Geometric Wavelet Scattering Networks on Compact Riemannian Manifolds

The Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of convolutional neural networks. Inspired by recent interest in geometric deep learning, which aims to generalize convolutional neural networks to manifold and graph-structured domains, we define a geometric scattering transform on manifolds. Similar to the Euclidean scattering transform, the geometric scattering transform is based on a cascade of wavelet filters and pointwise nonlinearities. It is invariant to local isometries and stable to certain types of diffeomorphisms. Empirical results demonstrate its utility on several geometric learning tasks. Our results generalize the deformation stability and local translation invariance of Euclidean scattering, and demonstrate the importance of linking the used filter structures to the underlying geometry of the data.Comment: 35 pages; 3 figures; 2 tables; v3: Revisions based on reviewer comment

Gabor frames and deep scattering networks in audio processing

This paper introduces Gabor scattering, a feature extractor based on Gabor frames and Mallat's scattering transform. By using a simple signal model for audio signals specific properties of Gabor scattering are studied. It is shown that for each layer, specific invariances to certain signal characteristics occur. Furthermore, deformation stability of the coefficient vector generated by the feature extractor is derived by using a decoupling technique which exploits the contractivity of general scattering networks. Deformations are introduced as changes in spectral shape and frequency modulation. The theoretical results are illustrated by numerical examples and experiments. Numerical evidence is given by evaluation on a synthetic and a "real" data set, that the invariances encoded by the Gabor scattering transform lead to higher performance in comparison with just using Gabor transform, especially when few training samples are available.Comment: 26 pages, 8 figures, 4 tables. Repository for reproducibility: https://gitlab.com/hararticles/gs-gt . Keywords: machine learning; scattering transform; Gabor transform; deep learning; time-frequency analysis; CNN. Accepted and published after peer revisio

Invariant Scattering Transform for Medical Imaging

Invariant scattering transform introduces new area of research that merges the signal processing with deep learning for computer vision. Nowadays, Deep Learning algorithms are able to solve a variety of problems in medical sector. Medical images are used to detect diseases brain cancer or tumor, Alzheimer's disease, breast cancer, Parkinson's disease and many others. During pandemic back in 2020, machine learning and deep learning has played a critical role to detect COVID-19 which included mutation analysis, prediction, diagnosis and decision making. Medical images like X-ray, MRI known as magnetic resonance imaging, CT scans are used for detecting diseases. There is another method in deep learning for medical imaging which is scattering transform. It builds useful signal representation for image classification. It is a wavelet technique; which is impactful for medical image classification problems. This research article discusses scattering transform as the efficient system for medical image analysis where it's figured by scattering the signal information implemented in a deep convolutional network. A step by step case study is manifested at this research work.Comment: 11 pages, 8 figures and 1 tabl

On-machine surface defect detection using light scattering and deep learning

This paper presents an on-machine surface defect detection system using light scattering and deep learning. A supervised deep learning model is used to mine the information related to defects from light scattering patterns. A convolutional neural network is trained on a large dataset of scattering patterns that are predicted by a rigorous forward scattering model. The model is valid for any surface topography with homogeneous materials and has been verified by comparing with experimental data. Once the neural network is trained, it allows for fast, accurate and robust defect detection. The system capability is validated on micro-structured surfaces produced by ultra-precision diamond machining