Pass-Band Optimal Reconstruction on the Body-Centered Cubic Lattice

In this paper, a pass-band optimal reconstruction technique is adapted to the Body-Centered Cubic (BCC) lattice. In order to perform the frequencydomain preprocessing, we derive a practical Discrete Fourier Transform (DFT) for BCC-sampled data. In the discrete frequency domain our DFT provides a natural isotropic periodicity on a FaceCentered Cubic (FCC) pattern, unlike the previous method, which leads to periodicity on a sheared Cartesian pattern. One of the most important advantages of our approach is that no specialized FFT implementation is required, as basically the well-known traditional FFT libraries can be directly used for calculating the discrete frequency coefficients. Furthermore, the proposed DFT can be easily adapted to FCC-sampled data as well. We show that a prefiltered pass-band optimal reconstruction based on our DFT can capture the high-frequency details much better than the previously proposed generalized interpolation method.