Reconstruction from projections imaging

Image reconstruction from projections is a basic process in computerized tomography (CT)... 

Finally, it is shown in terms of the presented example that the proposed adaptive reconstruction algorithm is valuable for image reconstruction from projections without any prior information even in the case of noisy data. The number of required projections can be determined by investigating the convergence properties of the reconstruction algorithm. 

G. T. Herman, Image Reconstruction from Projections, Academic Press, NY, 1980... 

Herman G.T. Image reconstruction from projections.. Computer Science and Applied Mathematics, New York Academic, 1980... 

Herman GT (1980) Image Reconstruction from Projection The Fundamentals of Computerized Tomography. New York, NY Academic Press. 

The first point has not been clearly recognized or appreciated in the early days of the method, so terms like radon transformation aad filtered backprojection were introduced [Herl, Manl], In practical realizations of image reconstruction from projections, however, numerical frers must, indeed, be used [Herl]. 

Use of the expression backprojection instead of reconstruction from projections is historical. Given a sufficient number of projections of an object acquired at different angles, the shape of the object can indeed be reconstructed with recognizable features, if the projections are just smnmed over the image plane in the directions over which... 

The gradient is static in the sample ftame so that the rotating spin density leads to a time-independent signal. The phase tp is varied in small steps for imaging with reconstruction from projections, or it is switched by multiples of n/2 for Fourier imaging methods. 

Fig, 8.6.2 2D MARF images of compressed polycrystalline adamantane. Left MARF images obtained by reconstruction from projections. Right shapes of the objects and dimensions. Adapted from i Mar2] with permission from the author. 

Herman, G.T. (2010) Fundamentals of Computerized Tomography Image Reconstruction from Projection, 2nd edn. Springer, New York. 

Computerized tomography is a technique by which three-dimensional (3-D) imaging of an object is made possible. The basic data are most often obtained in the form of projection data. Since the first tomographic system, known as X-ray CT, was designed by G. N. Hounsfield in 1972, many applications of the technology, based on 3-D image reconstruction from projection, have been developed. These include X-ray CT, radionuclide (isotope) emission CT (ECT), and nuclear magnetic resonance (NMR) CT. The basic forms of projection data are obtained from focused and collimated X rays, y rays, and... 

Since 1970, active research on image reconstruction from projection has been initiated mainly through the development of CT. This projection reconstruction is now applied to many areas of science. The most important area of its application has probably been CT projection reconstruction has remained the basic algorithm for CT since the inception of X-ray CT in 1972. 

Herman, G. T. Image Reconstruction from Projections The Fundamenbis of Computerized Tomography Academic Press New York, 1980. 

Smith B.D. Image reconstruction from cone-beam projections necessary and sufficient conditions and reconstruction methods., IEEE Trans. Med. Imaging, V. 4, 1985, p. 14-28. 

Before the data can be visualised, ie displayed in a two or three-dimensional representation, the ultrasonic responses from the interior of the test-piece must be reconstructed from the raw ultrasonic data. The reconstruction process projects ultrasonic indications into 3D space. As well as reconstructing the entire ultrasonic data set within an acquisition file, it is possible to define an arbitrary sub-volume of the test object over which reconstruction will take place. The image resolution may also be defined by the user. Clearly, larger volumes or greater resolution will increase the computation time for both the reconstruction and visualisation processes. 

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