Discrete Tomography Based on DC Programming and DCA

In this article, we present a new continuous approach based on DC (Difference of Convex functions) programming and DC algorithms (DCA) to the Discrete Tomography. We are concerned with the reconstruction of binary images from their projections in a smaller number of directions. We treat this problem as DC programs. DC programming and DCA, becoming now classic, have been introduced by PHAM DINH T. in 1985 and extensively developed by LE THI H. A. and PHAM DINH T. since 1994. The DCA has been successfully applied to a lot of various large-scale differentiable or nondifferentiable nonconvex programs for which it has provided quite often global solutions (see, and references therein). Preliminary numerical experiments show the efficiency of the proposed algorithms.