scholarly journals Compressed Sensing MRI Reconstruction Algorithm Based on Contourlet Transform and Alternating Direction Method

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Zhenyu Hu ◽  
Qiuye Wang ◽  
Congcong Ming ◽  
Lai Wang ◽  
Yuanqing Hu ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Computation Time ◽  
Reconstruction Algorithm ◽  
Alternating Direction Method ◽  
Contourlet Transform ◽  
Superior Performance ◽  
Reconstruction Method ◽  
Mr Images ◽  
Alternating Direction ◽  
Mri Reconstruction

Compressed sensing (CS) based methods have recently been used to reconstruct magnetic resonance (MR) images from undersampled measurements, which is known as CS-MRI. In traditional CS-MRI, wavelet transform can hardly capture the information of image curves and edges. In this paper, we present a new CS-MRI reconstruction algorithm based on contourlet transform and alternating direction method (ADM). The MR images are firstly represented by contourlet transform, which can describe the images’ curves and edges fully and accurately. Then the MR images are reconstructed by ADM, which is an effective CS reconstruction method. Numerical results validate the superior performance of the proposed algorithm in terms of reconstruction accuracy and computation time.

scholarly journals Compressed Sensing MRI Reconstruction from Highly Undersampledk-Space Data Using Nonsubsampled Shearlet Transform Sparsity Prior

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Min Yuan ◽  
Bingxin Yang ◽  
Yide Ma ◽  
Jiuwen Zhang ◽  
Runpu Zhang ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Directional Sensitivity ◽  
Reconstruction Method ◽  
Approximation Properties ◽  
Mr Images ◽  
Shearlet Transform ◽  
Nonsubsampled Shearlet Transform ◽  
Reconstruction Methods ◽  
Mri Reconstruction ◽  
Space Data

Compressed sensing has shown great potential in speeding up MR imaging by undersamplingk-space data. Generally sparsity is used as a priori knowledge to improve the quality of reconstructed image. Compressed sensing MR image (CS-MRI) reconstruction methods have employed widely used sparsifying transforms such as wavelet or total variation, which are not preeminent in dealing with MR images containing distributed discontinuities and cannot provide a sufficient sparse representation and the decomposition at any direction. In this paper, we propose a novel CS-MRI reconstruction method from highly undersampledk-space data using nonsubsampled shearlet transform (NSST) sparsity prior. In particular, we have implemented a flexible decomposition with an arbitrary even number of directional subbands at each level using NSST for MR images. The highly directional sensitivity of NSST and its optimal approximation properties lead to improvement in CS-MRI reconstruction applications. The experimental results demonstrate that the proposed method results in the high quality reconstruction, which is highly effective at preserving the intrinsic anisotropic features of MRI meanwhile suppressing the artifacts and added noise. The objective evaluation indices outperform all compared CS-MRI methods. In summary, NSST with even number directional decomposition is very competitive in CS-MRI applications as sparsity prior in terms of performance and computational efficiency.

An Algorithm Combining Analysis-based Blind Compressed Sensing and Nonlocal Low-rank Constraints for MRI Reconstruction

2019 ◽  
Vol 15 (3) ◽  
pp. 281-291 ◽  
Author(s):  
Mei Sun ◽  
Jinxu Tao ◽  
Zhongfu Ye ◽  
Bensheng Qiu ◽  
Jinzhang Xu ◽  
...  
Keyword(s):  
Compressed Sensing ◽  
Signal Reconstruction ◽  
Low Rank ◽  
Mr Images ◽  
Scanning Time ◽  
Previous State ◽  
Rank Approximation ◽  
Mri Reconstruction ◽  
Magnetic Resonance Imaging Mri ◽  
Rank Constraints

Background: In order to overcome the limitation of long scanning time, compressive sensing (CS) technology exploits the sparsity of image in some transform domain to reduce the amount of acquired data. Therefore, CS has been widely used in magnetic resonance imaging (MRI) reconstruction. </P><P> Discussion: Blind compressed sensing enables to recover the image successfully from highly under- sampled measurements, because of the data-driven adaption of the unknown transform basis priori. Moreover, analysis-based blind compressed sensing often leads to more efficient signal reconstruction with less time than synthesis-based blind compressed sensing. Recently, some experiments have shown that nonlocal low-rank property has the ability to preserve the details of the image for MRI reconstruction. Methods: Here, we focus on analysis-based blind compressed sensing, and combine it with additional nonlocal low-rank constraint to achieve better MR images from fewer measurements. Instead of nuclear norm, we exploit non-convex Schatten p-functionals for the rank approximation. </P><P> Results & Conclusion: Simulation results indicate that the proposed approach performs better than the previous state-of-the-art algorithms.

Gravity anomaly reconstruction based on nonequispaced Fourier transform

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. G83-G92
Author(s):  
Ya Xu ◽  
Fangzhou Nan ◽  
Weiping Cao ◽  
Song Huang ◽  
Tianyao Hao
Keyword(s):  
Fourier Transform ◽  
Compressed Sensing ◽  
Gravity Data ◽  
Signal Reconstruction ◽  
Gaussian Function ◽  
Reconstruction Algorithm ◽  
Data Reconstruction ◽  
Reconstruction Method ◽  
Grid Data ◽  
2D Data

Irregular sampled gravity data are often interpolated into regular grid data for convenience of data processing and interpretation. The compressed sensing theory provides a signal reconstruction method that can recover a sparse signal from far fewer samples. We have introduced a gravity data reconstruction method based on the nonequispaced Fourier transform (NFT) in the framework of compressed sensing theory. We have developed a sparsity analysis and a reconstruction algorithm with an iterative cooling thresholding method and applied to the gravity data of the Bishop model. For 2D data reconstruction, we use two methods to build the weighting factors: the Gaussian function and the Voronoi method. Both have good reconstruction results from the 2D data tests. The 2D reconstruction tests from different sampling rates and comparison with the minimum curvature and the kriging methods indicate that the reconstruction method based on the NFT has a good reconstruction result even with few sampling data.

scholarly journals Energy Preserved Sampling for Compressed Sensing MRI

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Yudong Zhang ◽  
Bradley S. Peterson ◽  
Genlin Ji ◽  
Zhengchao Dong
Keyword(s):  
Compressed Sensing ◽  
Cost Function ◽  
Computation Time ◽  
Reconstruction Algorithm ◽  
Simple Random Sampling ◽  
Variable Density ◽  
Reconstruction Algorithms ◽  
Iterative Thresholding ◽  
Thresholding Algorithm

The sampling patterns, cost functions, and reconstruction algorithms play important roles in optimizing compressed sensing magnetic resonance imaging (CS-MRI). Simple random sampling patterns did not take into account the energy distribution ink-space and resulted in suboptimal reconstruction of MR images. Therefore, a variety of variable density (VD) based samplings patterns had been developed. To further improve it, we propose a novel energy preserving sampling (ePRESS) method. Besides, we improve the cost function by introducing phase correction and region of support matrix, and we propose iterative thresholding algorithm (ITA) to solve the improved cost function. We evaluate the proposed ePRESS sampling method, improved cost function, and ITA reconstruction algorithm by 2D digital phantom and 2Din vivoMR brains of healthy volunteers. These assessments demonstrate that the proposed ePRESS method performs better than VD, POWER, and BKO; the improved cost function can achieve better reconstruction quality than conventional cost function; and the ITA is faster than SISTA and is competitive with FISTA in terms of computation time.

scholarly journals A CT Reconstruction Algorithm Based on Non-Aliasing Contourlet Transform and Compressive Sensing

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Lu-zhen Deng ◽  
Peng Feng ◽  
Mian-yi Chen ◽  
Peng He ◽  
Quang-sang Vo ◽  
...  
Keyword(s):  
Compressive Sensing ◽  
Iteration Process ◽  
Reconstruction Algorithm ◽  
Ct Images ◽  
Contourlet Transform ◽  
Projection Data ◽  
Reconstruction Technique ◽  
Reconstruction Method ◽  
Ct Reconstruction ◽  
Split Bregman

Compressive sensing (CS) theory has great potential for reconstructing CT images from sparse-views projection data. Currently, total variation (TV-) based CT reconstruction method is a hot research point in medical CT field, which uses the gradient operator as the sparse representation approach during the iteration process. However, the images reconstructed by this method often suffer the smoothing problem; to improve the quality of reconstructed images, this paper proposed a hybrid reconstruction method combining TV and non-aliasing Contourlet transform (NACT) and using the Split-Bregman method to solve the optimization problem. Finally, the simulation results show that the proposed algorithm can reconstruct high-quality CT images from few-views projection using less iteration numbers, which is more effective in suppressing noise and artefacts than algebraic reconstruction technique (ART) and TV-based reconstruction method.

scholarly journals Distributed Reconstruction via Alternating Direction Method

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Linyuan Wang ◽  
Ailong Cai ◽  
Hanming Zhang ◽  
Bin Yan ◽  
Lei Li ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Image Reconstruction ◽  
Total Variation ◽  
Reconstruction Algorithm ◽  
Alternating Direction Method ◽  
Ct Image ◽  
Total Variation Minimization ◽  
Considerable Research ◽  
Alternating Direction ◽  
Ct Image Reconstruction

With the development of compressive sensing theory, image reconstruction from few-view projections has received considerable research attentions in the field of computed tomography (CT). Total-variation- (TV-) based CT image reconstruction has been shown to be experimentally capable of producing accurate reconstructions from sparse-view data. In this study, a distributed reconstruction algorithm based on TV minimization has been developed. This algorithm is very simple as it uses the alternating direction method. The proposed method can accelerate the alternating direction total variation minimization (ADTVM) algorithm without losing accuracy.

Column distribution reconstruction algorithm via the alternating direction method

Optik ◽  
2015 ◽  
Vol 126 (9-10) ◽  
pp. 1006-1011
Author(s):  
Linyuan Wang ◽  
Ailong Cai ◽  
Hongkui Liu ◽  
Hanming Zhang ◽  
Bin Yan ◽  
...  
Keyword(s):  
Reconstruction Algorithm ◽  
Alternating Direction Method ◽  
Alternating Direction
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