Orthogonal Transform-Driven Data Augmentation for Limited Gaussian-Tainted Dataset

A large amount of data collected from sensors exhibits Gaussian noise characteristics, making denoising and related processing critical. However, data scarcity can lead to overfitting, posing challenges in training deep learning-based denoising methods. While various data augmentation methods have been proposed, they do not provide a means to augment original data to large-scale data while preserving the exact noise distribution. To address this, we introduce a novel data augmentation method for data with additive white Gaussian noise (AWGN). Our method is based on two main premises: first, orthogonal transforms preserve the probability distribution of AWGN; second, the signals we aim to recover generally exhibit smooth characteristics, unlike noise. Building on these premises, we propose adaptive smoothness-promoting orthogonal transforms for augmenting limited existing data. We evaluated the proposed method in Gaussian denoising tasks with limited data and confirmed that it achieves substantial improvement in deep learning model performance, comparable to those obtained with sufficient data.