# Self-Supervised Physics-Guided Deep Learning for Solving Inverse Problems in Imaging

2022-03

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Self-Supervised Physics-Guided Deep Learning for Solving Inverse Problems in Imaging

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2022-03

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Inverse problems in computational imaging seek to recover an unknown image of interest from observed measurements acquired using a known forward model. These inverse problems are often ill-conditioned, requiring some form of regularization. The corresponding objective function for inverse problems in computational imaging can often be solved using iterative optimization approaches that alternate between two sub-problems that enforce data consistency and promote the regularization approach, respectively. Such inverse problems arise in a multitude of imaging modalities, in particular in magnetic resonance imaging (MRI), which is the main application area for this thesis. Lengthy scan times remain a challenge in MRI, thus accelerating MRI scans has remained an open research problem over decades. Conventional accelerated MRI techniques acceleration rate is limited by noise amplification and residual artifacts. Recently, deep learning has emerged as an alternative approach for accelerated MRI. Among deep learning techniques, physics-guided deep learning (PG-DL) has drawn great interest, as it incorporates the known physical forward model into the network architecture. PG-DL unrolls a conventional iterative algorithm for solving a regularized least squares problem for a fixed number of iterations, and replaces the proximal operation corresponding to the regularizer implicitly with neural networks. These unrolled networks are trained end-to-end, with the goal of minimizing the difference between the network output and the corresponding reference data. Most of the existing deep learning approaches in MRI reconstruction are based on supervised learning, which requires ground-truth/ fully-sampled data for training. However, acquisition of fully-sampled data is infeasible in many applications due to physiological constraints, such as organ motion, or physical constraints, such as signal decay. In several other scenarios, such as high-resolution anatomical brain imaging, it is impractical to acquire fully-sampled datasets as the scan time becomes extremely lengthy. Therefore, enabling the training of PG-DL reconstruction without fully-sampled data is essential for the integration of deep learning reconstruction into clinical MRI practice. The present thesis introduces novel frameworks to enable the training of deep learning reconstruction methods for inverse imaging problems in the absence of ground-truth/fully-sampled data. First, we introduce self-supervised learning via data undersampling (SSDU) approach to enable database training without fully-sampled data. Succinctly, SSDU partitions available measurements into two disjoint sets. One of these sets is used in the data consistency units of the unrolled network, while the other is used to define the loss in the measurement domain. Subsequently, we extend SSDU for processing 3D datasets and provide solutions for GPU memory constraints and data scarcity issues faced in 3D processing. To cope with potential performance degradation at very high acceleration rates, we develop a multi-mask self-supervised learning approach, which retrospectively splits available measurements into multiple 2-tuples of disjoint sets to perform training and define a loss function. Furthermore, we introduce a zero-shot self-supervised learning approach to enable training from a single scan/sample without any external training databases. ZS-SSL partitions the available measurements from a single scan into three disjoint sets. Two of these sets are used to enforce data consistency and define loss during training for self-supervision, while the last set serves to self-validate, establishing an early stopping criterion. Finally, we introduce a self-supervised learning algorithm for referenceless image denoising. Self-supervised deep learning algorithms split the pixels for each image into two disjoint sets to perform training and defining loss. In existent self-supervised denoising approaches which are purely data-driven, the set of pixels used as input to the network is not re-utilized in the end-to-end training since the network is only comprised of a neural network. Reusing the pixels within the network would promote consistency with acquired measurements, thus leading to a more robust and improved denoising performance. To tackle this challenge, we build upon existent self-supervised learning algorithms and recast the denoising problem into a regularized image inpainting framework which allows use of algorithm unrolling for denoising.

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University of Minnesota Ph.D. dissertation. 2022. Major: Electrical Engineering. Advisor: Mehmet Akcakaya. 1 computer file (PDF); 176 pages.

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Yaman, Burhaneddin. (2022). Self-Supervised Physics-Guided Deep Learning for Solving Inverse Problems in Imaging. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/227925.

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