Deep neural networks (DNNs) have shown their power in various fields. For many tasks in image and signal processing, DNNs incorporated with task-oriented physical laws will provide more robust tools than using the general framework of DNNs.

In the first part of the thesis, we develop an elastic interaction-based loss function for medical image segmentation. Our proposed loss function for the deep neural network considers the elastic interaction between the predicted region and ground truth. Under the supervision of the proposed loss, the boundary of the prediction is attracted strongly by the object boundary and tends to stay connected. Experimental results show that our method improves considerably compared to commonly used pixel-wise loss functions and other recent loss functions on t...[ Read more ]

Deep neural networks (DNNs) have shown their power in various fields. For many tasks in image and signal processing, DNNs incorporated with task-oriented physical laws will provide more robust tools than using the general framework of DNNs.

In the first part of the thesis, we develop an elastic interaction-based loss function for medical image segmentation. Our proposed loss function for the deep neural network considers the elastic interaction between the predicted region and ground truth. Under the supervision of the proposed loss, the boundary of the prediction is attracted strongly by the object boundary and tends to stay connected. Experimental results show that our method improves considerably compared to commonly used pixel-wise loss functions and other recent loss functions on three retinal vessel segmentation datasets, DRIVE, STARE, and CHASEDB1.

In the second part, we present a hierarchical latent variable model with a global context to capture the long-term dependencies inside images for lossless image compression. The global context is summarized by the shared latent variables between patches which are constructed by an differentiable unsupervised clustering module. Experimental results show that our global context benefits the accurate probability modeling and improves compression ratio compared to multiple engineered codecs and latent variable models on three high-resolution image datasets.

Finally, we develop an operator-splitting-based neural network to solve evolutionary partial differential equations (PDEs). Such non-black-box network design is constructed from the physical rules and operators governing the underlying dynamics contains learnable parameters and is thus more flexible than the standard operator splitting scheme. To validate the particular structure inside DOSnet, we take the linear PDEs as the benchmark and explain the weight behavior theoretically. Furthermore, to demonstrate the advantages of our new AI-enhanced PDE solver, we also apply DOSnet to the Allen-Cahn equation and nonlinear Schrodinger equation (NLSE) which have important applications in signal processing for modern optical fiber transmission systems.