Linear Inverse Problem

Linear inverse problems involve recovering an unknown signal from incomplete or noisy measurements, aiming to find optimal solutions that balance accuracy and robustness. Current research heavily focuses on leveraging deep learning architectures, such as neural networks and diffusion models, often combined with iterative algorithms (e.g., ISTA, ADMM) or Bayesian inference methods, to incorporate prior information and improve reconstruction quality. These advancements are significantly impacting diverse fields, including medical imaging, signal processing, and computer vision, by enabling more accurate and efficient solutions to challenging inverse problems. The development of theoretically grounded methods with provable convergence guarantees remains a key area of ongoing investigation.