Signal Processing and Interpretable Deep Network for Image Reconstruction

图像恢复是一个逆问题，涉及到从损坏的输入测量数据中获得高质量的图像。它与许多现实世界的应用有关，包括医学成像和显微镜。例如，用于磁共振成像（MRI）的图像恢复技术可以通过收集一部分数据并推断整个数据来有效地降低扫描成本。近年来，随着人工智能的发展，许多基于学习的方法被开发出来用于处理图像恢复问题。这些方法通过对高质量和低质量图像对的学习来构造图像恢复模型，并以较快的速度获得了有竞争力的结果。尽管基于学习的方法取得了明显的成功，但其中许多方法都是基于这样一个假设而设计的：从高质量图像到低质量图像的退化过程是已知的和线性的。然而，在现实世界的情况下，退化过程是更加复杂和未知的在大多数情况下。因此，我的研究旨在通过提出一种新的可逆框架来处理图像恢复问题，从而打破这一障碍。可逆神经网络结构的灵活性具有模拟真实世界场景中未知的非线性退化过程的潜力。此外，所提出的方法可以通过提供轻量级的内存效率模型而适合于实际使用，因为它使用恒定量的内存来计算梯度，而不管网络的深度如何。

Image restoration is an inverse problem related to obtaining a high-quality image from corrupted input measured data. It is relevant to many real-world applications including medical imaging and microscopy. For example, image restoration technology for magnetic resonance imaging (MRI) can effectively reduce the scanning cost by collecting a proportion of data and inferring the whole data. Recently, with the development of artificial intelligence, many learning-based methods were developed for handling image restoration problems. These methods construct image-restoration models by learning from high-quality and low-quality image pairs and achieve competitive results with fast speed. Despite the evident success of the learning-based methods, many of them are designed based on an assumption that the degradation process from high-quality image to low-quality image is known and linear. However, the degradation processes in real-world scenarios are more complicated and unknown in most cases. Therefore, my research aims to break this obstacle by proposing a novel invertible framework to handle image restoration problems. The flexibility of invertible neural network structure has the potential to simulate unknown, non-linear degradation processes in real-world scenarios. Furthermore, the proposed method could be suitable for practical usage by providing a lightweight memory-efficient model because it uses a constant amount of memory to compute gradients, regardless of the depth of the network.