Imaging reconstruction

Fundamental of the Theory for Adaptive Image Reconstruction in X-Ray Tomography. 

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

The prior knowledge is assumed to be the discrete structure of the image, the statistical independence of the noise values, their stationarity and zero mean value. For this case, the image reconstruction problem can be represented as an adaptive stochastic estimation process [9] with the structure shown in Fig. 1. 

Fig. 2 Single slice of porosity in ferritic weld (a) original image, (b) image recontruction without noise, (c) image reconstruction with noise.

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... 

Recently, series of computerized defectoscopes AUGUR for inspected area image reconstruction have been developed in Russia in the framework of RF Minatom program. One of them is device with coherent data processing for expert inspection named AUGUR 4.2 . 

Altschuler M.D and Herman G. Fully three-dimensional image reconstruction using series expansion methods., A Review of Information Processing in Medical Imaging, Oak Ride National Lab., Oak Ride, TN, 1977, p.124-142. 

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

P.Y. lotibert, D. Miller, D. Placko, and E. Savin. New eddy current probe and associated preprocessings for 3d image reconstruction in non ferromagnetic tubes testing. In To be published in the proceedings of the Seventh ECNDT, 1998. 

New Eddy Current Probe and Associated Preprocessing for 3D Image Reconstruction in Non Ferromagnetic Tube Testing. 

Kalukin A.R., Effects of Internal Scattering on X-ray Microtomography Image Reconstruction , IEEE Transactions on Nuclear Science, vol. 44, No. 2, April 1997, pp. 142-147. 

The system is equipped with an DEC- Alpha Station running at 400 MHz. Therefore the time for image reconstruction is not important compared to the time for data acquisition and preparation of the sample. 

Figure 9 P-scan and T-scan images reconstructed from recorded A-scans...

FIGURE 17.28 Image reconstructions of the junctional channel complex of a foot structure. (Photo courtesy of Sidney FIAscher, Vanderbilt University)... 

Keywords image reconstruction, deconvolution, inverse problems, regularization... 

Figure 1 shows the simulation of a galaxy observed with a PSF which is typical of an adaptive optics system. The noisy blurred image in Fig. 1 will be used to compare various image reconstruction methods described in this course. 

Titterington, D.M., 1985, General structure of regularization procedures in image reconstruction, Astron. Astrophys. 144, 381... 

FIG. 1 Freeze-etching image of a bacterial cell of (a) Desulfotomaculum nigrificans (bar, 100 nm). Atomic force micrographs of the S-layer proteins of (b) Bacillus sphaericus CCM 2177 and (c) Bacillus stearothermophilus PV72/p2 recrystallized in monolayers on silicon wafers. Bars, 50 nm. The insets in (b) and (c) show the corresponding computer-image reconstructions. 

Image reconstruction in three dimensions from negatively stained and frozen hydrated crystals... 

---