Multigrid tomographic inversion with variable resolution data and image spaces

A generalized reconstruction framework for unconventional PET systems

PURPOSE

Quantitative estimation of the radionuclide activity concentration in positron emission tomography (PET) requires precise modeling of PET physics. The authors are focused on designing unconventional PET geometries for specific applications. This work reports the creation of a generalized reconstruction framework, capable of reconstructing tomographic PET data for systems that use right cuboidal detector elements positioned at arbitrary geometry using a regular Cartesian grid of image voxels.

METHODS

The authors report on a variety of design choices and optimization for the creation of the generalized framework. The image reconstruction algorithm is maximum likelihood-expectation-maximization. System geometry can be specified using a simple script. Given the geometry, a symmetry seeking algorithm finds existing symmetry in the geometry with respect to the image grid to improve the memory usage/speed. Normalization is approached from a geometry independent perspective. The system matrix is computed using the Siddon's algorithm and subcrystal approach. The program is parallelized through open multiprocessing and message passing interface libraries. A wide variety of systems can be modeled using the framework. This is made possible by modeling the underlying physics and data correction, while generalizing the geometry dependent features.

RESULTS

Application of the framework for three novel PET systems, each designed for a specific application, is presented to demonstrate the robustness of the framework in modeling PET systems of unconventional geometry. Three PET systems of unconventional geometry are studied. (1) Virtual-pinhole half-ring insert integrated into Biograph-40: although the insert device improves image quality over conventional whole-body scanner, the image quality varies depending on the position of the insert and the object. (2) Virtual-pinhole flat-panel insert integrated into Biograph-40: preliminary results from an investigation into a modular flat-panel insert are presented. (3) Plant PET system: a reconfigurable PET system for imaging plants, with resolution of greater than 3.3 mm, is shown. Using the automated symmetry seeking algorithm, the authors achieved a compression ratio of the storage and memory requirement by a factor of approximately 50 for the half-ring and flat-panel systems. For plant PET system, the compression ratio is approximately five. The ratio depends on the level of symmetry that exists in different geometries.

CONCLUSIONS

This work brings the field closer to arbitrary geometry reconstruction. A generalized reconstruction framework can be used to validate multiple hypotheses and the effort required to investigate each system is reduced. Memory usage/speed can be improved with certain optimizations.

A residual correction method for high-resolution PET reconstruction with application to on-the-fly Monte Carlo based model of positron range

PURPOSE

The quality of tomographic images is directly affected by the system model being used in image reconstruction. An accurate system matrix is desirable for high-resolution image reconstruction, but it often leads to high computation cost. In this work the authors present a maximum a posteriori reconstruction algorithm with residual correction to alleviate the tradeoff between the model accuracy and the computation efficiency in image reconstruction.

METHODS

Unlike conventional iterative methods that assume that the system matrix is accurate, the proposed method reconstructs an image with a simplified system matrix and then removes the reconstruction artifacts through residual correction. Since the time-consuming forward and back projection operations using the accurate system matrix are not required in every iteration, image reconstruction time can be greatly reduced.

RESULTS

The authors apply the new algorithm to high-resolution positron emission tomography reconstruction with an on-the-fly Monte Carlo (MC) based positron range model. Computer simulations show that the new method is an order of magnitude faster than the traditional MC-based method, whereas the visual quality and quantitative accuracy of the reconstructed images are much better than that obtained by using the simplified system matrix alone.

CONCLUSIONS

The residual correction method can reconstruct high-resolution images and is computationally efficient.