A new phasing algorithm has been used to determine the phases of diffuse elastic X-ray scattering from a non-periodic array of gold balls of 50 nm diameter. Two-dimensional real-space images, showing the charge-density distribution of the balls, have been reconstructed at 50 nm resolution from transmission diffraction patterns recorded at 550 eV energy. The reconstructed image fits well with a scanning-electron-microscope (SEM) image of the same sample. The algorithm, which uses only the density modification portion of the SIR2002 program, is compared with the results obtained via the Gerchberg-Saxton-Fienup HiO algorithm. The new algorithm requires no knowledge of the object's boundary and proceeds from low to high resolution. In this way, the relationship between density modification in crystallography and the HiO algorithm used in signal and image processing is elucidated.