Abstract
Magnetic particle tracking is a recently developed technology that can measure the translation and rotation of a particle in an opaque environment like a turbidity flow and fluidized-bed flow. The trajectory reconstruction usually relies on numerical optimization or filtering, which involve artificial parameters or thresholds. Existing analytical reconstruction algorithms have certain limitations and usually depend on the gradient of the magnetic field, which is not easy to measure accurately in many applications. This paper discusses a new semi-analytical solution and the related reconstruction algorithm. The new method can be used for an arbitrary sensor arrangement. To reduce the measurement uncertainty in practical applications, deep neural network (DNN)-based models are developed to denoise the reconstructed trajectory. Compared to traditional approaches such as wavelet-based filtering, the DNN-based denoisers are more accurate in the position reconstruction. However, they often over-smooth the velocity signal, and a hybrid method that combines the wavelet and DNN model provides a more accurate velocity reconstruction. All the DNN-based and wavelet methods perform well in the orientation reconstruction.
Highlights
Optical-based particle tracking technologies provide crucial knowledge and experimental guidance in the study of turbulence and complex flows [1, 2]
We evaluated the reconstruction performance by comparing it with pure Wavelet transform (WT), convolutional neural networks (CNN) and gated recurrent units (GRU) denoising methods
This indicates that the deep neural network (DNN) model alone may not be able to reduce the noise without trimming off the velocity signal, which is a limitation of the neural network approach when directly applied on highly noisy data without any preprocessing
Summary
Optical-based particle tracking technologies provide crucial knowledge and experimental guidance in the study of turbulence and complex flows [1, 2]. A scalar triangulation and ranging (STAR) method was proposed for real-time magnetic target localization [24], and this method was modified multiple times [25] These analytical methods possess a clear physical meaning and have been used in practical problems. The CNN-based methods are typically implemented in an encoding-decoding fashion, where latent features are first extracted by the encoder layers and details are compensated by the decoder layers to recover a clean version of the original signal [37] Another popular trend is to utilize RNN to preserve historical information and temporal coherence while denoising, which is effective when handling sequential data, e.g., time series [38]. We design a novel denoising algorithm by leveraging both unsupervised WT and supervised RNN models with gated recurrent units (GRU), aiming to reduce the noise of the particle trajectory and orientation time series.
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