Whenever possible I will put these references on reserve at the library.
Albert Tarantola, Inverse Problem Theory, Elsevier, 1987
This is the standard reference for the Bayesian view of geophysical inversion. Although Tarantola uses a more general formulation (for instance, he doesn't require noise to be additive), it seems to reduce to a conventional Bayesian anslysis in practice. This book has a wealth of information about stochastic processes and numerical methods for finite dimensional inversion. Tarantola is at the Institut de Physique du Globe de Paris.Robert Parker, Geophysical Inverse Theory, Princeton, 1994
This is the standard reference for frequentist inverse theory. One of the key goals is to compute strict bounds on models or model functional. Excellent discussion of functional analytic methods (for continuous problems), optimization, linear and quadratic programming. Nice exmples drawn from gravity and magnetic problems. Parker is at the Institute of Geophysics and Planetary Physics, UC San Diego.Leszek Plaskota, Nosy information and computational complexity, Cambridge, 1996.
A very advanced book treating the problem of inference of linear functionals in the presence of random and systematic noise. Plaskota is at the Institute of Applied Mathematics and Mechanics, University of Warsaw.Magnus Hestenes, Conjugate Direction Methods in Optimization, Springer, 1980.
Joseph Ruanaidh and William Fitzgerald, Numerical Bayesian Methods Applied to Signal Processing. Springer, 1996.
This is the standard reference on CD methods. Includes many useful, not widely known algorithms. An excellent place to learn about the application of CG to nonquadradic objective functions.
A nice introduction to Bayesian methods with an emphasis on computational issues. Has good discussions of Monte Carlo methods, density estimation, missing data, and lots more.
Papers
David Donoho, Statistical Estimation and Optimal Recovery, The
Annals of Statistics, 1994, 238-270.