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Minimally Invasive Surgeries can benefit from having miniaturized sensors on surgical graspers to provide additional information to the surgeons. In this work, a 6 mm ultrasound transducer was added to a surgical grasper, intended to measure acoustic properties of the tissue. However, the ultrasound sensor has a ringing artifact arising from the decaying oscillation of its piezo element, and at short travel distances, the artifact blends with the acoustic echo. Without a method to remove the artifact from the blended signal, this makes it impossible to measure one of the main characteristics of an ultrasound waveform – Time of Flight. In this paper, six filtering methods to clear the artifact from the ultrasound waveform were compared: Bandpass filter, Adaptive Least Mean Squares (LMS) filter, Spectrum Suppression (SPS), Recurrent Neural Network (RNN), Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU). Following each filtering method, four time of flight extraction methods were compared: Magnitude Threshold, Envelope Peak Detection, Cross-correlation and Short-time Fourier Transform (STFT). The RNN with Cross-correlation method pair was shown to be optimal for this task, performing with the root mean square error of 3.6 %. 

Recurrent neural networks (RNNs) have been successfully applied to a variety of problems involving sequential data, but their optimization is sensitive to parameter initialization, architecture, and optimizer hyperparameters. Considering RNNs as dynamical systems, a natural way to capture stability, i.e., the growth and decay over long iterates, are the Lyapunov Exponents (LEs), which form the Lyapunov spectrum. The LEs have a bearing on stability of RNN training dynamics since forward propagation of information is related to the backward propagation of error gradients. LEs measure the asymptotic rates of expansion and contraction of non-linear system trajectories, and generalize stability analysis to the time-varying attractors structuring the non-autonomous dynamics of data-driven RNNs. As a tool to understand and exploit stability of training dynamics, the Lyapunov spectrum fills an existing gap between prescriptive mathematical approaches of limited scope and computationally-expensive empirical approaches. To leverage this tool, we implement an efficient way to compute LEs for RNNs during training, discuss the aspects specific to standard RNN architectures driven by typical sequential datasets, and show that the Lyapunov spectrum can serve as a robust readout of training stability across hyperparameters. With this exposition-oriented contribution, we hope to draw attention to this under-studied, but theoretically grounded tool for understanding training stability in RNNs.