sources.bib

@article{Hoskins_2022,
doi = {10.1088/1361-6420/ac661f},
url = {https://dx.doi.org/10.1088/1361-6420/ac661f},
year = {2022},
month = {may},
publisher = {IOP Publishing},
volume = {38},
number = {7},
pages = {074001},
author = {Jeremy G Hoskins and John C Schotland},
title = {Analysis of the inverse Born series: an approach through geometric function theory},
journal = {Inverse Problems},
abstract = {We analyze the convergence and approximation error of the inverse Born series, obtaining results that hold under qualitatively weaker conditions than previously known. Our approach makes use of tools from geometric function theory in Banach spaces. An application to the inverse scattering problem with diffuse waves is described.}
}

@article{Ramlau_2018,
doi = {10.1088/1361-6420/aacf27},
url = {https://dx.doi.org/10.1088/1361-6420/aacf27},
year = {2018},
month = {jul},
publisher = {IOP Publishing},
volume = {34},
number = {9},
pages = {090201},
author = {Ronny Ramlau and Otmar Scherzer},
title = {The first 100 years of the Radon transform},
journal = {Inverse Problems},
abstract = {This special issue is honoring the 100th anniversary of the publication of the famous paper by Johann Radon (1917 Ber. über Verh. Königlich-Sächsischen Ges. Wiss. Leipzig 69 262–77).}
}

@article{DeFilippis_2023,
doi = {10.1088/1361-6420/ad07a5},
url = {https://dx.doi.org/10.1088/1361-6420/ad07a5},
year = {2023},
month = {nov},
publisher = {IOP Publishing},
volume = {39},
number = {12},
pages = {125015},
author = {Nicholas DeFilippis and Shari Moskow and John C Schotland},
title = {Born and inverse Born series for scattering problems with Kerr nonlinearities},
journal = {Inverse Problems},
abstract = {We consider the Born and inverse Born series for scalar waves with a cubic nonlinearity of Kerr type. We find a recursive formula for the operators in the Born series and prove their boundedness. This result gives conditions which guarantee convergence of the Born series, and subsequently yields conditions which guarantee convergence of the inverse Born series. We also use fixed point theory to give alternate explicit conditions for convergence of the Born series. We illustrate our results with numerical experiments.}
}

@article{Moskow_2008,
doi = {10.1088/0266-5611/24/6/065005},
url = {https://dx.doi.org/10.1088/0266-5611/24/6/065005},
year = {2008},
month = {sep},
publisher = {},
volume = {24},
number = {6},
pages = {065005},
author = {Shari Moskow and John C Schotland},
title = {Convergence and stability of the inverse scattering series for diffuse waves},
journal = {Inverse Problems},
abstract = {We analyze the inverse scattering series for diffuse waves in random media. In previous work the inverse series was used to develop fast, direct image reconstruction algorithms in optical tomography. Here we characterize the convergence, stability and approximation error of the series.}
}

@inbook{MoskowSchotland+2019+273+296,
url = {https://doi.org/10.1515/9783110560855-012},
title = {12. Inverse Born series},
booktitle = {The Radon Transform},
booktitle = {The First 100 Years and Beyond},
author = {Shari Moskow and John C. Schotland},
editor = {Ronny Ramlau and Otmar Scherzer},
publisher = {De Gruyter},
address = {Berlin, Boston},
pages = {273--296},
doi = {doi:10.1515/9783110560855-012},
isbn = {9783110560855},
year = {2019},
lastchecked = {2024-12-13}
}