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An Efficient Framework for Compressed Sensing

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An Efficient Framework for Compressed Sensing An Efficient Framework for Compressed Sensing Reconstruction of Highly Accelerated Dynamic Cardiac MRI Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Samuel T. Ting, B.S., M.S. Graduate Program in Biomedical Engineering The Ohio State University 2016 Dissertation Committee: Professor Orlando P. Simonetti, Advisor Professor Lee C. Potter Professor Rizwan Ahmad Professor Jun Liu c Copyright by Samuel T. Ting 2016 Abstract The research presented in this work seeks to develop, validate, and deploy prac- tical techniques for improving diagnosis of cardiovascular disease. In the philosophy of biomedical engineering, we seek to identify an existing medical problem having significant societal and economic effects and address this problem using engineering approaches. Cardiovascular disease is the leading cause of mortality in the United States, ac- counting for more deaths than any other major cause of death in every year since 1900 with the exception of the year 1918. Cardiovascular disease is estimated to account for almost one-third of all deaths in the United States, with more than 2150 deaths each day, or roughly 1 death every 40 seconds. In the past several decades, a growing array of imaging modalities have proven useful in aiding the diagnosis and evaluation of cardiovascular disease, including computed tomography, single photon emission computed tomography, and echocardiography. In particular, cardiac magnetic reso- nance imaging is an excellent diagnostic tool that can provide within a single exam a high quality evaluation of cardiac function, blood flow, perfusion, viability, and edema without the use of ionizing radiation. The scope of this work focuses on the application of engineering techniques for improving imaging using cardiac magnetic resonance with the goal of improving the utility of this powerful imaging modality. ii Dynamic cine imaging, or the capturing of movies of a single slice or volume within the heart or great vessel region, is used in nearly every cardiac magnetic resonance imaging exam, and adequate evaluation of cardiac function and morphology for diag- nosis and evaluation of cardiovascular disease depends heavily on both the spatial and temporal resolution as well as the image quality of the reconstruction cine images. This work focuses primarily on image reconstruction techniques utilized in cine imag- ing; however, the techniques discussed are also relevant to other dynamic and static imaging techniques based on cardiac magnetic resonance. Conventional segmented techniques for cardiac cine imaging require breath-holding as well as regular cardiac rhythm, and can be time-consuming to acquire. Inadequate breath-holding or irregu- lar cardiac rhythm can result in completely non-diagnostic images, limiting the utility of these techniques in a significant patient population. Real-time single-shot cardiac cine imaging enables free-breathing acquisition with significantly shortened imaging time and promises to significantly improve the utility of cine imaging for diagnosis and evaluation of cardiovascular disease. However, utility of real-time cine images depends heavily on the successful reconstruction of final cine images from undersam- pled data. Successful reconstruction of images from more highly undersampled data results directly in images exhibiting finer spatial and temporal resolution provided that image quality is sufficient. This work focuses primarily on the development, validation, and deployment of practical techniques for enabling the reconstruction of real-time cardiac cine images at the spatial and temporal resolutions and image quality needed for diagnostic utility. Particular emphasis is placed on the development of reconstruction approaches re- sulting in with short computation times that can be used in the clinical environment. iii Specifically, the use of compressed sensing signal recovery techniques is considered; such techniques show great promise in allowing successful reconstruction of highly undersampled data. The scope of this work concerns two primary topics related to signal recovery using compressed sensing: (1) long reconstruction times of these techniques, and (2) improved sparsity models for signal recovery from more highly undersampled data. Both of these aspects are relevant to the practical application of compressed sensing techniques in the context of improving image reconstruction of real-time cardiac cine images. First, algorithmic and implementational approaches are proposed for reducing the computational time for a compressed sensing reconstruction framework. Specific optimization algorithms based on the fast iterative/shrinkage al- gorithm (FISTA) are applied in the context of real-time cine image reconstruction to achieve efficient per-iteration computation time. Implementation within a code framework utilizing commercially available graphics processing units (GPUs) allows for practical and efficient implementation directly within the clinical environment. Second, patch-based sparsity models are proposed to enable compressed sensing sig- nal recovery from highly undersampled data. Numerical studies demonstrate that this approach can help improve image quality at higher undersampling ratios, en- abling real-time cine imaging at higher acceleration rates. In this work, it is shown that these techniques yield a holistic framework for achieving efficient reconstruction of real-time cine images with spatial and temporal resolution sufficient for use in the clinical environment. A thorough description of these techniques from both a theo- retical and practical view is provided { both of which may be of interest to the reader in terms of future work. iv To my family, especially little Benjamin. v Acknowledgments I would first and foremost like to thank my advisor Dr. Orlando P. Simonetti for his mentoring me and guiding me through this entire journey. His words have always been apt and timely, pointing me in the right direction throughout the course of my graduate work. I would also like to thank Dr. Yu Ding for his helpful advice during my initial exploratory years. I like to acknowledge Drs. Peter Kellman, Michael Hansen, and Hui Xue for their help with the Gadgetron. I also express my gratitude to Drs. Lee C. Potter and Rizwan Ahmad in providing helpful guidance through the forest of optimization. I would like to specifically acknowledge Debbie Scandling { thank you for helping with all the last minute scheduling of volunteers. I would also like to express my graditude to the cardiology fellows, specifically Juliana Serafim da Silveira and Jason Craft for taking the time to score images. I would also like to thank Nathan Lambda for the time he took to draw contours. To all the current students in the lab { Juliet Varghese, Ria Mazumdar, David Gross { thank you. Your presence has helped make this journey all the more exciting. I would also like to acknowledge all the past students in our group - Mihaela Jekic, Shivraman Giri, Eric Foster, Vijay Balasubramanian, Jacob Bender, Prashanth Palaniappan, Paras Parikh. I would like to thank my family, in particular my parents, for their love, care, and prayer throughout this entire journey. Thanks you for being there when I needed to talk, and for praying for me when I could not talk. vi To all the young people I have had the privilege of caring for during my journey, thank you. Little do you know that in your allowing me to care for you have I been equally well cared for. vii Vita 2004 . .B.S. Electrical Engineering, University of Washington. 2012 . .M.S. Biomedical Engineering, The Ohio State University. 2009 { present . Graduate Research Associate, The Ohio State University. Publications Research Publications S.T. Ting, P. Thavendiranathan, H. Houle, G. Pedrizzetti, S.V. Raman, M. Vannan, O.P. Simonetti. \Characterization of Vortex Flow in the Left Ventricle by Phase Con- trast Magnetic Resonance Imaging". ISMRM 18th Scientific Meeting and Exhibition, Stockholm, Sweden. May, 2010. S.T. Ting, Y. Ding, O.P. Simonetti. \Improved Real-time Blood Flow Velocity Quantification via Application of the Karhunen-Loeve Transform for Increased Signal- to-Noise Ratio". SCMR 14th Annual Scientific Sessions, Nice, France. January, 2011. S.T. Ting, Y. Ding, Y.C. Chung, O.P. Simonetti. \Noise Reduction in Real-Time Phase Velocity Images via the Karhunen-Loeve Transform". ISMRM 19th Scientific Meeting and Exhibition, Montreal, Canada. May, 2011. Y. Ding, H. Xue, R. Ahmad, S.T. Ting, O.P. Simonetti. \SC-GRAPPA: Self- constraint non-iterative GRAPPA reconstruction with closed-form solution". Medical Physics, 2012;39(12):7686-93. S.T. Ting, Y. Ding, S. Giri, O.P. Simonetti. \A SPIRiT Implementation of Steady- State First-Pass Perfusion (SSFPP): On Improving the Robustness of 3D Myocardial viii Perfusion Assessment". ISMRM Workshop on Data Sampling and Image Reconstruc- tion, Sedona, AZ, USA. February, 2013. Y. Ding, R. Ahmad, H. Xue, S.T. Ting, N. Jin, O.P. Simonetti. \Comparing Bound- ary Sharpness of of SENSE and GRAPPA". ISMRM Workshop on Data Sampling and Image Reconstruction, Sedona, AZ, USA. February, 2013. Y. Ding, H. Xue, R. Ahmad, S.T. Ting, N. Jin, L.C. Potter, O.P. Simonetti. \A Bilinear Noise Transfer Model for GRAPPA Reconstruction". ISMRM Workshop on Data Sampling and Image Reconstruction, Sedona, AZ, USA. February, 2013. S.T. Ting, Y. Ding, R. Ahmad, H. Xue, O.P. Simonetti. \Taming an Ill-Conditioned SPIRiT: Improved Iterative Image Reconstruction
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