Title :
Bandlimited Reconstruction of Multidimensional Images From Irregular Samples
Author :
Xie Xu ; Wenxing Ye ; Entezari, Alireza
Author_Institution :
Dept. of Comput. & Inf. Sci. & Eng., Univ. of Florida, Gainesville, FL, USA
Abstract :
We examine different sampling lattices and their respective bandlimited spaces for reconstruction of irregularly sampled multidimensional images. Considering an irregularly sampled dataset, we demonstrate that the non-tensor-product bandlimited approximations corresponding to the body-centered cubic and face-centered cubic lattices provide a more accurate reconstruction than the tensor-product bandlimited approximation associated with the commonly-used Cartesian lattice. Our practical algorithm uses multidimensional sinc functions that are tailored to these lattices and a regularization scheme that provides a variational framework for efficient implementation. Using a number of synthetic and real data sets we record improvements in the accuracy of reconstruction in a practical setting.
Keywords :
approximation theory; image reconstruction; image sampling; tensors; Cartesian lattice; bandlimited image reconstruction; body-centered cubic lattice; face-centered cubic lattice; irregular sampling lattice dataset; multidimensional image reconstruction; multidimensional sinc function; nontensor-product bandlimited approximation; regularization scheme; tensor-product bandlimited approximation; variational framework; Irregular sampling; interpolation and approximation; multidimensional signal processing; sinc;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2013.2265880