目录 1 Basic Principles of Tomography 1.1 Tomography 1.2 Projection 1.3 Image Reconstruction 1.4 Backprojection 1.5 Mathematical Expressions 1.6 Worked Examples 1.7 Summary Problems References2 Parallel-Beam Image Reconstruction 2.1 Fourier Transform 2.2 Central Slice Theorem 2.3 Reconstruction Algorithms 2.4 A Computer Simulation 2.5 ROI Reconstruction with Truncated Projections 2.6 Mathematical Expressions 2.7 Worked Examples 2.8 Summary Problems References3 Fan-Beam Image Reconstruction 3.1 Fan-Beam Geometry and Point Spread Function 3.2 Parallel-Beam to Fan-Beam Algorithm Conversion 3.3 Short Scan 3.4 Mathematical Expressions 3.5 Worked Examples 3.6 Summary Problems References4 Transmission and Emission Tomography 4.1 X-Ray Computed Tomography 4.2 Positron Emission Tomography and Single Photon Emission Computed Tomography 4.3 Attenuation Correction for Emission Tomography 4.4 Mathematical Expressions 4.5 Worked Examples 4.6 Summary Problems References5 3D Image Reconstruction 5.1 Parallel Line-Integral Data 5.2 Parallel Plane-Integral Data 5.3 Cone-Beam Data 5.4 Mathematical Expressions 5.5 Worked Examples 5.6 Summary Problems References6 Iterative Reconstruction 6.1 Solving a System of Linear Equations 6.2 Algebraic Reconstruction Technique 6.3 Gradient Descent Algorithms 6.4 Maximum-Likelihood Expectation-Maximization Algorithms 6.5 Ordered-Subset Expectation-Maximization Algorithm 6.6 Noise Handling 6.7 Noise Modeling as a Likelihood Function 6.8 Including Prior Knowledge 6.9 Mathematical Expressions 6.10 Reconstruction Using Highly Undersampled Data with 10 Minimization 6.11 Worked Examples 6.12 Summary Problems References7 MRI Reconstruction 7.1 The \\"M\\" 7.2 The \\"R\\" 7.3 The \\"T\\" 7.4 Mathematical Expressions 7.5 Worked Examples 7.6 Summary Problems References Index 作者介绍 What you have just done is a standard mathematical procedure calledbackprojection. If you backproject from all angles from You will produce an image similar to the one shown in Figure 1.9 (d). After backprojection, the image is still not quite the same as the orig-inal image but rather is a blurred version of it. To eliminate the blurring,we introduce "wings" around the spike in the projections beforebackprojection [see Figure 1.9 (e)]. The procedure of adding wingsaround the spike is called filtering. The use of the wings results in aclear image [see Figure 1.9 (f)]. This image reconstruction algorithm is very common and is referred to as a Filtered Backprojection (FBP) algorithm. In this section, we use a point source to illustrate the usefulness of filtering and backprojection with many views in image reconstruction. We must point out that if the object is a point source, we only need two views to reconstruct the image, just like the map making example in Section 1.1. …… 序言
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