Convolution, Rotation, and Data Fusion with Orthogonal Expansions

Integration;Hermite Functions;Bessel Functions;Recurrence Relations;Data Fusion;Rotation;Mechanical Engineering

Reynolds, Kristopher LewisChirikjian, Gregory ;

Johns Hopkins University

关键词: Integration;    Hermite Functions;    Bessel Functions;    Recurrence Relations;    Data Fusion;    Rotation;    Mechanical Engineering;   

Others  :  https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/60082/submission_fee_form.pdf?sequence=3&isAllowed=y

瑞士|英语

来源: JOHNS HOPKINS DSpace Repository

【 摘 要 】

This dissertation investigates certain special function classes, namely Hermite andBessel functions, and uncovers some useful properties relating multiplication, convolution,rotation, and coordinate conversion. These mathematical operations are performedon the underlying basis functions and are thus continuous in nature, lendingitself to higher accuracy and computational speed. Some integral transformations involvingthese special functions (e.g. Abel transform, 3h integrals, 3J integrals) possessrecurrence relations, and so given anite set of analytic starting conditions, higherorder forms of these integrals can be obtained quickly. It will be shown how theseintegrals and the aforementioned special function properties are used in engineeringapplications including data fusion, deconvolution, continuum normal mode analysis,cryo-electron microscopy (cryo-EM) and small angle X-ray scattering (SAXS).