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

Balázs Csébfalvi, Balázs Domonkos

Department of Control Engineering and Information Technology

Budapest University of Technology and Economics  

 

Non-prefiltered quintic box-spline reconstruction.

 

Interpolating prefiltered quintic box-spline reconstruction.

 

Pass-band optimal premultiplied quintic box-spline reconstruction.

Abstract:

In this paper, a pass-band optimal reconstruction technique is adapted to the Body-Centered Cubic (BCC) lattice. In order to perform the frequency-domain 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 Face-Centered 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.

Keywords:

Body-Centered Cubic Lattice, Reconstruction, Optimal Regular Volume Sampling, Generalized Interpolation.

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