Restoration of images with missing high-frequency components by minimizing the L1 norm of the solution vector

A novel algorithm for restoring an optical signal of spatial finite extent, which is subjected to low-pass frequency filtering, is presented. The problem is treated as an algebraic image restoration problem. The algorithm minimizes the L1 norm of the solution vector, subject to the constraints that the solution amplitude values are non-negative and bounded. Physically acceptable solutions of the resulting ill-posed system of equations are obtained by replacing the system by an approximate one of smaller rank. Numerical results show that this algorithm compares favorably with other known methods. Comments and conclusions are given.Peer reviewed: YesNRC publication: Ye