2 Parallel-beam image reconstruction
This chapter introduces the central slice theorem, which is the function of tomography. This theorem relates the two-dimensional (2D) image with its one-dimensional (1D) projections in the Fourier domain. From this theorem, many image reconstruction algorithms are derived. Among these algorithms, the filtered backprojection (FBP) algorithm is the most popular one, which consists of a ramp-filtering step and a backprojection step. The filtering can be implemented as a multiplication in the Fourier domain or as a convolution in the spatial domain. A special topic of region-of-interest (ROI) reconstruction with truncated projections is included in this chapter.
2.1 Fourier transform
The concept of the Fourier ...
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