Image reconstruction is an interesting yet challenging optimization problem that has several potential applications. The task is to reconstruct an image using a fixed number of transparent polygons. Traditional gradient-based algorithms cannot be applied to the problem since the optimization objective has no explicit expression and cannot be represented by computational graphs. Metaheuristic search algorithms are powerful optimization techniques for solving complex optimization problems, especially in the context of incomplete information or limited computational capability. In this paper, we developed a novel metaheuristic search algorithm named progressive learning hill climbing (ProHC) for image reconstruction. Instead of placing all the polygons on a blank canvas at once, ProHC starts from one polygon and gradually adds new polygons to the canvas until reaching the number limit. Furthermore, an energy-map-based initialization operator was designed to facilitate the generation of new solutions. To assess the performance of the proposed algorithm, we constructed a benchmark problem set containing four different types of images. The experimental results demonstrated that ProHC was able to produce visually pleasing reconstructions of the benchmark images. Moreover, the time consumed by ProHC was much shorter than that of the existing approach.
Keywords: energy map; hill climbing; image reconstruction; metaheuristic; progressive learning strategy.