Phase Retrieval Problem

Phase retrieval is the challenging inverse problem of reconstructing a signal from the magnitudes of its linear measurements, losing phase information. Current research focuses on developing robust and efficient algorithms, including alternating minimization, gradient descent variants (like mirror descent and accelerated methods), and deep learning architectures (e.g., U-Nets, vision transformers, and auto-encoders), to handle noisy and incomplete data, often incorporating regularization techniques to leverage prior knowledge about the signal structure. These advancements are crucial for various applications, such as imaging (e.g., ptychography, interferometric imaging, X-ray crystallography), where phase retrieval is essential for high-resolution reconstruction and improved signal recovery in the presence of noise and other artifacts.