论文信息 - Three-dimensional reconstruction from planar projections

Three-dimensional reconstruction from planar projections

The technique of direct three-dimensional reconstruction from planar projections is analyzed from a linear system viewpoint. It is found that unfiltered back projection and summation of the one-dimensional planar projections gives a point-spread function that behaves like 1/r in three-dimensional space. Thus an analogy between this reconstruction problem and the familiar electrostatic problem is set up. To correct the 1/r blurring, a Laplacian operation on the unfiltered summation image is required. Another method for reconstruction is to perform a second derivative operation on the one-dimensional planar projection set before the back projection. For spherically symmetric objects, this algorithm reduces to the Vest–Steel formula. The advantages of this reconstruction scheme as compard with reconstruction from line projections are also discussed.

[1] E. Kennaugh,et al. Transient and impulse response approximations , 1965 .

[2] M M Mueller,et al. Reconstruction of spherically symmetric objects from slit-imaged emission: limitations due to finite slit width. , 1979, Optics letters.

[3] C. Vest,et al. Reconstruction of spherically symmetric objects from slit-imaged emission: application to spatially resolved spectroscopy. , 1978, Optics letters.

[4] O. Nalcioglu,et al. Reconstruction of 3-D objects from cone beam projections , 1978, Proceedings of the IEEE.

[5] Benjamin Friedlander,et al. Direct three-dimensional image reconstruction , 1979 .

[6] Y. Das,et al. On radar target shape estimation using algorithms for reconstruction from projections , 1978 .

[7] Gene Gindi,et al. Three-dimensional radiographic imaging with a restricted view angle , 1979 .

[8] W. Swindell,et al. Analog reconstruction methods for transaxial tomography , 1977, Proceedings of the IEEE.

[9] E Tanaka,et al. Generalised correction functions for convolutional techniques in three-dimensional image reconstruction. , 1979, Physics in medicine and biology.

[10] A. Cormack. Reconstruction of densities from their projections, with applications in radiological physics. , 1973, Physics in medicine and biology.