Instruction systolic arrays (ISAs) have been developed in order to combine the speed and simplicity of systolic arrays with the flexibility of MIMD parallel computer systems. ISAs are available as square arrays of small RISC processors capable of performing integer and floating point arithmetic. In this paper we show that the systolic control flow can be used for an efficient reconstruction of images from its projections. The demand for fast image reconstruction arises in the field of computerized tomography. It is shown how the new parallel algorithm leads to a high-speed implementation on Systola 1024, the first commercial parallel computer with the ISA architecture.