Application of a constrained optimization algorithm to limited-view tomography

Jesse Kolman; Waleed S. Haddad; Dennis M. Goodman; Keith A. Nugent

doi:10.1117/12.179258

8 July 1994 Application of a constrained optimization algorithm to limited-view tomography

Jesse Kolman, Waleed S. Haddad, Dennis M. Goodman, Keith A. Nugent

Proceedings Volume 2299, Mathematical Methods in Medical Imaging III; (1994) https://doi.org/10.1117/12.179258
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

The quality of images reconstructed from projections obtained by transmission tomography depends on the range of angles over which measurements can be made as well as the number of projections. Conventional methods such as filtered backprojection suffer when the number of measurements is small, and methods such as ART produce noticeable artifacts when the angular range is limited. Another possible approach is the direct minimization of the squared error between the measurements and the projection of the reconstructed image onto the measurement space. Alternatively, the unfiltered backprojection of the data can be modeled as a linear blur of the desired image, and this blur can be removed with a deconvolution algorithm. One way to handle the latter approach is to minimize the squared error between the backprojection and the reconstructed image blurred by an appropriately chosen point spread function. These methods result in higher quality images when the angular range is limited and the number of projections is small. We use a conjugate gradient based constrained optimization algorithm to do the minimization. The available constraints on the variables are upper and lower bounds and a hyperplane constraint. Since the variables in this case are the image pixels, we can enforce known bounds on the pixel values, such as nonnegativity, as well as keep the sum of the pixels at its known value. These constraints greatly improve the reconstruction quality and increase the rate of convergence of the algorithm.

Citation Download Citation

Jesse Kolman, Waleed S. Haddad, Dennis M. Goodman, and Keith A. Nugent "Application of a constrained optimization algorithm to limited-view tomography", Proc. SPIE 2299, Mathematical Methods in Medical Imaging III, (8 July 1994); https://doi.org/10.1117/12.179258

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