2011/10/17 by Jianxun He, He, JIanxun, Heping Liu +1
Computer Science · Earth and Planetary Sciences · Mathematics · #43A85 #44A15 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1110.3570
openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathscr Q be the quaternion Heisenberg group, and let \mathbf P be the affine automorphism group of \mathscr Q. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of \mathbf P on L2(\mathscr Q). A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on \mathscr Q. A Semyanistri-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on \mathscr Q both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth.