Nonlinear Inverse Problem

Nonlinear inverse problems aim to recover an unknown signal from its nonlinearly transformed measurements, a challenge arising across diverse scientific fields. Current research heavily focuses on leveraging deep learning, employing architectures like diffusion models, invertible residual networks, and physics-informed neural networks, often enhanced by techniques such as self-supervised learning and momentum acceleration to improve robustness and efficiency. These advancements are significantly impacting various applications, from medical imaging (e.g., computed tomography artifact reduction) and audio signal processing to general image reconstruction, by enabling more accurate and efficient solutions to previously intractable problems.