Direct algebraic reconstruction and optimal sampling in vector field tomography

2 Sets S (bold line) and translations (dashed line) on the reciprocal lattice of the sampling scheme, i.e., S+2W ?t S k (left, W S is the standard sampling matrix) and S + 2W ?t I k (right, W I is the interlaced sampling matrix). Sampling the Radon transform with a rectangular scheme leads to a lattice in the Fourier space generated by ~ u 1 ; ~ u 2 (see left) for satisfying the non-overlapping condition (generalized Nyquist-Shannon condition). The lattice generated by the non-orthogonal vectors ~ u 0 1 ; ~ u 0 2 (right) satisses the non-overlapping condition more eeciently .