An evolutionary algorithm for discrete tomography

One of the main problems in discrete tomography is the reconstruction of binary matrices from their projections in a small number of directions. In this paper we consider a new algorithmic approach for reconstructing binary matrices from only two projections. This problem is usually underdetermined and the number of solutions can be very large. We present an evolutionary algorithm for finding the reconstruction which maximises an evaluation function, representing the “quality” of the reconstruction, and show that the algorithm can be successfully applied to a wide range of evaluation functions. We discuss the necessity of a problem-specific representation and tailored search-operators for obtaining satisfactory results. Our new search-operators can also be used in other discrete tomography algorithms.