SPEDEN is a computer program that reconstructs the electron density of single particles from their X-ray diffraction patterns, using a single-particle adaptation of the holographic method in crystallography [Szöke, Szöke & Somoza (1997). Acta Cryst. A53, 291-313]. The method, like its parent, is unique because it does not rely on 'back' transformation from the diffraction pattern into real space and on interpolation within measured data. It is designed to deal successfully with sparse, irregular, incomplete and noisy data. It is also designed to use prior information for ensuring sensible results and for reliable convergence. This article describes the theoretical basis for the reconstruction algorithm, its implementation, and quantitative results of tests on synthetic and experimentally obtained data. The program could be used for determining the structures of radiation-tolerant samples and, eventually, of large biological molecular structures without the need for crystallization.