The retrieval problems arising in atmospheric remote sensing belong to
the class of the - called discrete ill-posed problems. These problems
are unstable under data perturbations, and can be solved by numerical
regularization methods, in which the solution is stabilized by taking
additional information into account. The goal of this research monograph
is to present and analyze numerical algorithms for atmospheric
retrieval. The book is aimed at physicists and engineers with some ba-
ground in numerical linear algebra and matrix computations. Although
there are many practical details in this book, for a robust and ef?cient
implementation of all numerical algorithms, the reader should consult
the literature cited. The data model adopted in our analysis is
semi-stochastic. From a practical point of view, there are no signi?cant
differences between a semi-stochastic and a determin- tic framework; the
differences are relevant from a theoretical point of view, e.g., in the
convergence and convergence rates analysis. After an introductory
chapter providing the state of the art in passive atmospheric remote
sensing, Chapter 2 introduces the concept of ill-posedness for linear
discrete eq- tions. To illustrate the dif?culties associated with the
solution of discrete ill-posed pr- lems, we consider the temperature
retrieval by nadir sounding and analyze the solvability of the discrete
equation by using the singular value decomposition of the forward model
matrix.