Isotropic Gaussian Noise

Isotropic Gaussian noise, characterized by equal variance in all directions, is a common assumption in many statistical models and algorithms, particularly in machine learning and signal processing. However, recent research highlights the limitations of this assumption, focusing on developing methods that handle anisotropic (directionally dependent) noise, particularly within diffusion models, stochastic gradient descent, and point cloud registration. This shift is driven by the need for more accurate and robust models in applications where noise is inherently non-uniform, leading to improved performance in speech enhancement, deep learning, and other fields. The development of algorithms that explicitly model and account for anisotropic noise represents a significant advancement, improving both the accuracy and efficiency of various computational methods.