归因于Heisenberg群在数学方面的几何背景和在物理方面的量子力学背景，很多研究希望调和分析在Heisenberg群上可以得到与欧氏空间类似的理论框架。而随着欧氏空间Radon变换理论的逐渐成熟，Heisenberg群上的Radon变换理论的研究越来越受到关注。. 本项目主要拟通过Heisenberg 群Fourier变换和小波变换来研究该群上k-平面Radon变换的反演问题。首先，利用Heisenberg 群上k-平面Radon变换的性质，结合群Fourier变换与各种偏微分算子的关系，研究群Fourier变换逆公式下的k-平面Radon变换的反演公式。其次，结合上述性质和关系研究Heisenberg 群上小波变换，进而探讨小波变换逆公式下的k-平面Radon变换的反演公式。. 最后，我们期望这些结果可推广到一般的二步幂零李群上。

Due to the geometric background in mathematics and the quantum mechanics background in physics, the Heisenberg group attracts many people’s interest to extend the theory of harmonic analysis, which has done on Euclidean space, to the Heisenberg group. As the theory of the Radon transform on Euclidean space becomes more mature, researches on the Radon transform in the Heisenberg group attracts more concern.. This research is concerned with the inverse k-plane Radon transforms of the Heisenberg group via the group Fourier transform and wavelet transform. Firstly, by the properties of the k-plane Radon transform together with the relationship between the group Fourier transform and the partial differential operators, the inversion formula associated with inverse group Fourier transform is studied. Secondly, by using the wavelet transform and the properties of the k-plane Radon transform, a new inversion of k-plane Radon transform, associated with the inverse wavelet transform, is discussed.. At last, we expect these result can be extend to the nilpotent Lie group of step two.