A Signomial Programming Approach for Binary Image Restoration by Penalized Least Squares

The authors present a novel optimization approach, using signomial programming (SP), to restore noise-corrupted binary and grayscale images. The approach requires the minimization of a penalized least squares functional over binary variables, which has led to the design of various approximation methods in the past. In this brief, we minimize the functional as a SP problem which is then converted into a reversed geometric programming (GP) problem and solved using standard GP solvers. Numerical experiments show that the proposed approach restores both degraded binary and grayscale images with good accuracy, and is over 20 times faster than the positive semidefinite programming approach.