Wavelet-based Green Learning (GreenWave) is a new image classification framework that combines the multi-scale power of wavelet transforms with the efficiency and interpretability of Green Learning principles. It avoids backpropagation and replaces traditional deep learning architectures with a transparent, feedforward pipeline.

At its core, GreenWave begins by applying a discrete wavelet transform (DWT)—typically using Haar wavelets—to each image, capturing both local and global spatial structures at multiple resolutions. It extracts features from wavelet subbands (like LL, LH, HL, HH) as well as local image patches from different regions (e.g., east, south, west, north). These features are used to construct class templates via averaging over training examples.

GreenWave operates in three rounds of classification:
1. Round-1 classifies easy samples using cosine similarity between the input and class templates (one-vs-rest). It uses confidence metrics (like entropy) to decide which samples are “easy” and can exit the pipeline early.
2. Round-2 focuses on semi-hard samples using updated templates and discriminant feature test (DFT) masks to emphasize class-informative coefficients. It also introduces one-vs-one templates to resolve class confusion.
3. Round-3 targets the hardest samples using further refined templates and updated confusion masks, maximizing accuracy while maintaining interpretability.
Throughout all stages, GreenWave uses cosine similarity as its feature-matching metric and XGBoost classifiers for decision learning, completely bypassing gradient-based training.

Overall, GreenWave demonstrates that a non-backpropagation, wavelet-template-based system can achieve near state-of-the-art performance while being highly efficient, explainable, and modular. This makes it an ideal choice for low-resource or transparent AI applications.