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Image Formation in Spectral Computed Tomography
Published in Katsuyuki Taguchi, Ira Blevis, Krzysztof Iniewski, Spectral, Photon Counting Computed Tomography, 2020
Simon Rit, Cyril Mory, Peter B. Noël
None of the methods presented in subsection 19.2.1 makes any assumption on how the material sinograms are reconstructed once they have been decomposed. In fact, any tomographic reconstruction method can be used, including filtered backprojection algorithms. However, the decomposition is sensitive to noise and it is natural to account for this noise in an iterative reconstruction algorithm. A first solution is to use an estimate of the variance of the decomposed sinograms in a weighted least squares algorithm [61]. The material decomposition process also induces anti-correlated noise between the different materials [22], which suggests the use of reconstruction techniques that also account for covariances [60]. Variances and covariances can be estimated using the Cramér-Rao lower bound [56]. Sawatzky et al. [59] and Mory et al. [43] proposed such an approach. The core idea of these methods is that minimizing the usual least-squares data-attachment term yields the best linear unbiased estimator (BLUE) only when all data samples are uncorrelated and have equal variance. In all other cases, the BLUE is obtained by minimizing a generalized least squares (GLS) term, which involves the inverse of the covariance matrix of the noise. Although GLS is formally simple, it is computationally much more demanding since all material-specific CT maps fm must be reconstructed simultaneously. It is not clear yet whether the improvement in image quality is worth the increased computational complexity [43].
Tomography Reconstructions With Stochastic Level-Set Methods
Published in Ayman El-Baz, Jasjit S. Suri, Level Set Method in Medical Imaging Segmentation, 2019
Bruno Sixou, Lin Wang, Françoise Peyrin
The tomographic reconstruction from few projections is a very ill-posed problems with many applications in medical imaging or material science. The binary tomography methods can be used to set a simpler inverse problem [13]. The binary tomography problem can be formulated as an under-determined linear system of equations with the linear Radon projection operator R and binary constraints: Rf=pδf=(f1,…….fn)∈{0,1}n
Optical Deflectometry by Speckle Photography
Published in Wen-Jei Yang, Handbook of Flow Visualization, 2018
Computerized tomography is a means for extending the capabilities of optical line-of-sight methods to the measurement of three-dimensional flow fields; see, e.g., Hesselink [20]. Tomography requires that recordings be taken in different viewing directions (”projections”) covering 180° at equal intervals (or less than 180° flow exhibits a certain kind of symmetry). Several algorithms are available for reconstructing the three-dimensional density field from the information recorded in the various projections. For a given test field, the quality of the tomographic reconstruction depends on the number of projections taken, the covered total angular range of viewing directions, and the amount of information available from each projection (”signal density”). As mentioned before, the signal density is generally high in speckle photography.
Near-field subsurface tomography and holography based on bistatic measurements with variable base
Published in Inverse Problems in Science and Engineering, 2021
Konstantin P. Gaikovich, Yelena S. Maksimovitch, Vitaly A. Badeev
Inverse problems of the wave scattering, especially in the 3D electromagnetic tomography, are not only ill-posed, but also nonlinear and, hence, much more time-consuming – even in the calculation of scattered fields. It leads to a limitation of the grid size used at calculations and, hence, to a limitation of the achievable resolution, i.e. the ability to resolve the smallest details in an object. Another constraint of resolution is the Rayleigh diffraction limit (half-wavelength in the case of full view tomographic reconstruction). It seems obvious that the resolution can be increased by employing shorter wavelengths – but usually, as the wavelength decreases the penetration depth of the probing field decreases due to increasing absorption and scattering in searching media.