Haiquan Yang | Search PubMed

PubMed2006

View-independent reconstruction algorithms for cone beam CT with general saddle trajectory.

In Yang et al (2006 Phys. Med. Biol. 51 1157-72), an exact filtered backprojection (FBP) reconstruction algorithm was proposed for cone beam tomography with saddle trajectory based on the seminal works of Pack and Noo (2005a Inverse Problems 21 1105-20; 2005b 8th Int. Meeting on Fully 3D Reconstruction in Radiology and Nuclear Medicine (Salt Lake City) ed F Noo, H Kudo and L G Zeng pp 287-90). However, the artefacts due to discretization and/or sampling errors in the reconstructed images by this method were still visible, especially when the pitch is large. In this paper, two view-independent (VI) algorithms, which are similar to the FDK-type algorithms (Feldkamp et al 1984 J. Opt. Soc. Am. A 1 612-19), are proposed for planar detector geometry. The first VI algorithm involves two filtered projections and a small additional term (two-dimensional (2D) Radon transform term). One of the filtered projections is obtained by ramp filtering (as in the FDK algorithm for circular trajectory) and the other one is obtained by Hilbert transform. The 2D Radon transform term is just like the term which was first derived by Hu (1996 Scanning 18 572-81) for a circular trajectory. The second VI algorithm involves only one filtered projection term, which is obtained by differentiation followed by Hilbert transform and the 2D Radon transform term. Both algorithms involve only one backprojection step with a weighting factor as in the FDK algorithm. The simulation studies show that the pixel values of the reconstructed images by the VI algorithms are more accurate than those by the original view differencing (VD) algorithm, the streak artefacts are also reduced, and their computational times are comparable to that of the original VD algorithm. We also generalize the concept of saddle trajectory and the corresponding reconstruction algorithm. The generalized algorithm is also theoretically exact, has a shift-invariant FBP structure, and does not depend on the concept of pi-line.

Algorithms↗

PubMed2006

Exact cone beam reconstruction for a saddle trajectory.

We propose an exact shift-invariant filtered backprojection (FBP) algorithm for inversion of cone beam (CB) data in the case where the source trajectory is a saddle. The algorithm allows for axial truncation of the cone beam data. The algorithm involves only one family of filtering lines on the detector plane, and it does not depend on the existence of pi-lines. The algorithm is derived from a general formula in Pack and Noo (2005 Inverse Problems 21 1105-20). We also give the steps to implement the algorithm for planar detector geometry and discuss how to select the parameter of the saddle and the size of the detector when the trajectory is a standard saddle. The algorithm is tested by simulation studies.

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PubMed2002

An accurate iterative reconstruction algorithm for sparse objects: application to 3D blood vessel reconstruction from a limited number of projections.

Based on the duality of nonlinear programming, this paper proposes an accurate row-action type iterative algorithm which is appropriate to reconstruct sparse objects from a limited number of projections. The cost function we use is the Lp norm with p approximately 1.1. This norm allows us to pick up a sparse solution from a set of feasible solutions to the measurement equation. Furthermore, since it is both strictly convex and differentiable, we can use the duality of nonlinear programming to construct a row-action type iterative algorithm to find a solution. We also impose the bound constraint on pixel values to pick up a better solution. We demonstrate that this method works well in three-dimensional blood vessel reconstruction from a limited number of cone beam projections.

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