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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01 Jan 2022
TL;DR: In this paper , the authors proposed a complex-valued generative adversarial network (Co-VeGAN) framework, which is the first generative model exploring the use of complexvalued weights and operations.
Abstract: Compressed sensing (CS) is extensively used to reduce magnetic resonance imaging (MRI) acquisition time. State-of-the-art deep learning-based methods have proven effective in obtaining fast, high-quality reconstruction of CS-MR images. However, they treat the inherently complex-valued MRI data as real-valued entities by extracting the magnitude content or concatenating the complex-valued data as two real-valued channels for processing. In both cases, the phase content is discarded. To address the fundamental problem of real-valued deep networks, i.e. their inability to process complex-valued data, we propose a complex-valued generative adversarial network (Co-VeGAN) framework, which is the first-of-its-kind generative model exploring the use of complex-valued weights and operations. Further, since real-valued activation functions do not generalize well to the complex-valued space, we propose a novel complex-valued activation function that is sensitive to the input phase and has a learnable profile. Extensive evaluation of the proposed approach 1 on different datasets demonstrates that it significantly outperforms the existing CS-MRI reconstruction techniques.
4 citations
01 Jan 2022
TL;DR: Acomplex-valued generative adversarial network (Co-VeGAN) framework is proposed, which is the first-of-its-kind generative model exploring the use of complex-valued weights and operations and significantly outperforms the existing CS-MRI reconstruction techniques.
Abstract: Compressed sensing (CS) is extensively used to reduce magnetic resonance imaging (MRI) acquisition time. State-of-the-art deep learning-based methods have proven effective in obtaining fast, high-quality reconstruction of CS-MR images. However, they treat the inherently complex-valued MRI data as real-valued entities by extracting the magnitude content or concatenating the complex-valued data as two real-valued channels for processing. In both cases, the phase content is discarded. To address the fundamental problem of real-valued deep networks, i.e. their inability to process complex-valued data, we propose a complex-valued generative adversarial network (Co-VeGAN) framework, which is the first-of-its-kind generative model exploring the use of complex-valued weights and operations. Further, since real-valued activation functions do not generalize well to the complex-valued space, we propose a novel complex-valued activation function that is sensitive to the input phase and has a learnable profile. Extensive evaluation of the proposed approach 1 on different datasets demonstrates that it significantly outperforms the existing CS-MRI reconstruction techniques.
4 citations
TL;DR: In this article, Parametric mapping with multi-contrast CMR is used for the non-invasive diagnosis of a variety of cardiovascular diseases, such as stroke and heart failure.
Abstract: 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 ...
4 citations
TL;DR: A compressed sensing image reconstruction algorithm based on hybrid ALWOA strategy, which combines the ant lion optimization algorithm and the whale optimization algorithm, which produces a global search with faster convergence is proposed.
Abstract: In the field of image compression, the compressed sensing image reconstruction has made great achievements due to proper use of the image sparsity without the Nyquist sampling law constraint. For image information distribution, great deals of researches indicate that there exists obvious structural and statistical prior’s regularity and by the traditional compression algorithm it is difficult to achieve. In this paper, we propose a compressed sensing image reconstruction algorithm based on hybrid ALWOA strategy, which combines the ant lion optimization algorithm and the whale optimization algorithm. The hybrid algorithm produces a global search with faster convergence. By continuously learning the proposed hybrid method can find optimal solutions. The objective function for the image reconstruction process is taken as the l1 minimization problem. The reconstructed image is obtained by solving the l1 minimization problem. Extensive simulations have been conducted and the results show that the proposed method has achieved better performance when compared with traditional reconstruction algorithms.
4 citations
TL;DR: The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data and constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of theundersampling rates, the noise levels, and the image structures.
Abstract: Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.
4 citations
Additional excerpts
...The wavelet transform [11, 18, 19], curvelet [20], and finite difference operations [11, 13, 14] are among the commonly used transforms....
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References
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TL;DR: In this article, a structural similarity index is proposed for image quality assessment based on the degradation of structural information, which can be applied to both subjective ratings and objective methods on a database of images compressed with JPEG and JPEG2000.
Abstract: Objective methods for assessing perceptual image quality traditionally attempted to quantify the visibility of errors (differences) between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative complementary framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a structural similarity index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. A MATLAB implementation of the proposed algorithm is available online at http://www.cns.nyu.edu//spl sim/lcv/ssim/.
40,609 citations
Book•
01 Jan 1990TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Abstract: From the Publisher:
The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures. Like the first edition,this text can also be used for self-study by technical professionals since it discusses engineering issues in algorithm design as well as the mathematical aspects.
In its new edition,Introduction to Algorithms continues to provide a comprehensive introduction to the modern study of algorithms. The revision has been updated to reflect changes in the years since the book's original publication. New chapters on the role of algorithms in computing and on probabilistic analysis and randomized algorithms have been included. Sections throughout the book have been rewritten for increased clarity,and material has been added wherever a fuller explanation has seemed useful or new information warrants expanded coverage.
As in the classic first edition,this new edition of Introduction to Algorithms presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers. Further,the algorithms are presented in pseudocode to make the book easily accessible to students from all programming language backgrounds.
Each chapter presents an algorithm,a design technique,an application area,or a related topic. The chapters are not dependent on one another,so the instructor can organize his or her use of the book in the way that best suits the course's needs. Additionally,the new edition offers a 25% increase over the first edition in the number of problems,giving the book 155 problems and over 900 exercises thatreinforcethe concepts the students are learning.
21,651 citations
TL;DR: A novel algorithm for adapting dictionaries in order to achieve sparse signal representations, the K-SVD algorithm, an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data.
Abstract: In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data
8,905 citations
"Image reconstruction of compressed ..." refers methods in this paper
...Assuming that image patches are linear combinations of element patches, Aharon et al. have used K-SVD to train a patch-based dictionary (Aharon et al., 2006; Ravishankar and Bresler, 2011)....
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TL;DR: It is proved that replacing the usual quadratic regularizing penalties by weighted 𝓁p‐penalized penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem.
Abstract: We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary preassigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted p-penalties on the coefficients of such expansions, with 1 ≤ p ≤ 2, still regularizes the problem. Use of such p-penalized problems with p < 2 is often advocated when one expects the underlying ideal noiseless solution to have a sparse expansion with respect to the basis under consideration. To compute the corresponding regularized solutions, we analyze 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. © 2004 Wiley Periodicals, Inc.
4,339 citations
Additional excerpts
...When β → +∞ , expression (6) approaches (5) (Daubechies et al., 2004; Junfeng et al., 2010)....
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...(6) When β → +∞ , expression (6) approaches (5) (Daubechies et al., 2004; Junfeng et al., 2010)....
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