Image Reconstruction from Sparse Data

Thursday 15 May 2014

Brian E. Moore¹, Rajesh R. Nadakuditi¹, and Jeffrey A. Fessler^1
1Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, United States

Low-rank plus sparse matrix decomposition algorithms have seen fruitful application in dynamic contrast-enhanced MRI because the data is well modeled as the superposition of a low-rank static background and temporally sparse dynamic contrast enhancement. In this setting, we propose a novel algorithm that replaces the standard nuclear norm with a recently discovered optimal rank regularizer from random matrix theory. This regularizer preserves the quality of high signal-to-noise ratio image features while maintaining data compressibility, resulting in better qualitative and quantitative image reconstruction than existing nuclear norm techniques. We substantiate these claims on undersampled multicoil cardiac perfusion MRI data.

Dan Zhu¹, Martin Uecker², Joseph Y Cheng³, Zhongyuan Bi¹, Kui Ying⁴, and Michael Lustig^2
1Biomedical Engineering, Tsinghua University, Beijing, China, ²Electrical Engineering and Computer Sciences, University of California, Berkeley, California, United States, ³Electrical Engineering, Stanford University, California, United States, ⁴Department of Engineering Physics, Tsinghua University, Beijing, China

The goal of this work is to develop a practical calibration method for parallel MRI which is robust against both under-sampling and corruption of the calibration data. Previously, it has been demonstrated that robust low-rank matrix completion can reconstruct corrupted and under-sampled k-space data without specific auto-calibration data (ACS). Here, we show a generalized formulation for motion-robust auto-calibration and reconstruction from under-sampled data that is incorporated into ESPIRiT. The method is general and can incorporate navigation information when available. The feasibility of the method was demonstrated in simulation and in-vivo experiments.

Ricardo Otazo¹, Thomas Koesters¹, Emmanuel Candès², and Daniel K Sodickson^1
1Bernard and Irene Schwartz Center for Biomedical Imaging, Department of Radiology, New York University School of Medicine, New York, NY, United States, ²Departments of Mathematics and Statistics, Stanford University, Stanford, CA, United States

A non-rigid motion model is incorporated into the low-rank plus sparse (L+S) reconstruction approach for free-breathing accelerated dynamic MRI with separation of background and dynamic components. The motion operator registers the time-series of images, which improves low-rank and sparsity conditions along the temporal domain and enhances temporal fidelity in the reconstructed images. The motion-guided L+S reconstruction approach is tested in prospectively undersampled dynamic cardiac and abdominal data sets acquired during free-breathing.

Bo Zhao¹, Aiqi Sun², Ke Ma², Rui Li², Anthony Christodoulou¹, Chun Yuan^2,3, and Zhi-Pei Liang^1
1Department of Electrical and Computer Engineering and Beckman Institute, University of Illinois at Urbana-Champaign, Urbana, IL, United States,²Department of Biomedical Engineering and Center for Biomedical Imaging Research, Tsinghua University, Beijing, China, ³Department of Radiology, University of Washington, WA, United States

A novel method is presented for real-time phase contrast (PC) cardiovascular flow imaging. It integrates a real-time data acquisition scheme (without ECG gating and respiration control) with constrained reconstruction using joint low-rank and sparsity constraints. It achieves a temporal resolution of 34.4 msec and spatial resolution of 2.58 mm in a 2D real-time flow imaging experiment with three velocity encoding directions. The method should prove useful for real-time cardiovascular flow imaging.

Enhao Gong¹ and John M Pauly^1
1Electrical Engineering, Stanford University, Stanford, CA, United States

Parallel Imaging (PI) and Compressed Sensing (CS) enable MR acceleration by exploiting channel-correlation and sparsity. However, the acceleration capability is limited by channel-encoding, increased noise and blurred details. In this work, a novel algorithm is proposed to further improve the undersampled MRI reconstruction by exploiting the correlation between image details in different bands of spatial-frequencies. Dictionaries of image patches in different spatial-frequency bands were learned from database and undersampled MR images were reconstructed by solving as a sparse representation of the dictionary. The proposed algorithm demonstrated great advantages and were integrated with PI-CS to further push acceleration.

Jingwei Zhuo^1,2 and Justin P. Haldar^1
1Signal and Image Processing Institute, University of Southern California, Los Angeles, CA, United States, ²Electronic Engineering, Tsinghua University, China

This work presents P-LORAKS, a novel approach to constrained image reconstruction from parallel imaging data. Similar to the original LORAKS (low-rank matrix modeling of local k-space neighborhoods) method, P-LORAKS uses low-rank matrix models to generate parsimonious constrained reconstruction representations of images with limited spatial support and/or slowly varying phase. Combining LORAKS with parallel imaging data leads to further improvements in image reconstruction quality. Results are illustrated with real data, where P-LORAKS compares favorably to existing parallel imaging methods like SPIRiT and SAKE.

Johannes F. M. Schmidt¹ and Sebastian Kozerke^1,2
1Institute for Biomedical Engineering, University and ETH Zurich, Zurich, Switzerland, ²Imaging Sciences and Biomedical Engineering, King's College London, London, United Kingdom

MR image reconstruction exploiting nonlinear transforms has successfully been implemented using projections onto principal components in a high-dimensional kernel feature space, employing kernel PCA. Image quality was found to improve considerably relative to standard CS reconstruction with wavelet and finite-differences transforms.

Yasir Q Mohsin¹, Zhili Yang², Sajan Goud Lingala³, and Mathews Jacob^4
1Electrical Eng, University of Iowa, Iowa City, IA, United States, ²Electrical Engineering, Univeristy of Rochester, NY, United States, ³BME, University of Iowa, IA, United States, ⁴Electrical Eng, University of Iowa, IA, United States

The focus of this abstract is to recover dynamic MRI data from highly under-sampled measurements. Compressed sensing schemes that exploit sparsity in Fourier and gradient domains have enjoyed a lot of success in breath-held cardiac MRI. However, these schemes often result in un-acceptable spatio-temporal blurring and residual alias artifacts, when applied to free breathing cardiac MRI with or without cardiac gating. The main reason is the high inter-frame motion, often introduced by respiration. Methods that combine motion estimation and compensation (ME-MC) have been shown to improve the results in this context, but they come with considerably increased computational complexity. In addition, the joint estimation of the motion model parameters and the signal involves a complex non-convex optimization criterion, which is often difficult to solve. Our main objective is to introduce a novel framework for motion-compensated dynamic MR image recovery that does not suffer from the above mentioned drawbacks.

Yanjie Zhu¹, Qiegen Liu², Qinwei Zhang³, Jing Yuan³, and Dong Liang^1
1Paul C. Lauterbur Research Centre for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, Guangdong, China, ²Department of Electronic Information Engineering, Nanchang University, Nanchang, Jiangxi, China, ³Department of Imaging and Interventional Radiology, The Chinese University of Hong Kong, Shatin, Hong Kong

Long scanning time hinders the widespread application of T1¦Ñ in clinics. A new approach utilizing the advantages of both fixed and adaptive transform is proposed to accelerate T1¦Ñ imaging under the framework of compressed sensing. Specifically, PCA is applied first along the parameter direction, and the dictionary learning technique is used to reconstruct the PC coefficients. Additionally, a coherence constraint is introduced to guarantee the sparse representation ability of learned dictionary. Experimental results demonstrate that the proposed method can improve the accuracy of estimated T1¦Ñ map compared with the one without coherence constraint and conventional dictionary learning based method.

Suhyung Park¹, Chul-Ho Sohn², and Jaeseok Park^1
1Department of Brain and Cognitive Engineering, Korea University, Seoul, Seoul, Korea, ²Department of Radiology, Seoul National University Hospital, Seoul, Korea

Compressed sensing (CS) [1,2] exploits the sparsity of an image in a transform domain. However, it has been shown that CS suffers particularly from loss of low contrast image features with increasing reduction factor. To retain image details, in this work we introduce a novel CS algorithm exploiting feature-based complementary dual decomposition with joint estimation of local scale mixture (LSM) model and images. Images are decomposed into dual block sparse components: total variation (TV) for piecewise smooth parts and wavelets for residuals. The LSM model parameters of residuals in the wavelet domain are estimated and then employed as a regional constraint in spatially adaptive reconstruction of high frequency subbands to restore image details missing in piecewise smooth parts. Experiments demonstrate the superior performance of the proposed method in preserving low-contrast image features even at high reduction factors.