Image reconstruction in optical tomography using local basis functions

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Abstract
We demonstrate the effect of representing the solution of a reconstruction as a linear expansion of local basis functions, i.e., functions that have limited support over the domain. Local basis functions are computationally efficient because they lead to linear systems that are sparse. We present two different types of local basis functions: piecewise polynomial regular and irregular functions, and radially symmetric functions on a regular grid (blobs). We demonstrate that the use of higher order polynomial basis functions as well as radially symmetric functions with appropriate choice of shape parameters can reduce the image artifact present in low-order polynomial bases. © 2003 SPIE and IS&T.