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Ahmad M, Shahzad T, Masood K, Rashid K, Tanveer M, Iqbal R, Hussain N, Shahid A, Fazal-E-Aleem. Local and Non-local Regularization Techniques in Emission (PET/SPECT) Tomographic Image Reconstruction Methods. J Digit Imaging 2016; 29:394-402. [PMID: 26714680 PMCID: PMC4879038 DOI: 10.1007/s10278-015-9853-x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022] Open
Abstract
Emission tomographic image reconstruction is an ill-posed problem due to limited and noisy data and various image-degrading effects affecting the data and leads to noisy reconstructions. Explicit regularization, through iterative reconstruction methods, is considered better to compensate for reconstruction-based noise. Local smoothing and edge-preserving regularization methods can reduce reconstruction-based noise. However, these methods produce overly smoothed images or blocky artefacts in the final image because they can only exploit local image properties. Recently, non-local regularization techniques have been introduced, to overcome these problems, by incorporating geometrical global continuity and connectivity present in the objective image. These techniques can overcome drawbacks of local regularization methods; however, they also have certain limitations, such as choice of the regularization function, neighbourhood size or calibration of several empirical parameters involved. This work compares different local and non-local regularization techniques used in emission tomographic imaging in general and emission computed tomography in specific for improved quality of the resultant images.
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Affiliation(s)
- Munir Ahmad
- Institute of Nuclear Medicine and Oncology (INMOL), New Campus Road, Lahore, PC 10068, Pakistan.
- Department of Physics, The University of Lahore, Pakistan, 1-KM Raiwind Road, Lahore, 54000, Punjab, Pakistan.
| | - Tasawar Shahzad
- Department of Physics, The University of Lahore, Pakistan, 1-KM Raiwind Road, Lahore, 54000, Punjab, Pakistan
| | - Khalid Masood
- Institute of Nuclear Medicine and Oncology (INMOL), New Campus Road, Lahore, PC 10068, Pakistan
| | - Khalid Rashid
- Applied Physics, Pakistan Council of Science and Industrial Research (PCSIR), Ferozpur Road, Lahore, Pakistan
| | - Muhammad Tanveer
- Department of Physics, The University of Lahore, Pakistan, 1-KM Raiwind Road, Lahore, 54000, Punjab, Pakistan
| | - Rabail Iqbal
- Department of Physics, The University of Lahore, Pakistan, 1-KM Raiwind Road, Lahore, 54000, Punjab, Pakistan
| | - Nasir Hussain
- Institute of Nuclear Medicine and Oncology (INMOL), New Campus Road, Lahore, PC 10068, Pakistan
| | - Abubakar Shahid
- Institute of Nuclear Medicine and Oncology (INMOL), New Campus Road, Lahore, PC 10068, Pakistan
| | - Fazal-E-Aleem
- Department of Physics, The University of Lahore, Pakistan, 1-KM Raiwind Road, Lahore, 54000, Punjab, Pakistan
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Fang S, Li L, Wu W, Wei J, Zhang B, Kim DH, Yuan C, Guo H. Multiscale coherence regularization reconstruction using a nonlocal operator for fast variable-density spiral imaging. Magn Reson Imaging 2016; 34:964-73. [PMID: 27108356 DOI: 10.1016/j.mri.2016.04.012] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2015] [Revised: 04/06/2016] [Accepted: 04/17/2016] [Indexed: 11/17/2022]
Abstract
PURPOSE Nonlinear reconstruction can suppress pseudo-incoherent aliasing artifacts from variable-density spiral (VDS) trajectories when interleaves are undersampled for acquisition acceleration during MR imaging. However, large-scale aliasing artifact suppression often conflicts with fine-scale structure preservation and may cause deterioration of image quality in the reconstructed images. To address this issue, a sequential, multiscale coherence regularization algorithm using a nonlocal operator (mCORNOL) is proposed. METHODS mCORNOL is formed by exploiting the scale-control capacity of nonlocal operators in image structure measurement. By changing the scale of the structure measurement, the smoothing constraint scales can be adjusted. Starting with a large value, mCORNOL gradually reduces the smoothing constraint scale until it reaches the same level as the noise. Therefore, the large-scale smoothing constraint dominates the first few iterations of the reconstruction and removes aliasing artifacts as well as fine structures. In the following iterations, the smoothing constraint is restricted to a smaller and smaller scale, so the fidelity term progressively dominates and restores lost structures. Thus, aliasing artifact removal and structure preservation can be decoupled and achieved sequentially, which alleviates the conflicts between them. RESULTS Numerical simulation and in vivo experiment results demonstrate the superiority of mCORNOL for aliasing artifact suppression and image structure preservation at high reduction factors, compared to SENSE, Total Variation and the original CORNOL reconstruction. CONCLUSIONS mCORNOL reconstruction provides an effective way to improve image quality for undersampled VDS acquisitions.
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Affiliation(s)
- Sheng Fang
- Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University
| | - Lyu Li
- Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, China
| | - Wenchuan Wu
- Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, China
| | - Juan Wei
- Philips Research Asia, Shanghai, China
| | | | - Dong-Hyun Kim
- Department of Electrical and Electronic Engineering, Yonsei University, Seoul, Korea
| | - Chun Yuan
- Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, China; Department of Radiology, University of Washington, Seattle, Washington, USA
| | - Hua Guo
- Center for Biomedical Imaging Research, Department of Biomedical Engineering, Tsinghua University, Beijing, China.
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Yang B, Yuan M, Ma Y, Zhang J, Zhan K. Local sparsity enhanced compressed sensing magnetic resonance imaging in uniform discrete curvelet domain. BMC Med Imaging 2015; 15:28. [PMID: 26253135 PMCID: PMC4528851 DOI: 10.1186/s12880-015-0065-0] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2014] [Accepted: 06/16/2015] [Indexed: 11/20/2022] Open
Abstract
Background Compressed sensing(CS) has been well applied to speed up imaging by exploring image sparsity over predefined basis functions or learnt dictionary. Firstly, the sparse representation is generally obtained in a single transform domain by using wavelet-like methods, which cannot produce optimal sparsity considering sparsity, data adaptivity and computational complexity. Secondly, most state-of-the-art reconstruction models seldom consider composite regularization upon the various structural features of images and transform coefficients sub-bands. Therefore, these two points lead to high sampling rates for reconstructing high-quality images. Methods In this paper, an efficient composite sparsity structure is proposed. It learns adaptive dictionary from lowpass uniform discrete curvelet transform sub-band coefficients patches. Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data. It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l1 sparse regularization and constraining k-space measurements fidelity. A new augmented Lagrangian method is then introduced to optimize the reconstruction model. It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm. Results Experimental results on in vivo data show that the proposed method obtains high-quality reconstructed images. The reconstructed images exhibit the least aliasing artifacts and reconstruction error among current CS MRI methods. Conclusions The proposed sparsity structure can fit and provide hierarchical sparsity for magnetic resonance images simultaneously, bridging the gap between predefined sparse representation methods and explicit dictionary. The new augmented Lagrangian method provides solutions fully complying to the composite regularization reconstruction model with fast convergence speed.
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Affiliation(s)
- Bingxin Yang
- School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China.
| | - Min Yuan
- School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China.
| | - Yide Ma
- School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China.
| | - Jiuwen Zhang
- School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China.
| | - Kun Zhan
- School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China.
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Li Q, Qu X, Liu Y, Guo D, Lai Z, Ye J, Chen Z. Accelerating patch-based directional wavelets with multicore parallel computing in compressed sensing MRI. Magn Reson Imaging 2015; 33:649-58. [PMID: 25620521 DOI: 10.1016/j.mri.2015.01.014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2014] [Revised: 08/23/2014] [Accepted: 01/18/2015] [Indexed: 10/24/2022]
Abstract
Compressed sensing MRI (CS-MRI) is a promising technology to accelerate magnetic resonance imaging. Both improving the image quality and reducing the computation time are important for this technology. Recently, a patch-based directional wavelet (PBDW) has been applied in CS-MRI to improve edge reconstruction. However, this method is time consuming since it involves extensive computations, including geometric direction estimation and numerous iterations of wavelet transform. To accelerate computations of PBDW, we propose a general parallelization of patch-based processing by taking the advantage of multicore processors. Additionally, two pertinent optimizations, excluding smooth patches and pre-arranged insertion sort, that make use of sparsity in MR images are also proposed. Simulation results demonstrate that the acceleration factor with the parallel architecture of PBDW approaches the number of central processing unit cores, and that pertinent optimizations are also effective to make further accelerations. The proposed approaches allow compressed sensing MRI reconstruction to be accomplished within several seconds.
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Affiliation(s)
- Qiyue Li
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance Research, Xiamen University, Xiamen 361005, China; Department of Communication Engineering, Xiamen University, Xiamen 361005, China
| | - Xiaobo Qu
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance Research, Xiamen University, Xiamen 361005, China.
| | - Yunsong Liu
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance Research, Xiamen University, Xiamen 361005, China
| | - Di Guo
- School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, China
| | - Zongying Lai
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance Research, Xiamen University, Xiamen 361005, China; Department of Communication Engineering, Xiamen University, Xiamen 361005, China
| | - Jing Ye
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance Research, Xiamen University, Xiamen 361005, China
| | - Zhong Chen
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance Research, Xiamen University, Xiamen 361005, China; Department of Communication Engineering, Xiamen University, Xiamen 361005, China
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Qu X, Hou Y, Lam F, Guo D, Zhong J, Chen Z. Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator. Med Image Anal 2014; 18:843-56. [PMID: 24176973 DOI: 10.1016/j.media.2013.09.007] [Citation(s) in RCA: 234] [Impact Index Per Article: 23.4] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2013] [Revised: 08/24/2013] [Accepted: 09/23/2013] [Indexed: 11/29/2022]
Affiliation(s)
- Xiaobo Qu
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen 361005, China.
| | - Yingkun Hou
- School of Information Science and Technology, Taishan University, Taian 271021, China
| | - Fan Lam
- Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
| | - Di Guo
- School of Computer and Information Engineering, Xiamen University of Technology, Xiamen 361024, China
| | - Jianhui Zhong
- Department of Imaging Sciences, University of Rochester, Box 648, Elmwood Avenue, Rochester, NY 14642-8648, USA
| | - Zhong Chen
- Department of Electronic Science, Fujian Provincial Key Laboratory of Plasma and Magnetic Resonance, State Key Laboratory of Physical Chemistry of Solid Surfaces, Xiamen University, Xiamen 361005, China.
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Ning B, Qu X, Guo D, Hu C, Chen Z. Magnetic resonance image reconstruction using trained geometric directions in 2D redundant wavelets domain and non-convex optimization. Magn Reson Imaging 2013; 31:1611-22. [DOI: 10.1016/j.mri.2013.07.010] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2013] [Revised: 07/03/2013] [Accepted: 07/21/2013] [Indexed: 11/24/2022]
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Abstract
PURPOSE To introduce a linear shift-invariant relationship between the partial derivatives of k space signals acquired using multichannel receive coils and to demonstrate that k space derivatives can be used for image unwrapping. METHODS Fourier transform of k space derivatives contains information on the spatial origins of aliased pixels; therefore, images can be reconstructed by k space derivatives. Fully sampled phantom and brain images acquired at 3 T using a standard eight channel receive coil were used to validate the k space derivatives theorem by unwrapping aliased images. RESULTS Derivative encoding leads to new methods for parallel imaging reconstruction in both k space and image domains. Noise amplification in sensitivity encoding image reconstruction, which is considered to produce the optimal SNR, can be further reduced using k space derivative encoding without making any assumptions on the characteristics of the images to be reconstructed. CONCLUSIONS This work demonstrated that the partial derivative of the k space signal acquired from one coil with respect to one direction can be expressed as a sum of partial derivatives of signals from multiple coils with respect to the perpendicular k space direction(s). This relationship between the partial derivatives of k space signals is linear and shift-invariant in the Cartesian coordinate system.
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Affiliation(s)
- Jun Shen
- National Institute of Mental Health Intramural Research Program, NIH, Bethesda, MD 20892-1527, USA.
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