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Journal ArticleDOI

Image reconstruction of compressed sensing MRI using graph-based redundant wavelet transform.

01 Jan 2016-Medical Image Analysis (Elsevier)-Vol. 27, pp 93-104
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.
Citations
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Journal ArticleDOI
TL;DR: Experimental results on CT images, X-ray images and MRI images from medical image datasets and quantitative analyses by structural similarity index measurement, average gradient, relative enhancement in contrast (REC) and information entropy demonstrate that the results of the proposed LM&GM method are competitive and overwhelm those of the existing methods.

37 citations

Journal ArticleDOI
TL;DR: A novel algorithm, called WaveICA, which is based on the wavelet transform method with independent component analysis, as the threshold processing method to capture and remove batch effects for large-scale metabolomics data is proposed.

35 citations

Journal ArticleDOI
TL;DR: The aim of this paper is to improve edges of brain MRI by incorporating the gradient information of another contrast high-resolution image by establishing a relation model of gradient value between different contrast images to restore a high- resolution image from its input low-resolution version.
Abstract: In magnetic resonance imaging (MRI), the super-resolution technology has played a great role in improving image quality. The aim of this paper is to improve edges of brain MRI by incorporating the gradient information of another contrast high-resolution image. Multi-contrast images are assumed to possess the same gradient direction in a local pattern. We proposed to establish a relation model of gradient value between different contrast images to restore a high-resolution image from its input low-resolution version. The similarity of image patches is employed to estimate intensity parameters, leading a more accurate reconstructed image. Then, an iterative back-projection filter is applied to the reconstructed image to further increase the image quality. The new approach is verified on synthetic and real brain MRI images and achieves higher visual quality and higher objective quality criteria than the compared state-of-the-art super-resolution approaches. The gradient information of the multi-contrast MRI images is very useful. With a proper relation model, the proposed method enhances image edges in MRI image super-resolution. Improving the MRI image resolution from very low-resolution observations is challenging. We tackle this problem by first modeling the relation of gradient value in multi-contrast MRI and then performing fast supper-resolution methods. This relation model may be helpful for other MRI reconstruction problems.

30 citations


Cites background from "Image reconstruction of compressed ..."

  • ...Last, this modeling may benefit improving reconstruction of fast imaging in MRI [22], [33]–[38] and reconstruction of multi-contrast MRI images in fast sampling [39]–[41]....

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Journal ArticleDOI
TL;DR: In this paper, a pre-trained generative adversarial network (GAN) and transfer learning was used to improve the reconstruction performance of a small number of training samples for real clinical applications.

29 citations

Journal ArticleDOI
TL;DR: Experimental results demonstrate that the image quality of low-resolution images can be remarkably improved with the proposed method if this weight is borrowed from a high resolution image with another contrast.
Abstract: Low-resolution images may be acquired in magnetic resonance imaging (MRI) due to limited data acquisition time or other physical constraints, and their resolutions can be improved with super-resolution methods. Since MRI can offer images of an object with different contrasts, e.g., T1-weighted or T2-weighted, the shared information between inter-contrast images can be used to benefit super-resolution. In this study, an MRI image super-resolution approach to enhance in-plane resolution is proposed by exploring the statistical information estimated from another contrast MRI image that shares similar anatomical structures. We assume some edge structures are shown both in T1-weighted and T2-weighted MRI brain images acquired of the same subject, and the proposed approach aims to recover such kind of structures to generate a high-resolution image from its low-resolution counterpart. The statistical information produces a local weight of image that are found to be nearly invariant to the image contrast and thus this weight can be used to transfer the shared information from one contrast to another. We analyze this property with comprehensive mathematics as well as numerical experiments. Experimental results demonstrate that the image quality of low-resolution images can be remarkably improved with the proposed method if this weight is borrowed from a high resolution image with another contrast. Multi-contrast MRI Image Super-resolution with Contrast-invariant Regression Weights

29 citations

References
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Journal ArticleDOI
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 1990
TL;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

01 Jan 2005

19,250 citations

Journal ArticleDOI
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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Journal ArticleDOI
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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