Sampling theorems for bandlimited functions in the two-dimensional LCT and the LCHT domains

Sampling theorems for the two-dimensional linear canonical transform (LCT) in polar coordinates deserve special attention in medical imaging such as computerized tomography and magnetic resonance imaging due to the superiority of solving the traditional non-bandlimited images processing problems. Two types of interpolation formulae that interpolate in both radius and azimuth the angularly periodic and highest frequency limited functions with different bandwidth constraints, the LCT and the linear canonical Hankel transform (LCHT), are derived. The first interpolation formula is essentially equivalent to the latest one for bandlimited functions in the LCT domain while enjoys more concise and general mathematical derivations. Thanks to the consistency of the LCHT's order for bandlimited functions in the LCHT domain, the second interpolation formula outperforms the first one in computational complexity. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

Sampling theorems for the two-dimensional linear canonical transform in polar coordinates play a crucial role in medical imaging, offering superior solutions for non-bandlimited image processing problems. Two types of interpolation formulae, the LCT and the LCHT, are derived for angularly periodic and highest frequency limited functions, with the latter outperforming the former in computational complexity. The selection of interpolation formula can significantly impact the efficiency of computations in image processing.