This paper addresses the tomographic imaging of time-varying distributions, when the temporal variation during acquisition of the data is high, precluding Nyquist rate sampling. This paper concentrates on the open (and hitherto unstudied) problem of nonperiodic temporal variation, which cannot he reduced to the time-invariant case by synchronous acquisition. The impact of the order of acquisition of different views on the L₂ norm of the image-domain reconstruction error is determined for band-limited temporal variation. Based on this analysis, a novel technique for lowering the sampling rate requirement while preserving image quality is proposed and investigated. This technique involves an unconventional projection sampling order which is designed to minimize the L₂ image-domain reconstruction error of a representative test image. A computationally efficient design procedure reduces the image data into a Grammian matrix which is independent of the sampling order. Further savings in the design procedure are realized by using a Zernike polynomial series representation for the test image. To illustrate the approach, reconstructions of a computer phantom using the best and conventional linear sampling orders are compared, showing a seven-fold decrease in the error norm by using the best scheme. The results indicate the potential for efficient acquisition and tomographic reconstruction of time-varying data. Application of the techniques are foreseen in X-ray computer tomography and magnetic resonance imaging.

Date Published: 1 May 1990
PDF: 13 pages
Proc. SPIE 1245, Biomedical Image Processing, (1 May 1990); doi: 10.1117/12.19546

Published in SPIE Proceedings Vol. 1245:
Biomedical Image Processing
Alan Conrad Bovik; William E. Higgins, Editor(s)