Exponential Signal Reconstruction With Deep Hankel Matrix Factorization

Exponential function is a basic form of temporal signals, 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 severe artifacts in its spectrum, which is the Fourier transform of exponentials. Thus, reliable spectrum reconstruction is highly expected in the fast data acquisition 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 imitating the iterative process in the model-based state-of-the-art exponentials' reconstruction method with the 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 than compared methods.

Automated summary

Exponential function is a common form of temporal signals, and acquiring this signal quickly is an important problem in signal processing. In this study, we propose a deep learning method that mimics the iterative process in the model-based exponentials' reconstruction method, and the neural network structure is designed accordingly. Experimental results demonstrate that this method achieves more accurate and reliable data acquisition and signal reconstruction compared to other methods.