The periodic step gradient descent algorithm — General analysis and application to the super resolution reconstruction problem

Solving image reconstruction problems, especially complex problems like Super Resolution reconstruction, is very demanding computationally. Iterative algorithms are the practical tool frequently used for this purpose. This paper reviews the Periodic Step Gradient Descent (PSGD) algorithm, suggested as a sub-optimal algorithm for solving reconstruction problems (with emphasis on Super Resolution reconstruction problems). The PSGD differs from well-known iterative algorithms in the way the data of the problem at hand is processed. Whereas iterative algorithms process the entire given data in order to update the result, the PSGD updates the result progressively. This paper provides an analysis of the PSGD. We show that the PSGD has an efficient implementation, easy to achieve convergence conditions and fast convergence speed when applied to a Super Resolution reconstruction problem. The performance of the PSGD when applied to a Super Resolution reconstruction problem, is demonstrated by simulations and compared to the performance of other well-known algorithms.