2017/07/25 by Córdova, Santiago, Vera, Daniel
Computer Science · Earth and Planetary Sciences · Medicine · #42C40 #44A12 #92C55 #94A08 #FOS: Mathematics #Functional Analysis (math.FA) #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1707.08185
openalex publication_date 2017/07/25 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28
We find a new and simple inversion formula of the Radon transform RT with the only use of the shearlet system and of well-known properties of RT. No intertwining relation of differential operators in Euclidean space and Radon domain is used. As a consequence, an additive noise is not incremented. Since the continuum theory of shearlets has a straight translation to the discrete theory, we find a fast, stable and computable algorithm that recovers a digital image from noisy samples of the Radon transform preserving edges. In the process, we find a more natural and easier-to-construct density-compensation weight functions for the ShearLab toolbox.