Due to its potential application in signal analysis and image processing, quaternionic Fourier analysis has received increasing attention. This paper addresses quaternionic subspace Gabor frames under the condition that the products of time-frequency shift parameters are rational numbers. We characterize subspace quaternionic Gabor frames in terms of quaternionic Zak transformation matrices. For an arbitrary subspace Gabor frame, we give a parametric expression of its Gabor duals of type I and type II, and characterize the uniqueness Gabor duals of type I and type II. And as an application, given a Gabor frame for the whole space \(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\), we give a parametric expression of its all Gabor duals, and derive its unique Gabor dual of type II. Some examples are also provided.

由于其在信号分析和图像处理中的潜在应用，四元数傅立叶分析越来越受到关注。本文在时频平移参数的乘积为有理数的条件下，提出了四元子空间Gabor框架。我们用四元数 Zak 变换矩阵来表征子空间四元数 Gabor 框架。对于任意子空间Gabor框架，给出了其I型和II型Gabor对偶的参数表达式，并刻画了I型和II型Gabor对偶的唯一性。作为一个应用，给定整个空间的 Gabor 框架 \(L^{2}({\mathbb {R}}^{2},\,{\mathbb {H}})\)，我们给出一个参数其所有 Gabor 对偶的表达式，并推导出其独特的 II 型 Gabor 对偶。还提供了一些示例。