Maximum Entropy Reconstruction With Constraints: Reducing The Problem Using Duality Principles

Grant T. Gullberg; Dilip N. Ghosh Roy

doi:10.1117/12.966674

Abstract

Computed tomography (CT) can gain a significant increase in the signal-to-noise ratio using constraints to better define regions of known intensity. This is accomplished in positron emission tomography (PET) by reducing the region of unknown activity with time-coincidence circuitry. Mathematically, constraints can be implemented into reconstruction algorithms using a priori information, such as the use of an x-ray CT image to define regions of radionuclide uptake in single photon emission computed tomography (SPECT) or PET imaging. In addition to regional constraints, intensity constraints can also be included into the model equations. This may be especiallly useful where the data has a high degree of contrast as in DSA limited-angle tomography. The maximum entropy reconstruction problem with constraints is reduced to a dual optimization program using duality principles. The solution to the reconstruction problem is determined by solving for the optimum solution to this dual program. Inequality con-straints complicates the problem in that the derivatives of the function to be optimized may not exist at the boundary points. Using penalty function techniques, the problem can be structured as an unconstrained optimization program. This way, solutions can be determined using gradient type of algorithms which require an essentially smooth function as feasible solutions approach boundary points.

Citation Download Citation

Grant T. Gullberg, Grant T. Gullberg, Dilip N. Ghosh Roy, Dilip N. Ghosh Roy, } "Maximum Entropy Reconstruction With Constraints: Reducing The Problem Using Duality Principles", Proc. SPIE 0671, Physics and Engineering of Computerized Multidimensional Imaging and Processing, (1 January 1986); doi: 10.1117/12.966674; https://doi.org/10.1117/12.966674

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