@MASTERSTHESIS\{IMM2007-05257,
    author       = "C. E. Bruun and T. B. Nielsen",
    title        = "Algorithms and Software for Large-Scale Geophysical Reconstructions",
    year         = "2007",
    keywords     = "Toeplitz structures, Large-scale inversions, Ill-posed problems, Compression, {FFT} matrix-vector multiplication, Regularization methods, Upward continuation, Object-oriented implementation, MOOReTools",
    school       = "Informatics and Mathematical Modelling, Technical University of Denmark, {DTU}",
    address      = "Richard Petersens Plads, Building 321, {DK-}2800 Kgs. Lyngby",
    type         = "",
    note         = "Supervised by Professor Per Christian Hansen, {IMM,} {DTU}.",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5257-full.html",
    abstract     = "The main focus of the thesis is algorithms and software for large-scale geophysical reconstructions. Throughout the project we deal with a special Toeplitz structure of the coeffecient matrix that enables a significant loss-less compression.

The geophysical surveying problems dealt with in the thesis are by nature ill-posed. For this reason we use regularization methods to perform the reconstuctions. The methods used in the paper are {TSVD,} Tikhonov, and {CGLS}. We will describe the constraints in the surveying problems that need to be met in order to achieve the Toeplitz structures. Aside from enabling compression the Toeplitz structures makes it possible to use a {FFT} matrix-vector multiplication to achieve fast multiplications in the regularization methods. Multi-level observation sets are used to meet the constraints and a Fourier based upward continuation method can be used to achieve the multi-levels, however, for forward problems we are able to compute levels at different altitudes. The performance of the upward continuation method is investigated. 

The result of this thesis is a Matlab object-oriented package implemented within the frameworks of MOOReTools and expands the existing GravMagTools package. The package is tested and reconstructions are performed."
}