Improve robustness to mismatched sampling rate: An alternating deep low-rank approach for exponential function reconstruction and its biomedical magnetic resonance applications

Abstract

Undersampling accelerates signal acquisition at the expense of introducing artifacts. Removing these artifacts is a fundamental problem in signal processing and this task is also called signal reconstruction. Through modeling signals as the superimposed exponential functions, deep learning has achieved fast and high-fidelity signal reconstruction by training a mapping from the undersampled exponentials to the fully sampled ones. However, the mismatch, such as undersampling rates (25 % vs. 50 %), anatomical region (knee vs. brain), and contrast configurations (PDw vs. T₂w), between the training and target data will heavily compromise the reconstruction. To overcome this limitation, we propose Alternating Deep Low-Rank (ADLR), which combines deep learning solvers and classic optimization solvers. Experimental validation on the reconstruction of synthetic and real-world biomedical magnetic resonance signals demonstrates that ADLR can effectively alleviate the mismatch issue and achieve lower reconstruction errors than state-of-the-art methods.