Reconstruction from Projections
The principles of tomographic reconstruction are the subject of this chapter and are introduced so that the reader can understand what CT and microCT can and cannot do and what causes certain artefacts. The treatment here is limited to absorption tomography and concentrates on the physical underpinning and not the mathematics. The basic concepts of reconstruction from x-ray projections are covered first and are followed by introduction to the three generally accepted classes of reconstruction algorithms: iterative methods, analytic methods, and data-driven/learning-based artificial intelligence (AI) methods. Iterative reconstruction is illustrated using the algebraic reconstruction technique (ART), and other iterative algorithms are briefly covered. Two popular analytic reconstruction approaches are explained: the convolution back projection method and Fourier-based reconstruction algorithm. The newer AI-based/machine learning approaches to tomographic reconstruction are introduced. The chapter concludes by discussing performance limits for tomographic reconstruction and alternative methods for 3D mapping of structure.