The Fienup-Riordan algorithm is a mathematical technique used in the field of image reconstruction, particularly in the context of phase retrieval. It helps to recover an image from its Fourier transform data, which is often incomplete or noisy. This algorithm is particularly useful in applications like optical imaging and electron microscopy. Developed by Fienup and Riordan, the algorithm iteratively refines an estimate of the image by enforcing constraints in both the image and the Fourier domain. It is known for its effectiveness in producing high-quality images from limited data, making it a valuable tool in various scientific and engineering disciplines.