Quantized Constant-Q Gabor Atoms for Sparse Binary Representations of Cyber-Physical Signatures

Area of Science:

• Signal Processing
• Machine Learning
• Sensor Technology

Background:

• Uncalibrated, heterogeneous digital sensor systems, like smartphones, generate vast amounts of data, posing significant challenges for analysis.
• Existing methods struggle to effectively quantify and extract meaningful features from diverse, noisy sensor signals.

Purpose of the Study:

• To develop novel binary metrics for quantifying cyber-physical signal characteristics.
• To introduce a standardized constant-Q variation of the Gabor atom for wavelet transforms.
• To present and evaluate continuous wavelet transform (CWT) reconstruction formulas under varying signal-to-noise ratio (SNR) conditions.

Main Methods:

• Development of binary metrics for signal quantification.
• Standardization of a constant-Q Gabor atom for wavelet analysis.
• Application of two CWT reconstruction formulas.
• Utilizing wavelet entropy and SNR parametrization for CWT coefficient weighting.

Main Results:

• A sparse superposition of Nth order Gabor atoms effectively analyzed a synthetic blast transient.
• Wavelet entropy and an entropy-like SNR parametrization proved effective as weighting functions.
• The proposed methods demonstrated robustness under different signal-to-noise ratio (SNR) conditions.

Conclusions:

• The developed methods are suitable for sparse feature extraction from heterogeneous sensor data.
• The approach facilitates dictionary-based machine learning across multiple sensor modalities.
• This work addresses challenges in analyzing data from uncalibrated digital sensors.