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Optimization of Basic Magnetic Field Homogeneity in MR Tomography
Hadinec, Michal ; Brančík, Lubomír (referee) ; Frollo, Ivan (referee) ; Bartušek, Karel (advisor)
This thesis is concerned with problems of measuring and mapping of magnetic field in MR tomograph, for purpose of magnetic flux density homogeneity optimization. Attention is paid to mapping techniques on rotary symmetric volume and to ways of magnetic fields optimization with utilization of passive and active correction systems. Theoretical analysis of magnetic field decomposition with utilization of spherical harmonics and numerical decomposition is made. Mapping and approximation techniques of basic magnetic field are verified by experiments in the laboratory at the Institute of Scientific Instruments AS CR in Brno.
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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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Orthogonal bases and their application in signal processing
Kárský, Vilém ; Tůma, Martin (referee) ; Jura, Pavel (advisor)
This work is concentrates on finding basic properties of some orthogonal polynomials like a definition, weight function, orthogonality interval, recurrence relations, number of zeros and diferential eguations which they were suited on. Subsequently were founded formulas for calculating coefficients of the generalized Fourir series and I concentrate on calculating optimal free parameters on this orthogonal polynomials. In the end of this work are calculated and displayed spectrums of some functions in the bases of individual polynomials and was calculated and displayed aproximation error.
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Optimization of Basic Magnetic Field Homogeneity in MR Tomography
Hadinec, Michal ; Brančík, Lubomír (referee) ; Frollo, Ivan (referee) ; Bartušek, Karel (advisor)
This thesis is concerned with problems of measuring and mapping of magnetic field in MR tomograph, for purpose of magnetic flux density homogeneity optimization. Attention is paid to mapping techniques on rotary symmetric volume and to ways of magnetic fields optimization with utilization of passive and active correction systems. Theoretical analysis of magnetic field decomposition with utilization of spherical harmonics and numerical decomposition is made. Mapping and approximation techniques of basic magnetic field are verified by experiments in the laboratory at the Institute of Scientific Instruments AS CR in Brno.
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