Complex-valued Scattering Representations

Complex-valued deep learning has made significant progress with manifold geometry and group theory. It delivers leaner and better classifiers with novel complex-valued layer functions and network architectures, not only on naturally complex-valued data such as Magnetic Resonance imaging (MRI) but also on real-valued data such as RGB or multi-spectral images. However, current complex-valued representations for complex-valued and real-valued inputs are rudimentary, focusing on channel characteristics (e.g., sliding encoding) without capturing spatial and spatial-frequency properties of the input data. We propose Complex-valued Scattering Representations (CSR) as universal complex-valued representations and integrate them into complex-valued deep learning networks. To obtain CSR, We construct filters based on complex-valued Morlet wavelets with tunable parameters and develop learnable high-dimensional complex-valued ReLU as the non-linear activation function. By incorporating these novel components into complex-valued models, our models significantly outperform real-valued counterparts and existing complex-valued models on RGB, multi-spectral image (MSI), and MRI patch classification tasks, especially under limited labeled training data settings, greatly enhancing complex-valued networks on a broader range of applications.