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Near‐optimal spatial encoding for dynamically adaptive MRI: Mathematical principles and computational methods
Author(s) -
Zientara Gary P.,
Panych Lawrence P.,
Jolesz Ferenc A.
Publication year - 1999
Publication title -
international journal of imaging systems and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.359
H-Index - 47
eISSN - 1098-1098
pISSN - 0899-9457
DOI - 10.1002/(sici)1098-1098(1999)10:2<151::aid-ima6>3.0.co;2-y
Subject(s) - encoding (memory) , computer science , linear subspace , algorithm , basis (linear algebra) , computation , rank (graph theory) , computational complexity theory , image (mathematics) , subspace topology , mathematics , artificial intelligence , geometry , combinatorics
The mathematical principles of near‐optimal two‐dimensional spatial encoding for dynamically adaptive magnetic resonance imaging (MRI) are presented together with a survey of numerical methods applicable for the computation of these encodes. Two main classes of linear algebraic techniques are identified—rank revealing orthogonal decompositions and Krylov subspace methods—that are specially suited for the determination of efficient adaptive non‐Fourier spatial encoding. Simulation results are presented to demonstrate usage. The key property of these methods is their ability to compute reduced vector basis sets, used as encoding profiles, that span the column and row vector subspaces of an image estimate array. Efficient encoding in MRI is possible since MR images typically represent rank deficient matrices. New methods for computing hybrid encodings based on near‐optimal encodes are also described. An analysis of the applicability and efficiency of near‐optimal encoding is presented using the principal angles between vector basis sets of the theoretical ideal image and that from an image estimate actually used for acquisition. © 1999 John Wiley & Sons, Inc. Int J Imaging Syst Technol, 10, 151–165, 1999