounted for 59.02% and HP-negatives accounted for 37.67%, showing significant differences (P < 0.05). Finally, the size of the ulcer lesion in HP-positives and HP-negatives was compared. It was found that 71.57% of HP-positives had ulcers with a diameter of 0-1 cm, and 28.43% had ulcers with a diameter of ≥1 cm. Compared with HP-negatives, the difference was statistically significant (P < 0.05). In conclusion, N-KSVD-based ultrasound combined with gastroscopy demonstrated good denoising effects and was effective in the diagnosis of GIB caused by HP.

Homotopic Gradients of Generative Density Priors for MR Image Reconstruction

Deep learning, particularly the generative model, has demonstrated tremendous potential to significantly speed up image reconstruction with reduced measurements recently. Rather than the existing generative models that often optimize the density priors, in this work, by taking advantage of the denoising score matching, homotopic gradients of generative density priors (HGGDP) are exploited for magnetic resonance imaging (MRI) reconstruction. More precisely, to tackle the low-dimensional manifold and low data density region issues in generative density prior, we estimate the target gradients in higher-dimensional space. We train a more powerful noise conditional score network by forming high-dimensional tensor as the network input at the training phase. More artificial noise is also injected in the embedding space. At the reconstruction stage, a homotopy method is employed to pursue the density prior, such as to boost the reconstruction performance. Experiment results implied the remarkable performance of HGGDP in terms of high reconstruction accuracy. Only 10% of the k-space data can still generate image of high quality as effectively as standard MRI reconstructions with the fully sampled data.

Optimizing multicontrast MRI reconstruction with shareable feature aggregation and selection

This paper proposes a new method for optimizing feature sharing in deep neural network-based, rapid, multicontrast magnetic resonance imaging (MC-MRI). Using the shareable information of MC images for accelerated MC-MRI reconstruction, current algorithms stack the MC images or features without optimizing the sharing protocols, leading to suboptimal reconstruction results. In this paper, we propose a novel feature aggregation and selection scheme in a deep neural network to better leverage the MC features and improve the reconstruction results. First, we propose to extract and use the shareable information by mapping the MC images into multiresolution feature maps with multilevel layers of the neural network. In this way, the extracted features capture complementary image properties, including local patterns from the shallow layers and semantic information from the deep layers. Then, an explicit selection module is designed to compile the extracted features optimally. That is, larger weights are learned to incorporate the constructive, shareable features; and smaller weights are assigned to the unshareable information. We conduct comparative studies on publicly available T2-weighted and T2-weighted fluid attenuated inversion recovery brain images, and the results show that the proposed network consistently outperforms existing algorithms. In addition, the proposed method can recover the images with high fidelity under 16 times acceleration. The ablation studies are conducted to evaluate the effectiveness of the proposed feature aggregation and selection mechanism. The results and the visualization of the weighted features show that the proposed method does effectively improve the usage of the useful features and suppress useless information, leading to overall enhanced reconstruction results. Additionally, the selection module can zero-out repeated and redundant features and improve network efficiency.

Deep learning in magnetic resonance image reconstruction

Magnetic resonance (MR) imaging visualises soft tissue contrast in exquisite detail without harmful ionising radiation. In this work, we provide a state-of-the-art review on the use of deep learning in MR image reconstruction from different image acquisition types involving compressed sensing techniques, parallel image acquisition and multi-contrast imaging. Publications with deep learning-based image reconstruction for MR imaging were identified from the literature (PubMed and Google Scholar), and a comprehensive description of each of the works was provided. A detailed comparison that highlights the differences, the data used and the performance of each of these works were also made. A discussion of the potential use cases for each of these methods is provided. The sparse image reconstruction methods were found to be most popular in using deep learning for improved performance, accelerating acquisitions by around 4-8 times. Multi-contrast image reconstruction methods rely on at least one pre-acquired image, but can achieve 16-fold, and even up to 32- to 50-fold acceleration depending on the set-up. Parallel imaging provides frameworks to be integrated in many of these methods for additional speed-up potential. The successful use of compressed sensing techniques and multi-contrast imaging with deep learning and parallel acquisition methods could yield significant MR acquisition speed-ups within clinical routines in the near future.

Synergistic multi-contrast cardiac magnetic resonance image reconstruction

Cardiac magnetic resonance imaging (CMR) is an important tool for the non-invasive diagnosis of a variety of cardiovascular diseases. Parametric mapping with multi-contrast CMR is able to quantify tissue alterations in myocardial disease and promises to improve patient care. However, magnetic resonance imaging is an inherently slow imaging modality, resulting in long acquisition times for parametric mapping which acquires a series of cardiac images with different contrasts for signal fitting or dictionary matching. Furthermore, extra efforts to deal with respiratory and cardiac motion by triggering and gating further increase the scan time. Several techniques have been developed to speed up CMR acquisitions, which usually acquire less data than that required by the Nyquist-Shannon sampling theorem, followed by regularized reconstruction to mitigate undersampling artefacts. Recent advances in CMR parametric mapping speed up CMR by synergistically exploiting spatial-temporal and contrast redundancies. In this article, we will review the recent developments in multi-contrast CMR image reconstruction for parametric mapping with special focus on low-rank and model-based reconstructions. Deep learning-based multi-contrast reconstruction has recently been proposed in other magnetic resonance applications. These developments will be covered to introduce the general methodology. Current technical limitations and potential future directions are discussed. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Deep unregistered multi-contrast MRI reconstruction

Multiple magnetic resonance images of different contrasts are normally acquired for clinical diagnosis. Recently, research has shown that the previously acquired multi-contrast (MC) images of the same patient can be used as anatomical prior to accelerating magnetic resonance imaging (MRI). However, current MC-MRI networks are based on the assumption that the images are perfectly registered, which is rarely the case in real-world applications. In this paper, we propose an end-to-end deep neural network to reconstruct highly accelerated images by exploiting the shareable information from potentially misaligned reference images of an arbitrary contrast. Specifically, a spatial transformation (ST) module is designed and integrated into the reconstruction network to align the pre-acquired reference images with the images to be reconstructed. The misalignment is further alleviated by maximizing the normalized cross-correlation (NCC) between the MC images. The visualization of feature maps demonstrates that the proposed method effectively reduces the misalignment between the images for shareable information extraction when applied to the publicly available brain datasets. Additionally, the experimental results on these datasets show the proposed network allows the robust exploitation of shareable information across the misaligned MC images, leading to improved reconstruction results.

Utilizing shared information between gradient-spoiled and RF-spoiled steady-state MRI signals

This work presents an analytical relationship between gradient-spoiled and RF-spoiled steady-state signals. The two echoes acquired in double-echo in steady-state scans are shown to lie on a line in the signal plane, where the two axes represent the amplitudes of each echo. The location along the line depends on the amount of spoiling and the diffusivity. The line terminates in a point corresponding to an RF-spoiled signal. In addition to the main contribution of demonstrating this signal relationship, we also include the secondary contribution of preliminary results from an example application of the relationship, in the form of a heuristic denoising method when both types of scans are performed. This is investigated in simulations, phantom scans, and in vivo scans. For the signal model, the main topic of this study, simulations confirmed its accuracy and explored its dependency on signal parameters and image noise. For the secondary topic of its preliminary application to reduce noise, simulations demonstrated the denoising method giving a reduction in noise-induced standard deviation of about 30%. The relative effect of the method on the signals is shown to depend on the slope of the described line, which is demonstrated to be zero at the Ernst angle. The phantom scans show a similar effect as the simulations. In vivo scans showed a slightly lower average improvement of about 28%.

On the regularization of feature fusion and mapping for fast MR multi-contrast imaging via iterative networks

Multi-contrast (MC) Magnetic Resonance Imaging (MRI) of the same patient usually requires long scanning times, despite the images sharing redundant information. In this work, we propose a new iterative network that utilizes the sharable information among MC images for MRI acceleration. The proposed network has reinforced data fidelity control and anatomy guidance through an iterative optimization procedure of Gradient Descent, leading to reduced uncertainties and improved reconstruction results. Through a convolutional network, the new method incorporates a learnable regularization unit that is capable of extracting, fusing, and mapping shareable information among different contrasts. Specifically, a dilated inception block is proposed to promote multi-scale feature extractions and increase the receptive field diversity for contextual information incorporation. Lastly, an optimal MC information feeding protocol is built through the design of a complementary feature extractor block. Comprehensive experiments demonstrated the superiority of the proposed network, both qualitatively and quantitatively.

A Deep Framework Assembling Principled Modules for CS-MRI: Unrolling Perspective, Convergence Behaviors, and Practical Modeling

Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse problem to reconstruct aliasing-free MR images from the sparse k -space data. Conventional methods typically optimize an energy function, producing restoration of high quality, but their iterative numerical solvers unavoidably bring extremely large time consumption. Recent deep techniques provide fast restoration by either learning direct prediction to final reconstruction or plugging learned modules into the energy optimizer. Nevertheless, these data-driven predictors cannot guarantee the reconstruction following principled constraints underlying the domain knowledge so that the reliability of their reconstruction process is questionable. In this paper, we propose a deep framework assembling principled modules for CS-MRI that fuses learning strategy with the iterative solver of a conventional reconstruction energy. This framework embeds an optimal condition checking mechanism, fostering efficient and reliable reconstruction. We also apply the framework to three practical tasks, i.e., complex-valued data reconstruction, parallel imaging and reconstruction with Rician noise. Extensive experiments on both benchmark and manufacturer-testing images demonstrate that the proposed method reliably converges to the optimal solution more efficiently and accurately than the state-of-the-art in various scenarios.

Adaptive sparsity level and dictionary size estimation for image reconstruction in accelerated 2D radial cine MRI

PURPOSE

In the past, dictionary learning (DL) and sparse coding (SC) have been proposed for the regularization of image reconstruction problems. The regularization is given by a sparse approximation of all image patches using a learned dictionary, that is, an overcomplete set of basis functions learned from data. Despite its competitiveness, DL and SC require the tuning of two essential hyperparameters: the sparsity level S - the number of basis functions of the dictionary, called atoms, which are used to approximate each patch, and K - the overall number of such atoms in the dictionary. These two hyperparameters usually have to be chosen a priori and are determined by repetitive and computationally expensive experiments. Furthermore, the final reported values vary depending on the specific situation. As a result, the clinical application of the method is limited, as standardized reconstruction protocols have to be used.

METHODS

In this work, we use adaptive DL and propose a novel adaptive sparse coding algorithm for two-dimensional (2D) radial cine MR image reconstruction. Using adaptive DL and adaptive SC, the optimal dictionary size K as well as the optimal sparsity level S are chosen dependent on the considered data.

RESULTS

Our three main results are the following: First, adaptive DL and adaptive SC deliver results which are comparable or better than the most widely used nonadaptive version of DL and SC. Second, the time needed for the regularization is accelerated due to the fact that the sparsity level S is never overestimated. Finally, the a priori choice of S and K is no longer needed but is optimally chosen dependent on the data under consideration.

CONCLUSIONS

Adaptive DL and adaptive SC can highly facilitate the application of DL- and SC-based regularization methods. While in this work we focused on 2D radial cine MR image reconstruction, we expect the method to be applicable to different imaging modalities as well.