Algorithms for subpixel registration
Computer Vision, Graphics, and Image Processing
Enumerative combinatorics
Image interpolation and resampling
Handbook of medical imaging
IEEE Transactions on Signal Processing
Integer fast Fourier transform
IEEE Transactions on Signal Processing
Lossless subband coding system based on rounding transform
IEEE Transactions on Signal Processing
Fast multiplierless approximations of the DCT with the liftingscheme
IEEE Transactions on Signal Processing
Matrix factorizations for reversible integer mapping
IEEE Transactions on Signal Processing
Modulo transforms - an alternative to lifting
IEEE Transactions on Signal Processing
Convolution-based interpolation for fast, high-quality rotation of images
IEEE Transactions on Image Processing
| Hi-index | 35.68 |
Except some extremely special cases, signal resampling was generally considered to be irreversible because of strong attenuation of high frequencies after interpolation. In this paper, we prove that signal resampling based on polynomial interpolation can be reversible even for integer signals, i.e., the original signal can be reconstructed losslessly from the resampled data. By using matrix factorization, we also propose a reversible method for uniform shifted resampling and uniform scaled and shifted resampling. The new factorization yields three elementary integer-reversible matrices. The method is actually a new way to compute linear transforms and a lossless integer implementation of linear transforms with the factor matrices. It can be applied to integer signals by in-place integer-reversible computation, which needs no auxiliary memory to keep the original sample data for the transformation during the process or for "undo" recovery after the process. Some examples of low-order resampling solutions are also presented in this paper and our experiments show that the resampling error relative to the original signal is comparable to that of the traditional irreversible resampling.