PMID: 8587940Nov 1, 1995Paper

Linear dimension reduction of sequences of medical images: I. Optimal inner products

Physics in Medicine and Biology
F Hermansen, Adriaan A Lammertsma

Abstract

A general theory is presented for minimizing noise in linear dimension reduction of sequences of medical images when the factors and the covariance matrix and mean of the noise are given. A dimension reduction is optimal when all diagonal elements in the covariance matrix of the noise in the signal (factor) space are minimized. This occurs when the noise in the signal space is uncorrelated with the residual noise. Expressions are given for the resulting covariance matrix of the noise in the signal space. Many optimal inner products exist, which all result in the same optimal dimension reduction. Given any pair of inner products for signal space and residual space, a combined inner product exists that is also optimal. If the covariance matrices of the noise in different pixel vectors are not multiples of each other, different pixel vectors may have different optimal inner products. The averaging process in generating images from tomographic projections tends to make the covariance matrices more uniform.

References

May 1, 1991·Journal of Cerebral Blood Flow and Metabolism : Official Journal of the International Society of Cerebral Blood Flow and Metabolism·T YokoiK Uemura
Jan 1, 1984·Annals of Neurology·E J HoffmanM E Phelps
Jan 1, 1982·Journal of Cerebral Blood Flow and Metabolism : Official Journal of the International Society of Cerebral Blood Flow and Metabolism·S C HuangM E Phelps
Nov 1, 1995·Physics in Medicine and Biology·F HermansenA A Lammertsma

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Citations

Aug 22, 2009·Physica Medica : PM : an International Journal Devoted to the Applications of Physics to Medicine and Biology : Official Journal of the Italian Association of Biomedical Physics (AIFB)·P VeltriV Carbone
Oct 13, 2012·IEEE Transactions on Bio-medical Engineering·Rostom MabroukLayachi Bentabet
Apr 9, 1998·IEEE Transactions on Medical Imaging·C M KaoM N Wernick
Jul 1, 2015·European Journal of Nuclear Medicine and Molecular Imaging·Roberto SciagràAlberto Pupi
Dec 10, 1999·Physics in Medicine and Biology·M SámalH Bergmann
Aug 1, 1996·Physics in Medicine and Biology·F Hermansen, A A Lammertsma
Nov 1, 1995·Physics in Medicine and Biology·F HermansenA A Lammertsma

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