We propose a novel method for information storage, based on tomographic principles. With this method information is stored in planar slices of some three-dimensional media by optical methods. The information is recovered by detecting line integrals and applying algorithms for the reconstruction from projections. We show that only one projection suffices for exact information decoding. Reconstruction can be done by optical means, in an linear algebra optical processor. An advantage of this kind of memory is that it can be easily connected to optical processors in a completely optical setup.