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.

极坐标中的二维线性典范变换（LCT）的采样定理由于解决了传统的非带限图像处理问题的优越性，在医学成像（如计算机断层扫描和磁共振成像）中值得特别注意。得出了两种类型的插值公式：LCT和线性规范汉克尔变换（LCHT），它们可以在半径和方位角上对具有不同带宽约束的角周期和最高频率限制函数进行插值。第一个插值公式实质上等效于LCT域中的带限函数的最新插值公式，同时享有更为简洁和通用的数学推导。由于LCHT在LCHT域中对带限功能的命令的一致性，