Scattering Parameters Parameterization

Introduction

Research Focus:

• Inverse problem: given dataset $\rightarrow$ input parameters.
• Simulated microwave transmission data originally used to detect intracranial bleeding after trauma or stroke

Sixteen antennas were placed around the head model used in the simulations.

Dataset

Dataset Description:

• Scattering parameters (S-parameters) for antenna pairs.
• 1000 pre-simulated healthy samples
• S-parameters from 16 antennas $\rightarrow$ 136 complex-valued curves.
• Antennas 2, 6, 7, 11, and 14 are utilized as amplitude components.

S-parameter $S_{26}$ representing coupling between antennas 2 & 6 for three samples from the dataset.

Input Parameters:

• Rescaling of head in the x, y, & z dimensions.
• Variation in hair layer thickness.

Method

Three Models Employed:

1. Basic Feedforward Neural Network
2. RNN incorporating a Long Short-Term Memory (LSTM)
3. RNN incorporating a Gated Recurrent Unit (GRU)

Shared Network Settings:

• Data split: 80% training & 20% validation.
• Optimizer: Adam
• Loss function: mean squared error (MSE)
• Epochs: 10.
• Batch size: 32.

Multiple Train-Test Splits:

• Iterations: 5.
• Validation with Average MSE & standard deviation.

Results -- Single Train-Test Splits

Example of Predicted & True Label of Different Models

Label	X	Y	Z	Hair
Predicted Basic	0.827	0.848	0.796	0.938
Predicted LSTM	0.840	0.837	0.814	1.094
Predicted GRU	0.862	0.812	0.852	0.973
True	0.844	0.851	0.834	1.0

Training & Validation Results for Different Models

Certainly, here's the information organized into tables:

Training & Validation Results for Different Models

Metric	Basic	LSTM	GRU
Training -- 1st Epoch	0.3311	0.1941	0.2465
Validation -- 1st Epoch	0.0774	0.0256	0.0488
Training -- 10th Epoch	0.0053	0.0017	0.0024
Validation -- 10th Epoch	0.0054	0.0019	0.0030

Metric	Basic	LSTM	GRU
Average Euclidean Distance	0.1219	0.0703	0.0925

Results -- Multiple Train-Test Splits

Validation of Multiple Train-Test Splits

Model	Average MSE for 5 Splits	Standard Deviation
Basic	0.0059	0.0021
LSTM	0.0052	0.0016
GRU	0.0048	0.0007

• Final result: GRU outperforms LSTM and Basic Model

Prospective Research

• Utilize data from all 16 antennas.
• Dataset contains bleeding samples $\rightarrow$ incorporate these samples.
• Explore data augmentation & transformers.

References

• Fhager, A. (2003). Microwave-Based Detection of Traumatic Intracranial Hematomas.
• Goodfellow, I., Bengio, Y., Courville, A., & Bengio, Y. (2016). Deep Learning (Vol. 1). MIT press Cambridge.