The Living Thing / Notebooks : Inverse problems

As seen in tomography, sparsity constraints, solvers, variational inference, deconvolution

Robert Ackroyd had some nice phrasing around the connections (indeed isomorphisms) between statistical estimation theory and inverse problem solving.

I thought I had something to say about this general perspective on inverse problems, but I don’t yet.

Refs

BoSc16
Borgerding, M., & Schniter, P. (2016) Onsager-Corrected Deep Networks for Sparse Linear Inverse Problems. arXiv:1612.01183 [Cs, Math].
Buit12
Bui-Thanh, T. (2012) A Gentle Tutorial on Statistical Inversion using the Bayesian Paradigm.
DaDD04
Daubechies, I., Defrise, M., & De Mol, C. (2004) An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Communications on Pure and Applied Mathematics, 57(11), 1413–1457. DOI.
MoTa95
Mosegaard, K., & Tarantola, A. (1995) Monte Carlo sampling of solutions to inverse problems. Journal of Geophysical Research, 100(B7), 12431.
Osul86
O’Sullivan, F. (1986) A Statistical Perspective on Ill-Posed Inverse Problems. Statistical Science, 1(4), 502–518. DOI.
ScSt12
Schwab, C., & Stuart, A. M.(2012) Sparse deterministic approximation of Bayesian inverse problems. Inverse Problems, 28(4), 045003. DOI.
Stua10
Stuart, A. M.(2010) Inverse problems: A Bayesian perspective. Acta Numerica, 19, 451–559. DOI.
TrWr10
Tropp, J. A., & Wright, S. J.(2010) Computational Methods for Sparse Solution of Linear Inverse Problems. Proceedings of the IEEE, 98(6), 948–958. DOI.