By Holger Scherl
This ebook considers the sphere of computed tomography together with a evaluation of cutting-edge reconstruction algorithms and a concise review of the latest architectures. Holger Scherl introduces the reader to the reconstruction challenge in computed tomography and its significant medical demanding situations that diversity from computational potency to the success of Tuy's sufficiency . The assessed architectures together with multi- and many-core structures, cellphone broadband engine structure, photograph processing devices, and box programmable gate arrays. the writer makes a speciality of the interaction among those fresh structures and smooth computed tomography reconstruction algorithms.
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Extra resources for Evaluation of State-of-the-Art Hardware Architectures for Fast Cone-Beam CT Reconstructions
They are often initialized to zero or very small positive values. , the FDK method or simply the result of an unﬁltered back-projection step. Streak artifacts appearing around high-contrast structures disappear very slowly with the iterations when the initial voxel volume is uniformly initialized. These artifacts are rapidly suppressed when an initial FDK reconstruction is used as a starting point at the expense of the injection of additional noise. This noise is, however, eﬀectively removed after ﬁve to ten iterations [Zbij 03].
Thus, especially the ﬁltering of projections incurs much more computations to be performed by the image reconstruction hardware. The M-line approach can be applied for C-arm CT [Hopp 06]. It is, however, required that Tuy’s data completeness condition for image reconstruction is fulﬁlled [Tuy 83]. According to Tuy it is possible to reconstruct the point x in a theoretically exact manner if and only if every plane through x intersects the source trajectory at least once. This intersection should not happen tangentially to the trajectory and not at an endpoint of the trajectory.
In this section we will analyze their time complexity. 1 the ﬁltering step can be implemented in the spatial or in the frequency domain. In the following we estimate the number of required ﬂoating-point operations required to implement each variant. In the spatial domain the 1-D discrete convolution of the image rows of g with a ﬁlter kernel given as a 1-D mask h and consisting of NM = 2m + 1 elements (cf. 8) can be computed by m h(k)g(ˇ u − k, vˇ) . 19) ﬂoating-point operations for Np projection images consisting of Nv rows and Nu columns.