Model-based Magnetic Resonance Image (MRI) Reconstruction and its Applications
Model-based reconstruction methods are widely used for accelerated MRI. This process primarily involves establishing a model—whether deterministic or probabilistic—for the acquired data, creating a corresponding inverse problem using prior knowledge, and finding the optimal estimator via appropriate optimization algorithms and computational methods. Commonly used priors include sparsity and low-rank, supported by theories such as compressed sensing. My goal is to investigate improved MRI image reconstruction methods and their applications.
Reference: (†: equal contribution)
[1] T. H. Kim, B. Bilgic, D. Polak, K. Setsompop, J. P. Haldar. Wave-LORAKS: Combining Wave Encoding with Structured Low-Rank Matrix Modeling for More Highly Accelerated 3D Imaging. Magnetic Resonance in Medicine, 81:1620-1633, 2019. https://onlinelibrary.wiley.com/doi/10.1002/mrm.27511
[2] R. A. Lobos, T. H. Kim, W. S. Hoge, J. P. Haldar. Navigator-free EPI Ghost Correction with Structured Low-Rank Matrix Models: New Theory and Methods. IEEE Transactions on Medical Imaging, 37:2390- 2402, 2018. https://ieeexplore.ieee.org/document/8329142/
[3] B. Bilgic† , T. H. Kim† , C. Liao, M. K. Manhard, L. L. Wald, J. P. Haldar, K. Setsompop. Improving Parallel Imaging by Jointly Reconstructing Multi-Contrast Data. Magnetic Resonance in Medicine, 80: 619-632, 2018. https://onlinelibrary.wiley.com/doi/abs/10.1002/mrm.27076 (co-1st author)
[4] T. H. Kim, K. Setsompop, J. P. Haldar. LORAKS Makes Better SENSE: Phase-Constrained Partial Fourier SENSE Reconstruction without Phase Calibration. Magnetic Resonance in Medicine, 77:1021- 1035, 2017. http://onlinelibrary.wiley.com/doi/10.1002/mrm.26182
Physics-based Deep Learning for MRI
Recent studies have delved into the application of artificial neural networks (ANNs) and deep learning (DL) techniques in MRI reconstruction. However, the direct application of generic DL models to medical imaging can potentially lead to several severe issues. A notable concern is 'hallucination,' where the ANN might generate a non-existent lesion or erase an existing one, which is particularly critical in the field of medical imaging. My aim is to develop robust ANN-based MRI reconstruction methods that exploit physics-based DL approaches to mitigate such problems.
Reference:
[5] T. H. Kim, Z. Zhang, J. Cho, B. Gagoski, J. P. Haldar, B. Bilgic. Robust multi-shot EPI with untrained artificial neural networks: Unsupervised scan-specific deep learning for blip up-down acquisition (BUDA). International Society for Magnetic Resonance in Medicine Annual Meeting, 2021, p. 224.
https://index.mirasmart.com/ISMRM2021/PDFfiles/0224.html
[6] T. H. Kim, J. P. Haldar. Learning how to interpolate Fourier data with unknown autoregressive structure. Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, 2019. https://ieeexplore.ieee.org/abstract/document/9048755
[7] T. H. Kim, J. P. Haldar. Learning-based computational MRI reconstruction without big data: From structured low-rank matrices to recurrent neural networks. Wavelets and Sparsity XVIII, Proceedings of SPIE, San Diego, 2019. https://www.spiedigitallibrary.org/conference-proceedings-of-spie/11138/1113817/Learning-based-computational-MRI-reconstruction-without-big-data--from/10.1117/12.2527584.full?SSO=1
[8] T. H. Kim, P. Garg, J. P. Haldar. LORAKI: Autocalibrated Recurrent Neural Networks for Autoregressive Reconstruction in k-Space. arXiv:1904.09390
Numerical Algorithms for ill-posed Inverse Problems
Image reconstruction is fundamentally an inverse problem that involves deriving the desired image from a limited set of observations. However, modern computers face challenges in directly computing large-scale inverse mappings due to their complexity. As a result, numerical methods have become prevalent in various fields such as optimal control, deep learning, and constrained optimization. My objective is to explore novel numerical algorithms aimed at improving computational efficiency in solving large-scale inverse problems.
[9] T. H. Kim, J. P. Haldar. Efficient Iterative Solutions to Complex-Valued Nonlinear Least-Squares Problems with Mixed Linear and Antilinear Operators. Optimization and Engineering, 23:749-768, 2022. https://link.springer.com/article/10.1007/s11081-021-09604-4
Image Quality Assessment
To evaluate image reconstruction, it is necessary to employ a metric for assessing image quality. Generally, metrics such as Mean Squared Error (MSE), Peak Signal-to-Noise Ratio (PSNR), and Structural Similarity Index (SSIM) are widely utilized when a ground-truth image is available. However, each metric measures only specific properties of images and may not comprehensively represent all image characteristics. My research aims to investigate novel techniques for image quality assessment.
[10] T. H. Kim, J. P. Haldar. The Fourier Radial Error Spectrum Plot: A more nuanced quantitative evaluation of image reconstruction quality. IEEE International Symposium on Biomedical Imaging, Washington, DC, 2018. pp. 61–64. https://ieeexplore.ieee.org/document/8363523/