2010/05/21 by Markus Hegland, Hegland, Markus, Bernd Hofmann +1
Engineering · Mathematics · #47A52 (Primary) #65J20 (Secondary) #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in inverse problems #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1005.3883
openalex publication_date 2010/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Based on the variable Hilbert scale interpolation inequality bounds for the\nerror of regularisation methods are derived under range inclusions. In this\ncontext, new formulae for the modulus of continuity of the inverse of bounded\noperators with non-closed range are given. Even if one can show the equivalence\nof this approach to the version used previously in the literature, the new\nformulae and corresponding conditions are simpler than the former ones. Several\nexamples from image processing and spectral enhancement illustrate how the new\nerror bounds can be applied.\n