Efficient Generalizable Deep Learning for Inverse Problems

Inverse problems are common in daily life. In recent years, the interest in developing deep learning for inverse problems has increased greatly. However, since deep learning is known as a black box model, it remains a challenging topic to efficiently boost its generalizability beyond training data. My work thereby focuses on developing end-to-end deep learning methods of high efficiency and generalizability for solving inverse problems. I investigate two kinds of inverse problems: measurement-to-image inverse problems, such as ultrasound transmission tomography (UTT), and image-to-image inverse problems, such as image denoising. 

Specifically, for fully data-driven UTT image reconstruction, I investigate three aspects of deep learning methods: data generation, data preprocessing, and neural network architecture. I develop and test a series of data generation and data augmentation techniques, as well as network architecture improvement techniques including multiple down- and up-samplings, integration of Fourier transform, and preprocessing network to enhance efficiently neural networks' imaging quality and generalizability to real measurement data. The experiments on UTT image reconstruction with measurement data from two real machines prove the effectiveness of the proposed methods.

As for image denoising, I propose an efficient non-parameter-sharing group equivariant convolutional neural network by using a weighted aggregation of Monte Carlo sampled decomposed filters. The proposed network serves as an efficient alternative to standard CNN layers and therefore can be easily integrated into the state-of-the-art deep neural networks. The experiments on image classification and denoising of synthetic and real noisy images show the superior efficiency of the proposed networks to the state-of-the-art standard CNNs and parameter-sharing group equivariant CNNs.