Integral Transforms

Integral transforms are mathematical tools that map functions into alternative spaces for easier analysis and manipulation, finding applications across diverse scientific fields. Current research emphasizes developing novel integral transform-based architectures, such as neural networks incorporating adaptive generalized integral transforms or integral autoencoders with data-driven kernels, to solve complex problems like partial differential equations and image processing tasks. These advancements improve the efficiency and robustness of existing methods, particularly in handling noisy data and complex geometries, leading to enhanced accuracy and broader applicability in scientific computing and machine learning. The development of these new methods is impacting fields ranging from medical imaging to quantum computing.