منابع مشابه
Group reconstruction systems
We consider classes of reconstruction systems (RS’s) for finite dimensional real or complex Hilbert spaces H, called group reconstruction systems (GRS’s), that are associated with representations of finite groups G. These GRS’s generalize frames with high degree of symmetry, such as harmonic or geometrically uniform ones. Their canonical dual and canonical Parseval are shown to be GRS’s. We est...
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This paper considers group reconstruction systems (GRS’s), for finite dimensional real or complex Hilbert spaces H, that are associated with unitary representations of finite abelian groups. The relation between these GRS’s and the generalized Fourier matrix is established. A special type of Parseval GRS, called harmonic reconstruction system (HRS), is defined. It is shown that there exist HRS’...
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PURPOSE MR fingerprinting (MRF) is a technique for quantitative tissue mapping using pseudorandom measurements. To estimate tissue properties such as T1 , T2 , proton density, and B0 , the rapidly acquired data are compared against a large dictionary of Bloch simulations. This matching process can be a very computationally demanding portion of MRF reconstruction. THEORY AND METHODS We introdu...
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ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2011
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1481