A Hybrid Scattering Transform for Signals with Isolated Singularities.

Area of Science:

• Signal Processing
• Machine Learning
• Image Analysis

Background:

• Convolutional Neural Networks (CNNs) utilize filters, often resembling wavelets in early layers, for stability and invariance.
• The scattering transform, a wavelet-based CNN model, explains these early-layer filter properties.
• Understanding filter selection for later CNN layers remains an open research question.

Purpose of the Study:

• To investigate optimal filter types for later layers in scattering transform networks.
• To propose and analyze a novel two-layer hybrid scattering transform architecture.
• To characterize signal information and enable synthesis using the proposed transform.

Main Methods:

• A two-layer hybrid scattering transform was developed.
• The first layer employs wavelet filters to induce signal sparsity.
• The second layer utilizes Gabor filters to exploit the sparsity generated by the first layer.

Main Results:

• The proposed hybrid transform effectively characterizes information in signals with isolated singularities.
• Gabor filter measurements in the second layer facilitate the synthesis of sparse signals.
• The study demonstrates the utility of combining wavelet and Gabor filters for advanced signal representation.

Conclusions:

• Hybrid scattering transforms offer a powerful framework for analyzing and synthesizing signals with singularities.
• The proposed architecture provides insights into designing effective filters for deep learning models.
• This work contributes to a deeper understanding of the mathematical underpinnings of CNNs.