New Tomographic Reconstruction Algorithms for Faster CT Scans


CT scanners are gathering more data than ever, far exceeding the ability of the hardware and software to process and analyze the data and consequently slowing down diagnosis. This is becoming a more serious issue as the field moves from fan-beam (2-D and spiral) to cone-beam (fast volumetric or 3-D) acquisition. These algorithms were developed to address this problem. This suite of patented and patent-pending algorithms reconstructs tomographic images for standard (i.e., 2-D) and volumetric (i.e., 3-D) CT scans 10 to 100 times faster than conventional methods for typical image sizes, lowering scanning costs, increasing throughput, enabling improved image quality, and freeing up precious computer resources.

Fast Hierarchical Backprojection Method for Imaging 

This method involves backprojecting a sinogram to a tomographic image by subdividing it into subsinograms corresponding to subimages as small as a single pixel. The subsinograms are backprojected to produce corresponding subimages, and the subimages then are aggregated to create the full tomographic image. As with several of the algorithms described above, speed is greatly enhanced through the use of an approximate decomposition algorithm.

Fast Hierarchical Backprojection for 3-D Radon Transform

With this method, data from a 3-D sinogram are backprojected to form a 3-D volume. An input sinogram is subdivided into subsinograms, which are further subdivided until they represent volumes as small as a single voxel. The subvolumes then are aggregated to form a final volume. Again, this algorithm combines an accurate but slow subdivision algorithm with a faster but less accurate subdivision algorithm, reaching an accurate result quickly.

Fast Hierarchical Native Fan-Beam Tomographic Reconstruction Algorithms

This family of native divergent beam algorithms can be used to reconstruct all divergent-beam tomographic data, including single- and multi-slice 2-D fan-beam and 3-D cone-beam with arbitrary scan trajectories, including single circle and spiral trajectories for short and long objects. The algorithms operate directly on the data without prior rebinning to parallel beam projections. Both reprojection and backprojection functions are available.

Multilevel Domain Decomposition Method for Fast Reprojection of Images

The method involves decomposing an image into one or more subimages, reprojecting the subimages into sinograms (i.e., arrays of numbers), scaling the sinograms, and aggregating the subimage sinograms into a single sinogram of the entire image.

Fast Hierarchical Reprojection Algorithm for Tomography

This variation on the above reprojection method combines an exact algorithm, which is accurate but slow, with an approximation algorithm, which is less accurate but fast, to create an accurate result in a short time.

Fast Hierarchical Reprojection Algorithm for 3-D Radon Transforms

This algorithm is based on 3-D radon transform, which is a mathematical model used in volumetric imaging. It begins by dividing the 3-D image into subvolumes as small as a single voxel. These subvolumes then are reprojected at various orientations to form subsinograms. The subsinograms are then successively aggregated and processed to form a full sinogram for the initial volume. Like the previous algorithm, this technology combines a highly accurate slow subdivision algorithm with a faster but less accurate subdivision algorithm to quickly obtain an accurate result.


Qualified companies are invited to license the algorithms as well as enter into agreements that will allow evaluation and suitable modifications to the algorithms that may be necessary for use in specific applications.

  • Medical/Biomedical Imaging: The dramatically faster image reconstructions enabled by these algorithms will benefit all tomographic acquisition modalities:
  • Computed tomography (CT): Single- and multi-slice spiral, cone-beam cine, and cone-beam spiral partial and whole-body scans
  • Positron emission tomography (PET) and single-photon computed tomography (SPECT): Iterative and cone-beam reconstruction methods
  • Magnetic resonance imaging (MRI): Projection reconstruction methods, particularly for cardiac cine
  • Micro CT scanners: Small-animal scans for drug assays in the pharmaceutical industry or for other biomedical research

Industrial Imaging: By reconstructing tomograms faster than do previous methods, these algorithms dramatically increase the number of items that can be scanned per hour (i.e., throughput), eliminating the "image reconstruction bottleneck" and significantly reducing manufacturing/ inspections costs. These algorithms can be used with any industry inspection using CT scans:

  • Aerospace: Aircraft and spacecraft parts such as turbine blades
  • Automotive: Engine parts, brake calipers, steering rods, crank shafts, blocks
  • Electronics: Circuit boards and semiconductors
  • Logging: Quality assessment of logs and optimum cutting of lumber
  • Other applications: Materials characterization, nuclear reactors

Security Imaging: The faster imaging speeds enabled by these algorithms will offer dramatic improvements in 3-D CT inspection of baggage or containers for the detection of weapons, explosives, or other hazardous materials. This will be a tremendous benefit as U.S. airports strive to meet new federal baggage inspection requirements.


  • Dramatically faster 3-D imaging: The reconstruction of cone-beam data gathered for 3-D or volumetric imaging is extremely demanding computationally, in particular for spiral cone-beam or cardiac cine; therefore, the algorithms offer a critical improvement in reconstruction speed.
  • Reduced scanning costs: Faster image reconstruction leads to higher throughput, which significantly reduces the per-scan cost. In addition, incorporating the algorithms significantly reduces the cost of the reconstruction computer required to satisfy the speed requirements, usually eliminating the need for special-purpose hardware acceleration.
  • Improved image quality: The algorithms enable the use of more powerful reconstruction and artifact correction methods (e.g., iterative techniques) than currently feasible, producing more accurate images.
  • Increased availability of computer resources: More efficient reconstruction requires less computational resources for image processing, making more computing power available for enhanced image analysis.
  • Superior to other methods: Other software-based acceleration methods have poor efficiency and image quality; the University's algorithms overcome these problems. And unlike hardware-based acceleration methods, the University's algorithms can enjoy the year-to-year speed improvements in general-purpose computers, achieving even faster image reconstruction without any additional development costs. At the same time, they are adaptable to special purpose hardware implementations if such are desired to meet extreme speed requirements.