頁籤選單縮合
題 名 | Quantum Holography and Magnetic Resonance Tomography: An Ensemble Quantum Computing Approach |
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作 者 | Schempp,Walter; | 書刊名 | Taiwanese Journal of Mathematics |
卷 期 | 2:3 1998.09[民87.09] |
頁 次 | 頁257-285 |
分類號 | 310 |
關鍵詞 | Quantum holography; Radiodiagnostics; Harmonic analysis on the heisenberg group; |
語 文 | 英文(English) |
英文摘要 | Coherent wavelets form a unified basis of the multichannel perfect reconstruction analysis-synthesis filter bank of high resolution radar imaging and clinical magnetic resonance imaging (MRI). The filter bank construction is performed by the Kepplerian temporospatial phase detection strategy which allows for the stroboscopic and synchronous cross sectional quadrature filtering of phase histories in local frequency encoding multichannels with respect to the rotating corrdinate frame of reference. The Kepplerian strategy and the associated filter bank construction take place in symplectic affine planes which are immersed as coaduoint orbits of the Heisenberg two-step nilpotent Lie group G into the foliated three-dimensional real projective space P(R×Lie(G)��). Due to the factorization of transvections into affine dilations of opposite ratio, the Heisenberg group G under its natural sub-Riemannian metric acts on the line bundle realizing the projective space P(R×Lie(G)��). Its elliptic non-Euclidean geometry wihtout absolute quadric, associated to the unitary dual G, governs the design of the coils inside the bore of the MRI scanner system. It determines the distributional reproducing kernel of the tracial read-out process of quantum holograms excited and coexisting in the MRI scanner system. Thus the pathway of this paper leads from Keppler's approach to projective geometry to the Heisenberg approach to the sub-Riemannian geometry of quantum physics, and finally to the enormously appealing topic of ensemble quantum computing. |
本系統中英文摘要資訊取自各篇刊載內容。