Construction of a full row-rank matrix system for multiple scanning directions in discrete tomography

A full row-rank system matrix generated by scans along two directions in discrete tomography was recently studied. In this paper, we generalize the result to multiple directions. Let Ax=h be a reduced binary linear system generated by scans along three directions. Using geometry, it is shown in this paper that the linearly dependent rows of the system matrix AA can be explicitly identified and a full row-rank matrix can be obtained after the removal of those rows. The results could be extended to any number of multiple directions. Therefore, certain software packages requiring a full row-rank system matrix can be adopted to reconstruct an image. Meanwhile, the cost of computation is reduced by using a full row-rank matrix.