Implementations, comparisons, and an investigation of heuristic techniques for cone-beam tomography

Volume fusion for two-circular-orbit cone-beam tomography

By using the Feldkamp-Davis-Kress (FDK) algorithm, we can efficiently produce a digital volume, called the FDK volume, from cone-beam data acquired along a circular scan orbit. Due to the insufficiency of the cone-beam data set, the FDK volume suffers from nonuniform reproduction exactness. Specifically, the midplane (on the scan-orbit plane) can be exactly reproduced, and the reproduction exactness of off-midplanes decreases as the distance from the midplane increases. We describe the longitudinal falling-off degradation by a hatlike function and the spatial distribution over the object domain by an exactness volume. With two orthogonal circular scan orbits, we can reconstruct two FDK volumes and generate two exactness volumes. We propose a volume fusion scheme to combine the two FDK volumes into a single volume. Let Va and Vb denote the two FDK volumes, let Ea and Eb denote the exactness volumes for orbits Gamma(a) and Gamma(b), respectively, then the volume fusion is defined by Vab=VaWa+VbWb, with Wa=Ea/(Ea+Eb) and Wb=1-Wa. In the result, the overall reproduction exactness of Vab is expected to outperform that of Va, or Vb, or (Va+Vb)/2. In principle, this volume-fusion scheme is applicable for general cone-beam tomography with multiple nonorthogonal and noncircular orbits.

Feldkamp-type VOI reconstruction from super-short-scan cone-beam data

Based on the fan-beam reconstruction formula recently developed by Noo et al. [Phys. Med. Biol. 47, 2525-2546 (2002)] we develop a Feldkamp-type algorithm for the reconstruction of a volume of interest (VOI) from super-short-scan data. With either a circular or spiral scanning locus in our VOI reconstruction scheme, we first estimate fan-beam data from cone-beam data using the popular "cosine correction" scheme, and perform reconstruction based on Noo's FBP-type fan-beam reconstruction. Our proposed algorithm is tested using the three-dimensional (3-D) Shepp-Logan phantom. The experimental results show that the new algorithm can be applied to multi-source 4-D CT with significantly superior temporal resolution and temporal consistency relative to the Katsevich algorithm, which is the state of the art for exact helical cone-beam reconstruction.

O(N3 log N) backprojection algorithm for the 3-D radon transform

We present a novel backprojection algorithm for three-dimensional (3-D) radon transform data that requires O(N3 log2 N) operations for reconstruction of an N x N x N volume from O(N2) plane-integral projections. Our algorithm uses a hierarchical decomposition of the 3-D radon transform to recursively decompose the backprojection operation. Simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection, which requires O(N5) computations under the same circumstances.