Mathematical Background of Parallel Magnetic Resonance Imaging

by Benjamin Kocurov
Doctoral thesis
Date of Examination:2025-07-02
Date of issue:2025-10-07
Advisor:Prof. Dr. Gerlind Plonka-Hoch
Referee:Prof. Dr. Gerlind Plonka-Hoch
Referee:Prof. Dr. Martin Uecker
Persistent Address: http://dx.doi.org/10.53846/goediss-11535

 

 

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Abstract

English

We provide mathematical analyses of reconstruction methods in parallel Magnetic Resonance Imaging (pMRI). We start with a discussion of the mathematical model and then discuss multiple methods such as SENSE, (AUTO-)SMASH, GRAPPA, ESPIRiT and the new MOCCA method. The methods ESPIRiT and MOCCA are shown to be equivalent to the assumption of coil sensitivities modelled by trigonometric polynomials of a low degree.
Keywords: Parallel Magnetic Resonance Imaging; Parallel MRI; subspace methods; low-rank matrix methods; ESPIRiT; GRAPPA; SENSE; SMASH; MOCCA; trigonometric polynomials; Fourier transform
 
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