X-ray imaging is a fundamental diagnostic tool for inertial confinement fusion (ICF) research and provides data on the size and the shape of the core in implosions. We report on the feasibility and performance analyses of an ignition x-ray imager to be used on cryogenic deuterium-tritium implosions at the National Ignition Facility. The system is intended to provide time-integrated, broadband, moderate-energy x-ray core images of imploding inertial confinement fusion capsules. It is optimized with respect to spatial-resolution, signal-to-background, and signal-to-noise ratios, taking into account the extreme operating conditions expected at NIF due to high expected neutrons yields, gamma rays, and x rays from laser-plasma interactions.