Numerical Regularization for Atmospheric Inverse Problems

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The retrieval problems in atmospheric remote sensing are classified as discrete ill-posed problems, which are unstable under data perturbations. These can be addressed using numerical regularization methods that stabilize solutions by incorporating additional information. This research monograph presents and analyzes numerical algorithms for atmospheric retrieval, targeting physicists and engineers with a background in numerical linear algebra and matrix computations. While the book contains practical details, readers are encouraged to consult the cited literature for robust and efficient algorithm implementation. The adopted data model is semi-stochastic, with no significant practical differences from a deterministic framework, although theoretical distinctions exist, particularly regarding convergence and rates. Following an introductory chapter on the state of the art in passive atmospheric remote sensing, Chapter 2 discusses ill-posedness in linear discrete equations. To illustrate the challenges of solving discrete ill-posed problems, the text examines temperature retrieval through nadir sounding and analyzes the solvability of the discrete equation using the singular value decomposition of the forward model matrix.