Surveys on solution methods for inverse problems

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Mathematics of thermoacoustic tomography (2007, background): “…University of Arizona, Tucson, AZ 77843-3368, USA email: leonk@math.arizona.edu (Received 10 April 2007; revised 12 February 2008) The article presents a survey of mathematical problems, techniques and challenges arising in thermoacoustic tomography and its sibling photoacoustic tomography.”
Electrical impedance tomography (2002, background): “Since uniqueness does not hold for anisotropic EIT, we rephrase the question as: does the DtN map γ determine γ , up to a diffeomorphism ? The answer is affirmative for real-valued γ = σ , in two dimensions, if σ ∈ C2,α( ), 0 < α < 1 and ∂ is C3,α (see [141]1) and in three dimensions, if σ is analyt”
Inverse problems as statistics (2002, background): “A shorter, preliminary version of the paper without the original results appeared in Surveys on Solution Methods for Inverse Problems [56].”
Determining a Function from Its Mean Values Over a Family of Spheres (2004, methodology): “In [21] there is an announcement of a uniqueness theorem more general than our Theorem 1, which can be proved using techniques from microlocal analysis in the analytic category as exposed in section 3 of [2].”
A tutorial on inverse problems for anomalous diffusion processes (2015, unknown): “Since all its derivatives vanish at s = 0, the classical theory of Volterra integral equations of the first kind [56] implies the extreme ill-conditioning of the problem.”