A systolic array for inversion of a finite Radon transform (Q1185925)

The finite Radon transform of an \(N\times N\) matrix \(X\) is defined to be \[ R(d,\langle i,j\rangle)=\sum_{ik+j\ell=d\bmod N} X(k\ell). \] The relation of \(R\) to the 2D discrete Fourier transform of \(X\) is given which is analogous to the projection slice theorem of the classical Radon transform. Based on this relation an \(N^ 2\log N\) algorithm for computing \(X\) from \(R\) is given. The implementation of this algorithm on a systolic array is described.