Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform.
TL;DR: A graph-based redundant wavelet transform is introduced to sparsely represent magnetic resonance images in iterative image reconstructions and outperforms several state-of-the-art reconstruction methods in removing artifacts and achieves fewer reconstruction errors on the tested datasets.
About: This article is published in Medical Image Analysis.The article was published on 2016-01-01. It has received 150 citations till now. The article focuses on the topics: Iterative reconstruction & Wavelet transform.
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TL;DR: 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.
Abstract: 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.
835 citations
Cites background from "Image reconstruction of compressed ..."
..., total variation (TV) [17]–[19], discrete cosine transforms [20]–[22] and discrete wavelet transforms [23]–[25]....
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TL;DR: Two versions of a novel deep learning architecture are proposed, dubbed as ADMM-CSNet, by combining the traditional model-based CS method and data-driven deep learning method for image reconstruction from sparsely sampled measurements, which achieved favorable reconstruction accuracy in fast computational speed compared with the traditional and the other deep learning methods.
Abstract: Compressive sensing (CS) is an effective technique for reconstructing image from a small amount of sampled data. It has been widely applied in medical imaging, remote sensing, image compression, etc. In this paper, we propose two versions of a novel deep learning architecture, dubbed as ADMM-CSNet, by combining the traditional model-based CS method and data-driven deep learning method for image reconstruction from sparsely sampled measurements. We first consider a generalized CS model for image reconstruction with undetermined regularizations in undetermined transform domains, and then two efficient solvers using Alternating Direction Method of Multipliers (ADMM) algorithm for optimizing the model are proposed. We further unroll and generalize the ADMM algorithm to be two deep architectures, in which all parameters of the CS model and the ADMM algorithm are discriminatively learned by end-to-end training. For both applications of fast CS complex-valued MR imaging and CS imaging of real-valued natural images, the proposed ADMM-CSNet achieved favorable reconstruction accuracy in fast computational speed compared with the traditional and the other deep learning methods.
470 citations
TL;DR: Wang et al. as discussed by the authors proposed a projected iterative soft thresholding algorithm (pISTA) and its acceleration pFISTA for CS-MRI image reconstruction, which exploit sparsity of the magnetic resonance (MR) images under the redundant representation of tight frames.
Abstract: Compressed sensing (CS) has exhibited great potential for accelerating magnetic resonance imaging (MRI). In CS-MRI, we want to reconstruct a high-quality image from very few samples in a short time. In this paper, we propose a fast algorithm, called projected iterative soft-thresholding algorithm (pISTA), and its acceleration pFISTA for CS-MRI image reconstruction. The proposed algorithms exploit sparsity of the magnetic resonance (MR) images under the redundant representation of tight frames. We prove that pISTA and pFISTA converge to a minimizer of a convex function with a balanced tight frame sparsity formulation. The pFISTA introduces only one adjustable parameter, the step size, and we provide an explicit rule to set this parameter. Numerical experiment results demonstrate that pFISTA leads to faster convergence speeds than the state-of-art counterpart does, while achieving comparable reconstruction errors. Moreover, reconstruction errors incurred by pFISTA appear insensitive to the step size.
128 citations
TL;DR: Experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank.
Abstract: Signals are generally modeled as a superposition of exponential functions in spectroscopy of chemistry, biology, and medical imaging. For fast data acquisition or other inevitable reasons, however, only a small amount of samples may be acquired, and thus, how to recover the full signal becomes an active research topic, but existing approaches cannot efficiently recover $N$ -dimensional exponential signals with $N\geq 3$ . In this paper, we study the problem of recovering $N$ -dimensional (particularly $N\geq 3$ ) exponential signals from partial observations, and formulate this problem as a low-rank tensor completion problem with exponential factor vectors. The full signal is reconstructed by simultaneously exploiting the CANDECOMP/PARAFAC tensor structure and the exponential structure of the associated factor vectors. The latter is promoted by minimizing an objective function involving the nuclear norm of Hankel matrices. Experimental results on simulated and real magnetic resonance spectroscopy data show that the proposed approach can successfully recover full signals from very limited samples and is robust to the estimated tensor rank.
94 citations
TL;DR: Wang et al. as discussed by the authors proposed the first deep learning model for multi-contrast CS-MRI reconstruction, which achieved information sharing through feature sharing units, which significantly reduced the number of model parameters.
Abstract: Compressed sensing (CS) theory can accelerate multi-contrast magnetic resonance imaging (MRI) by sampling fewer measurements within each contrast. However, conventional optimization-based reconstruction models suffer several limitations, including a strict assumption of shared sparse support, time-consuming optimization, and “shallow” models with difficulties in encoding the patterns contained in massive MRI data. In this paper, we propose the first deep learning model for multi-contrast CS-MRI reconstruction. We achieve information sharing through feature sharing units, which significantly reduces the number of model parameters. The feature sharing unit combines with a data fidelity unit to comprise an inference block, which are then cascaded with dense connections, allowing for efficient information transmission across different depths of the network. Experiments on various multi-contrast MRI datasets show that the proposed model outperforms both state-of-the-art single-contrast and multi-contrast MRI methods in accuracy and efficiency. We demonstrate that improved reconstruction quality can bring benefits to subsequent medical image analysis. Furthermore, the robustness of the proposed model to misregistration shows its potential in real MRI applications.
83 citations
References
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Abstract: We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the coefficients of such expansions, with 1 < or = p < or =2, still regularizes the problem. If p < 2, regularized solutions of such l^p-penalized problems will have sparser expansions, with respect to the basis under consideration. To compute the corresponding regularized solutions we propose an iterative algorithm that amounts to a Landweber iteration with thresholding (or nonlinear shrinkage) applied at each iteration step. We prove that this algorithm converges in norm. We also review some potential applications of this method.
3,640 citations
TL;DR: The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation, and there is also an emphasis on the understanding of the driving factors in applications.
Abstract: This article reviews the requirements for successful compressed sensing (CS), describes their natural fit to MRI, and gives examples of four interesting applications of CS in MRI. The authors emphasize on an intuitive understanding of CS by describing the CS reconstruction as a process of interference cancellation. There is also an emphasis on the understanding of the driving factors in applications, including limitations imposed by MRI hardware, by the characteristics of different types of images, and by clinical concerns.
2,134 citations
"Image reconstruction of compressed ..." refers methods in this paper
...…et al., 2014; Zhang et al., 2012), incoherent undersampling artifacts (Greiser and von Kienlin, 2003; Tsai and Nishimura, 2000), and an effective nonlinear reconstruction algorithm (Aelterman et al., 2011; Lustig et al., 2008; Majumdar and Ward, 2011, 2012; Majumdar et al., 2013; Yue et al., 2012)....
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TL;DR: It is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support.
Abstract: Two separately motivated implementations of the wavelet transform are brought together. It is observed that these algorithms are both special cases of a single filter bank structure, the discrete wavelet transform, the behavior of which is governed by the choice of filters. In fact, the a trous algorithm is more properly viewed as a nonorthonormal multiresolution algorithm for which the discrete wavelet transform is exact. Moreover, it is shown that the commonly used Lagrange a trous filters are in one-to-one correspondence with the convolutional squares of the Daubechies filters for orthonormal wavelets of compact support. A systematic framework for the discrete wavelet transform is provided, and conditions are derived under which it computes the continuous wavelet transform exactly. Suitable filter constraints for finite energy and boundedness of the discrete transform are also derived. Relevant signal processing parameters are examined, and it is observed that orthonormality is balanced by restrictions on resolution. >
1,856 citations
"Image reconstruction of compressed ..." refers background in this paper
...3) are expected to be sparsely represented with a redundant 1D wavelet (Shensa, 1992)....
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Book•
01 Jan 1980TL;DR: This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency.
Abstract: ....The most comprehensive guide to designing practical and efficient algorithms!.... The Algorithm Design Manual, Second Edition "...the book is an algorithm-implementation treasure trove, and putting all of these implementations in one place was no small feat. The list of implementations [and] extensive bibliography make the book an invaluable resource for everyone interested in the subject." --ACM Computing Reviews "It has all the right ingredients: rich contents, friendly, personal language, subtle humor, the right references, and a plethora of pointers to resources."-- P. Takis Metaxas, Wellesley College "This is the most approachable book on algorithms I have." -- Megan Squire, Elon University, USA This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding onthe first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students. The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instructionon methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography. NEW to the second edition: Doubles the tutorial material and exercises over the first edition Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them Includes several NEW "war stories" relating experiences from real-world applications Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java ADDITIONAL Learning Tools: Exercises include "job interview problems" from major software companies Highlighted take-home lesson boxes emphasize essential concepts Provides comprehensive references to both survey articles and the primary literature Exercises points to relevant programming contest challenge problems Many algorithms presented with actual code (written in C) as well as pseudo-code A full set of lecture slides and additional material available at www.algorist.com Written by a well-known algorithms researcher who received the IEEE Computer Science and Engineering Teaching Award, this new edition of The Algorithm Design Manual is an essential learning tool for students needing a solid grounding in algorithms, as well as a special text/reference for professionals who need an authoritative and insightful guide. Professor Skiena is also author of the popular Springer text, Programming Challenges: The Programming Contest Training Manual.
1,272 citations
TL;DR: 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 are demonstrated.
Abstract: 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.
1,015 citations
"Image reconstruction of compressed ..." refers background or methods in this paper
...Both methods significantly improve the image reconstruction over the predefined basis method (Ning et al., 2013; Qu et al., 2012; Ravishankar and Bresler, 2011)....
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...10(b-d) show that the proposed method preserves edges much better than DLMRI and WaTMRI do....
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...Comparison with state-of-the-art methods In this section, we compare the proposed method with dictionary learning MRI (DLMRI) (Ravishankar and Bresler, 2011), which is based on K-SVD decomposition, wavelet tree-structured MRI (WaTMRI) (Chen and Huang, 2014), which enforces the sparsity based on…...
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...The image reconstruction may become unsatisfactory when the data are highly undersampled because of the insufficiently sparse representations (Qu et al., 2012; Ravishankar and Bresler, 2011)....
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...As mentioned above, the geometric direction of each patch can be used to improve edge reconstructions (Ning et al., 2013; Qu et al., 2012), and K-SVD trains a dictionary to sparsely represent all patches (Ravishankar and Bresler, 2011)....
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