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Technology Summary

For an NxN image, InstaRecon's algorithms reduce computational complexity of backprojection  from the traditional O(N^{3}) to O(N^2log N. Similarly, for 3D reconstruction of an NxNxN volume, the complexity of backprojection is reduced from O(N^4) to O(N^3 log N). For typical image sizes, with N=512, the speedup is an unparalleled 20 to 100-fold. Similar speedups are available for reprojection, which is used in beam-hardening correction in CT, and in iterative algorithms. Furthermore, the speedup relative to conventional backprojection increases as N/ log N, or almost proportionally to image size. Because the other steps in tomographic reconstruction  take only a small fraction of the computation (and this fraction becomes even smaller for larger images), backprojection/reprojection is the bottleneck operation in tomographic reconstruction. Therefore the speedups provided by InstaRecon's backprojection/reprojection algorithms directly affect the total speed of reconstruction algorithms. Such speedups are critical for next-generation real-time imaging systems in medical, security, and industrial imaging.

Superior to other methods: The only means for speeding up the reconstruction with current technology is to use more powerful hardware: faster and/or more processors. In contrast, InstaRecon's technology provides a speedup  (up to 100 fold for currently typical image size) algorithmically, that is, by use of a more advanced mathematical algorithm. Such speedup is provided for any type of implementation, whether software or hardware-based. This acceleration translates to a proportional reduction in the hardware required to achieve a given speed and resolution objective, and therefore significant cost reduction for the reconstruction engine, and/or improved accuracy, resolution, and speed specs for the scanner. Many applications that currently require expensive and inflexible special-purpose hardware to achieve acceptable speed can be satisfied by software-based solutions on standard off-the-shelf single or multi-processor PCs. This provides an inexpensive upgrade path, as processor technology continues to follow Moore's Law. For the most demanding applications, implementations on field programmable reconfigurable hardware enable more complex algorithms and higher quality reconstructions, which would be otherwise infeasible.

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Medical/Biomedical Imaging
The dramatically faster image reconstructions enabled by InstaRecon 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
  
• 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 current 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
  
• Electronics: Circuit boards and semiconductors
  
• Logging: Quality assessment of logs and optimum cutting of lumber
  
• Other applications: Materials characterization, nuclear reactors

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International patent applications have been filed.

Technology Details

Backprojection
Fast Hierarchical Backprojection Method for Imaging  (U.S. Patent #6,282,257)

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. This algorithm combines an accurate but slow subdivision algorithm with a faster but less accurate subdivision algorithm, reaching an accurate result with greatly reduced computation.

Backprojection for 3-D Radon Transform
Fast Hierarchical Backprojection for 3-D Radon Transform (U.S. Patent #6,307,911)

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 with greatly reduced computation.

Divergent-Beam Tomographic Backprojection/Reprojection
Methods and Apparatus for Fast Divergent-Beam Tomography  U.S. Patent #6,771,732)

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.

Reprojection 1
Multilevel Domain Decomposition Method for Fast Reprojection of Images (U.S. Patent #6,263,096)

The method involves decomposing an image into one or more subimages, reprojecting the subimages into sinograms, and aggregating the subimage sinograms into a single sinogram of the entire image.

Reprojection 2
Fast Hierarchical Reprojection Algorithm for Tomography (U.S. Patent #6,351,548)

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.

Reprojection for 3-D Radon Transforms

Fast Hierarchical Reprojection Algorithm for 3-D Radon Transforms (U.S. Patent #6,332,035 )

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 algorithms, this technology combines a highly accurate slow subdivision algorithm with a faster but less accurate subdivision algorithm to obtain an accurate result with greatly reduced computation.

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