Compensation of Some Time Dependent Deformations in Tomography

This work concerns 2D+t dynamic tomography. We show that a much larger class of deformations than the affine transforms can be compensated analytically within filtered back projection algorithms in 2D parallel beam and fan beam dynamic tomography. We present numerical experiments on the Shepp and Logan phantom showing that nonaffine deformations can be compensated. A generalization to 3D cone beam tomography is proposed

[1]  R J Jaszczak,et al.  A filtered-backprojection algorithm for fan-beam SPECT which corrects for patient motion. , 1995, Physics in medicine and biology.

[2]  Pierre Grangeat,et al.  Dynamic X-ray computed tomography , 2003, Proc. IEEE.

[3]  Hiroyuki Kudo,et al.  Image reconstruction from fan-beam projections on less than a short scan , 2002, Physics in medicine and biology.

[4]  W A Kalender,et al.  Electrocardiogram-correlated image reconstruction from subsecond spiral computed tomography scans of the heart. , 1998, Medical physics.

[5]  J. Bowsher,et al.  Simultaneous reconstruction and motion estimation for gated cardiac ECT , 2001, 2001 IEEE Nuclear Science Symposium Conference Record (Cat. No.01CH37310).

[6]  F. Noo,et al.  Cone-beam reconstruction using 1D filtering along the projection of M-lines , 2005 .

[7]  Pierre Grangeat,et al.  Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations. , 2004, Physics in medicine and biology.

[8]  Pierre Grangeat,et al.  Theoretical framework for a dynamic cone-beam reconstruction algorithm based on a dynamic particle model. , 2002, Physics in medicine and biology.

[9]  A. Katsevich.  A GENERAL SCHEME FOR CONSTRUCTING INVERSION ALGORITHMS FOR CONE BEAM CT , 2003 .

[10]  Cameron J. Ritchie,et al.  Respiratory compensation in projection imaging using a magnification and displacement model , 1996, IEEE Trans. Medical Imaging.

[11]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[12]  B. Ohnesorge,et al.  Heart Rate Adaptive Optimization of Spatial and Temporal Resolution for Electrocardiogram-Gated Multislice Spiral CT of the Heart , 2001, Journal of computer assisted tomography.

[13]  Nicholas Ayache,et al.  3D tomographic reconstruction of coronary arteries using a precomputed 4D motion field. , 2004, Physics in medicine and biology.

[14]  Weiguo Lu,et al.  Tomographic motion detection and correction directly in sinogram space. , 2002, Physics in medicine and biology.

[16]  Eric Todd Quinto,et al.  The invertibility of rotation invariant Radon transforms , 1983 .