Graff, MarieCheng, Tingwei2025-01-062025-01-062024https://hdl.handle.net/2292/70916Inverse problem is an essential field of applied mathematics that tackles the question of the reconstruction of some parameters included in a model (PDE) from measures only. Uncertainty quantification is also merging to add a stochastic layer to the reconstruction process to obtain statistical insights on this reconstruction. This thesis focuses on a linear inverse problem in reconstructing the source term of the Helmholtz equation. As the problem is ill-posed, we use the Adaptive Eigenspace Inversion as regularization. The novelty of this thesis lies in embedding Bayesian formula to Adaptive Eigenspace Inversion method. For the sake of comparison and to show the effectiveness of Adaptive Eigenspace Inversion in 2D, we performed numerical tests. Additionally, we have selected Tikhonov Regularization methods as the standard techniques for the comparison.https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htmThesisCopyright: the authorAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/