A method for restoring an optical image which is subjected to low-pass frequency filtering is presented. It is assumed that the object whose image is restored is of finite spatial extent. The problem is treated as an algebraic image-restoration problem which is then solved as a quadratic programming problem with bounded variables. The regularization technique for the ill-posed system is to replace the consistent system of the quadratic programming problem by an approximate system of smaller rank. The rank which gives a best or near-best solution is estimated. This method is a novel one, and it compares favorably with other known methods. Computer-simulated examples are presented. Comments and conclusions are given.
© 1983 Optical Society of America
Original Manuscript: November 2, 1982
Published: July 15, 1983
Nabih N. Abdelmalek, "Restoration of images with missing high-frequency components using quadratic programming," Appl. Opt. 22, 2182-2188 (1983)