Dynamic MRI (Magnetic Resonance Imaging) Reconstruction as a Moment Problem. Part 2. Riesz Bases in L(2)-Spaces of Vector Valued Functions

摘要

In Part I magnetic resonance imaging (MRI) is explained. At the end of Part I an inversion problem is formulated, which is solved in Part II: In order to solve this problem, the author uses the notion of Riesz bases in the space L2 (D,H), which will be explained here. Here D is a subset of IRn and L sup 2 (D,H), where H is a separable Hilbert space. It turns out that this inversion problem is equivalent to a collection of inversion problems in H. By solving these problem separately, he obtains a solution to the problem.