Cumulative Distribution Transform

The Signed Cumulative Distribution Transform (SCDT) is a signal representation technique extending the Cumulative Distribution Transform (CDT) to handle both positive and negative values, leveraging optimal transport theory. Current research focuses on applying SCDT and related transforms like the Radon Cumulative Distribution Transform (R-CDT) to image classification and signal parameter estimation, often employing nearest subspace search algorithms within the transformed space. These methods offer advantages in data efficiency, robustness to noise and outliers, and computational speed compared to some deep learning approaches, particularly in scenarios with limited training data or challenging conditions like varying illumination. The SCDT's success in these applications highlights its potential for improving various signal processing and machine learning tasks.