Landweber Iteration in Banach Spaces for Linear FDEM data inversion
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This study addresses the problem of identifying electromagnetic properties of the Earth’s near-surface layer using data acquired through surface-based measurements. The analysis relies on a linear integral model in the frequency domain. To approximate the solution of the continuous problem, we express the unknown profile as a linear combination of chosen basis functions and we consider three different collocation methods. The resulting discretized systems are highly ill-conditioned, a common challenge in geophysical applications. To overcome this difficulty and obtain meaningful solutions, particularly in cases where the underlying physical structures exhibit abrupt changes or limited smoothness, we employ an iterative regularization scheme based on Landweber iterations formulated within Banach spaces. This framework is especially suited for reconstructing nonsmooth features, often encountered in practical imaging scenarios. A set of numerical experiments demonstrates the effectiveness and reliability of the proposed method, outperforming traditional regularization techniques in recovering sharp transitions and sparse structures.