Incomplete Measurement

Incomplete measurement, the challenge of reconstructing signals or states from limited or noisy data, is a central problem across diverse scientific fields. Current research focuses on developing robust algorithms, including deep learning architectures like autoencoders and diffusion models, and Bayesian methods like plug-and-play algorithms, to address this issue in various applications, from medical imaging and atmospheric modeling to quantum state estimation and power grid management. These advancements aim to improve the accuracy and efficiency of signal reconstruction, particularly in scenarios where complete data acquisition is impractical or impossible. The impact spans improved data analysis in numerous scientific domains and the development of more efficient and reliable technologies in various engineering applications.