论文标题
用深Hankel矩阵分解的指数信号重建
Exponential Signal Reconstruction with Deep Hankel Matrix Factorization
论文作者
论文摘要
指数是一种基本信号形式，如何快速获取此信号是信号处理中的基本问题和前沿之一。为了实现这一目标，可以获取部分数据，但会导致其频谱中的严重伪像，这是指数的傅立叶变换。因此，在许多应用中的快速采样（例如化学，生物学和医学成像）中，高度期望可靠的频谱重建。在这项工作中，我们提出了一种深度学习方法，其神经网络结构的设计是通过在基于模型的最先进的指数重建方法中以低级别的Hankel矩阵分解来设计的。通过对合成数据和现实的生物磁共振信号的实验，我们证明了新方法会产生更低的重建误差，并保留低强度信号。
Exponential is a basic signal form, and how to fast acquire this signal is one of the fundamental problems and frontiers in signal processing. To achieve this goal, partial data may be acquired but result in the severe artifacts in its spectrum, which is the Fourier transform of exponentials. Thus, reliable spectrum reconstruction is highly expected in the fast sampling in many applications, such as chemistry, biology, and medical imaging. In this work, we propose a deep learning method whose neural network structure is designed by unrolling the iterative process in the model-based state-of-the-art exponentials reconstruction method with low-rank Hankel matrix factorization. With the experiments on synthetic data and realistic biological magnetic resonance signals, we demonstrate that the new method yields much lower reconstruction errors and preserves the low-intensity signals much better.
