Discrete Seismic Tomography

Open Access
Author:
Description:
Tomographic imaging reveals the interior of an object. Similar to a camera, it images an object by illuminating it with electromagnetic or acoustic waves (or a beam of photons). Due to its non-invasive nature, it has found applications in various fields of sciences and engineering. Recent challenges include fast and accurate reconstructions of high contrasts in the object from a limited number of tomographic measurements. To tackle this, prior information about the object under inspection is beneficial. One particular example is a discrete prior, where an object is made up of only a few homogeneous materials of known grey levels. The tomography that deals with this prior is known as discrete tomography. The discrete assumption holds approximately for many objects. In general, the low-contrast surrounding is not spatially invariant. This leads to a class of objects called partially discrete objects, where high-contrast materials lie in the non-homogeneous low-contrast background. This thesis develops algorithms based on the theory of convex optimization, regularization, and the level-set method to reconstruct discrete and partially discrete objects from limited measurements. In X-ray tomography, the challenge to reconstruct an object from limited measurements stems from the high levels of radiation dose from X-rays. Although the tomographic problem is linear, the discrete prior makes it non-convex. Many heuristic algorithms exist to image discrete objects from a few of their ray projections. These algorithms often require manual tuning of parameters and may suffer in the noisy scenario. We develop a convex program to recover the binary objects (i.e., objects composed of only two materials) that relies on the Lagrangian duality. The resulting problem is a l1-regularized least-squares problem (LASSO) that can be solved quickly. Based on small-scale experiments, we conjecture that if the binary tomography problem admits a unique solution, it can be recovered using the proposed formulation. In the case of multiple ...
Publisher:
Utrecht University
Contributors:
Sub Mathematical Modeling ; Mathematical Modeling ; Batenburg, K.J. ; Frank, Jason ; Mulder, W.A. ; van Leeuwen, Tristan
Year of Publication:
2019-12-16
Document Type:
Dissertation ; [Doctoral and postdoctoral thesis]
Language:
en
Subjects:
Computational imaging ; inverse problems ; optimization ; level-set method ; regularization theory
DDC:
004 Data processing & computer science (computed)
Rights:
info:eu-repo/semantics/OpenAccess
Relations:
URL:
https://dspace.library.uu.nl/handle/1874/387852
Content Provider:
Utrecht University Repository  Flag of Netherlands