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

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. Tw), 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.