Discrete Seismic Tomography
Abstract
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…
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