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  • Single-scattering tomography describes a model of photon transfer through a object in which photons are assumed to scatter at most once. The Broken Ray transform arises from this model, and was first investigated by Lucia Florescu, Vadim A. Markel, and John C. Schotland, [2], in 2010, followed by an inversion, [1], in the case of fixed initial and terminal directions. Later, in 2013, Katsevich and Krylov, [6], investigated settings where terminal rays were permitted to vary, either heading towards or away from a focal point, providing inversion formulas in two- and three-detector settings. In this thesis, we will explore these transforms, give them distributional meaning, and analyze how these transforms propagate singularities. This requires analysis of the relationships between a function and its antiderivative obtained from integration over a ray. This thesis also introduces the Polar Broken Ray transform, in which the source position is fixed, initial direction varies, and the scattering angle is held constant. We will discover that the Polar Broken Ray transform is injective on spaces of functions supported in an annulus that is bounded away from the origin, and also derive distributional meaning to the Polar Broken Ray transform, and derive a relationship between a wavefront set of a function and that of its Polar Broken Ray transform. Provided in the appendix are implementations of numerical inversions of the Broken Ray transform with fixed initial and terminal directions, as well as the Polar Broken Ray transform.
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  • description.provenance : Approved for entry into archive by Laura Wilson(laura.wilson@oregonstate.edu) on 2016-01-06T21:32:15Z (GMT) No. of bitstreams: 7 license_rdf: 1370 bytes, checksum: cd1af5ab51bcc7a5280cf305303530e9 (MD5) ShersonBrianJ2016.pdf: 6559908 bytes, checksum: c7c6dc127aa2d0bbb42119c7d209ba25 (MD5) brokenray-e3fc560d5ade71a9828c2b9c58e7877727ea205f.zip: 47683 bytes, checksum: f649ed3639a75fb195fe4e201a704268 (MD5) python-array2im-6af0e5fb88d2e31fb906a5c29c32e9008ab24ed8.zip: 3751 bytes, checksum: e68557f4e970a7b3e7b4e8b98b4491bc (MD5) python-rpncalc-6ffc837757be26353086a009de9db089dc2e96cd.zip: 9889 bytes, checksum: 204fdd0c666c33bef48504c1022f34b1 (MD5) python-parallel-b92727900fc8a8ed93ed174bed7b5af715487dba.zip: 3827 bytes, checksum: c417d04348e44eac505022a13b02f1a1 (MD5) python-iqueue-85f0ecb3ae5137d0e54dc79528019fa5b7d082d1.zip: 7636 bytes, checksum: 3eb76c09279ba4acbe92d1b4f169af6a (MD5)
  • description.provenance : Approved for entry into archive by Julie Kurtz(julie.kurtz@oregonstate.edu) on 2016-01-06T18:59:15Z (GMT) No. of bitstreams: 7 license_rdf: 1370 bytes, checksum: cd1af5ab51bcc7a5280cf305303530e9 (MD5) ShersonBrianJ2016.pdf: 6559908 bytes, checksum: c7c6dc127aa2d0bbb42119c7d209ba25 (MD5) brokenray-e3fc560d5ade71a9828c2b9c58e7877727ea205f.zip: 47683 bytes, checksum: f649ed3639a75fb195fe4e201a704268 (MD5) python-array2im-6af0e5fb88d2e31fb906a5c29c32e9008ab24ed8.zip: 3751 bytes, checksum: e68557f4e970a7b3e7b4e8b98b4491bc (MD5) python-rpncalc-6ffc837757be26353086a009de9db089dc2e96cd.zip: 9889 bytes, checksum: 204fdd0c666c33bef48504c1022f34b1 (MD5) python-parallel-b92727900fc8a8ed93ed174bed7b5af715487dba.zip: 3827 bytes, checksum: c417d04348e44eac505022a13b02f1a1 (MD5) python-iqueue-85f0ecb3ae5137d0e54dc79528019fa5b7d082d1.zip: 7636 bytes, checksum: 3eb76c09279ba4acbe92d1b4f169af6a (MD5)
  • description.provenance : Submitted by Brian Sherson (shersonb) on 2016-01-01T04:41:11Z No. of bitstreams: 7 license_rdf: 1370 bytes, checksum: cd1af5ab51bcc7a5280cf305303530e9 (MD5) ShersonBrianJ2016.pdf: 6559908 bytes, checksum: c7c6dc127aa2d0bbb42119c7d209ba25 (MD5) brokenray-e3fc560d5ade71a9828c2b9c58e7877727ea205f.zip: 47683 bytes, checksum: f649ed3639a75fb195fe4e201a704268 (MD5) python-array2im-6af0e5fb88d2e31fb906a5c29c32e9008ab24ed8.zip: 3751 bytes, checksum: e68557f4e970a7b3e7b4e8b98b4491bc (MD5) python-rpncalc-6ffc837757be26353086a009de9db089dc2e96cd.zip: 9889 bytes, checksum: 204fdd0c666c33bef48504c1022f34b1 (MD5) python-parallel-b92727900fc8a8ed93ed174bed7b5af715487dba.zip: 3827 bytes, checksum: c417d04348e44eac505022a13b02f1a1 (MD5) python-iqueue-85f0ecb3ae5137d0e54dc79528019fa5b7d082d1.zip: 7636 bytes, checksum: 3eb76c09279ba4acbe92d1b4f169af6a (MD5)
  • description.provenance : Made available in DSpace on 2016-01-06T21:32:15Z (GMT). No. of bitstreams: 7 license_rdf: 1370 bytes, checksum: cd1af5ab51bcc7a5280cf305303530e9 (MD5) ShersonBrianJ2016.pdf: 6559908 bytes, checksum: c7c6dc127aa2d0bbb42119c7d209ba25 (MD5) brokenray-e3fc560d5ade71a9828c2b9c58e7877727ea205f.zip: 47683 bytes, checksum: f649ed3639a75fb195fe4e201a704268 (MD5) python-array2im-6af0e5fb88d2e31fb906a5c29c32e9008ab24ed8.zip: 3751 bytes, checksum: e68557f4e970a7b3e7b4e8b98b4491bc (MD5) python-rpncalc-6ffc837757be26353086a009de9db089dc2e96cd.zip: 9889 bytes, checksum: 204fdd0c666c33bef48504c1022f34b1 (MD5) python-parallel-b92727900fc8a8ed93ed174bed7b5af715487dba.zip: 3827 bytes, checksum: c417d04348e44eac505022a13b02f1a1 (MD5) python-iqueue-85f0ecb3ae5137d0e54dc79528019fa5b7d082d1.zip: 7636 bytes, checksum: 3eb76c09279ba4acbe92d1b4f169af6a (MD5) Previous issue date: 2015-12-10

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