Reconstruction of Missing Samples in Antepartum and Intrapartum FHR Measurements Via Mini-Batch-Based Minimized Sparse Dictionary Learning
Yefei Zhang, Zhidong Zhao, Yanjun Deng, Xiaohong Zhang, Yu Zhang
Abstract
Fetal Heart Rate (FHR), an important recording in Cardiotocography (CTG)-based fetal health status monitoring, is the only information that clinical obstetricians can directly obtain and use. A challenge, however, is that missing samples are very common in FHR due to various causes such as fetal movements and sensor malfunctions. The aim is the development of an inpainting tool which is suitable for different missing lengths <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> and various total missing percentages <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> , as well as for use in online mode. This study focused on two major impediments to existing inpainting methods: the longer the missing length, the more difficult it is to recover with mathematical methods; the reliance on tens of thousands of training samples, and the computational burden caused by full batch-based dictionary learning algorithms. We present a regularized minimization approach to signal recovery, which combines a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${{\rm{L}}_{{0}{\rm{.6}}}}{\rm{ - norm}}$</tex-math></inline-formula> minimized sparse dictionary learning algorithm (MSDL) and a model optimization strategy for using a mini-batch version for signal recovery. Using 100 FHR recordings with 2 protocols designed to simulate missing clinical data scenarios, the combined method performed favorably in terms of 5 data analysis metrics and 3 clinical indicators. Comparing 4 inpainting methods, we were able to prove the superiority of the proposed algorithm for both large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$q$</tex-math></inline-formula> and large <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> . The experimental results showed the lowest values (2.64 (MAE), 4.68 (RMSE)) when <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{Q}} = {\rm{5\% }}$</tex-math></inline-formula> with short interval lengths. The developed architecture provides a reference value for the practical application of recovering missing samples online.