references.bib

@article{akiyama,
  title={First M87 event horizon telescope results. IV. Imaging the central supermassive black hole},
  author={Akiyama, Kazunori and Alberdi, Antxon and Alef, Walter and Asada, Keiichi and Azulay, Rebecca and Baczko, Anne-Kathrin and Ball, David and Balokovi{\'c}, Mislav and Barrett, John and Bintley, Dan and others},
  journal={The Astrophysical Journal Letters},
  volume={875},
  number={1},
  pages={L4},
  year={2019},
  publisher={IOP Publishing}
}

@article{hansen1990discrete,
  title={The discrete Picard condition for discrete ill-posed problems},
  author={Hansen, Per Christian},
  journal={BIT Numerical Mathematics},
  volume={30},
  number={4},
  pages={658--672},
  year={1990},
  publisher={Springer}
}

@article{ANDERSEN198481,
title = "Simultaneous Algebraic Reconstruction Technique (SART): A superior implementation of the ART algorithm",
journal = "Ultrasonic Imaging",
volume = "6",
number = "1",
pages = "81 - 94",
year = "1984",
issn = "0161-7346",
doi = "https://doi.org/10.1016/0161-7346(84)90008-7",
url = "http://www.sciencedirect.com/science/article/pii/0161734684900087",
author = "A.H. Andersen and A.C. Kak",
keywords = "Algebraic reconstruction, digital ray tracing, tomography, ultrasound",
abstract = "In this paper we have discussed what appears to be a superior implementation of the Algebraic Reconstruction Technique (ART). The method is based on 1) simultaneous application of the error correction terms as computed by ART for all rays in a given projection; 2) longitudinal weighting of the correction terms back-distributed along the rays; and 3) using bilinear elements for discrete approximation to the ray integrals of a continuous image. Since this implementation generates a good reconstruction in only one iteration, it also appears to have a computational advantage over the more traditional implementation of ART. Potential applications of this implementation include image reconstruction in conjunction with ray tracing for ultrasound and microwave tomography in which the curved nature of the rays leads to a non-uniform ray density across the image."
}

@Inbook{Dashti2017,
author="Dashti, Masoumeh
and Stuart, Andrew M.",
editor="Ghanem, Roger
and Higdon, David
and Owhadi, Houman",
title="The Bayesian Approach to Inverse Problems",
bookTitle="Handbook of Uncertainty Quantification",
year="2017",
publisher="Springer International Publishing",
address="Cham",
pages="311--428",
abstract="These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental in the quantification of uncertainty within applications involving the blending of mathematical models with data. The finite-dimensional situation is described first, along with some motivational examples. Then the development of probability measures on separable Banach space is undertaken, using a random series over an infinite set of functions to construct draws; these probability measures are used as priors in the Bayesian approach to inverse problems. Regularity of draws from the priors is studied in the natural Sobolev or Besov spaces implied by the choice of functions in the random series construction, and the Kolmogorov continuity theorem is used to extend regularity considerations to the space of H{\"o}lder continuous functions. Bayes' theorem is derived in this prior setting, and here interpreted as finding conditions under which the posterior is absolutely continuous with respect to the prior, and determining a formula for the Radon-Nikodym derivative in terms of the likelihood of the data. Having established the form of the posterior, we then describe various properties common to it in the infinite-dimensional setting. These properties include well-posedness, approximation theory, and the existence of maximum a posteriori estimators. We then describe measure-preserving dynamics, again on the infinite-dimensional space, including Markov chain Monte Carlo and sequential Monte Carlo methods, and measure-preserving reversible stochastic differential equations. By formulating the theory and algorithms on the underlying infinite-dimensional space, we obtain a framework suitable for rigorous analysis of the accuracy of reconstructions, of computational complexity, as well as naturally constructing algorithms which perform well under mesh refinement, since they are inherently well defined in infinite dimensions.",
isbn="978-3-319-12385-1",
doi="10.1007/978-3-319-12385-1_7",
url="https://arxiv.org/pdf/1302.6989.pdf"
}


@article{johnson1984density,
  title={Density of rocks and minerals},
  author={Johnson, Gordon R},
  journal={CRC handbook of physical properties of rocks},
  pages={1--38},
  year={1984},
  publisher={CRC Press}
}

@book{nocedal2006numerical,
  title={Numerical optimization},
  author={Nocedal, Jorge and Wright, Stephen},
  year={2006},
  publisher={Springer Science \& Business Media}
}

@book{Beck2017,
author = {Beck, Amir},
file = {:Users/tristanvanleeuwen/Documents/Mendeley Desktop/Beck - 2017 - First-Order Methods in Optimization.pdf:pdf;:Users/tristanvanleeuwen/Documents/Mendeley Desktop/Beck - 2017 - First-Order Methods in Optimization(2).pdf:pdf},
mendeley-groups = {books},
publisher = {Society for Industrial and Applied Mathematics},
title = {{First-Order Methods in Optimization}},
year = {2017}
}