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How to do Physics-based Learning

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 Added by Michael Kellman
 Publication date 2020
and research's language is English




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The goal of this tutorial is to explain step-by-step how to implement physics-based learning for the rapid prototyping of a computational imaging system. We provide a basic overview of physics-based learning, the construction of a physics-based network, and its reduction to practice. Specifically, we advocate exploiting the auto-differentiation functionality twice, once to build a physics-based network and again to perform physics-based learning. Thus, the user need only implement the forward model process for their system, speeding up prototyping time. We provide an open-source Pytorch implementation of a physics-based network and training procedure for a generic sparse recovery problem

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Purpose: To improve reconstruction fidelity of fine structures and textures in deep learning (DL) based reconstructions. Methods: A novel patch-based Unsupervised Feature Loss (UFLoss) is proposed and incorporated into the training of DL-based reconstruction frameworks in order to preserve perceptual similarity and high-order statistics. The UFLoss provides instance-level discrimination by mapping similar instances to similar low-dimensional feature vectors and is trained without any human annotation. By adding an additional loss function on the low-dimensional feature space during training, the reconstruction frameworks from under-sampled or corrupted data can reproduce more realistic images that are closer to the original with finer textures, sharper edges, and improved overall image quality. The performance of the proposed UFLoss is demonstrated on unrolled networks for accelerated 2D and 3D knee MRI reconstruction with retrospective under-sampling. Quantitative metrics including NRMSE, SSIM, and our proposed UFLoss were used to evaluate the performance of the proposed method and compare it with others. Results: In-vivo experiments indicate that adding the UFLoss encourages sharper edges and more faithful contrasts compared to traditional and learning-based methods with pure l2 loss. More detailed textures can be seen in both 2D and 3D knee MR images. Quantitative results indicate that reconstruction with UFLoss can provide comparable NRMSE and a higher SSIM while achieving a much lower UFLoss value. Conclusion: We present UFLoss, a patch-based unsupervised learned feature loss, which allows the training of DL-based reconstruction to obtain more detailed texture, finer features, and sharper edges with higher overall image quality under DL-based reconstruction frameworks.
Deep learning (DL) has emerged as a tool for improving accelerated MRI reconstruction. A common strategy among DL methods is the physics-based approach, where a regularized iterative algorithm alternating between data consistency and a regularizer is unrolled for a finite number of iterations. This unrolled network is then trained end-to-end in a supervised manner, using fully-sampled data as ground truth for the network output. However, in a number of scenarios, it is difficult to obtain fully-sampled datasets, due to physiological constraints such as organ motion or physical constraints such as signal decay. In this work, we tackle this issue and propose a self-supervised learning strategy that enables physics-based DL reconstruction without fully-sampled data. Our approach is to divide the acquired sub-sampled points for each scan into training and validation subsets. During training, data consistency is enforced over the training subset, while the validation subset is used to define the loss function. Results show that the proposed self-supervised learning method successfully reconstructs images without fully-sampled data, performing similarly to the supervised approach that is trained with fully-sampled references. This has implications for physics-based inverse problem approaches for other settings, where fully-sampled data is not available or possible to acquire.
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