Location

Brunswick, ME

Start Date

1-1-1992 12:00 AM

Description

This paper addresses the reconstruction of incomplete projection data such as obtained in limited angle X-ray tomography, including cases where a priori object geometry information is available. A variational approach is taken in which the missing projection data is determined through optimization of a functional measure of non-physical or undesirable solution (image) attributes. The focus of the research is on the prescription of appropriate functional measures, and in particular on the application of a functional which minimizes the support (i.e. area) of the solution image. The connection between functional attributes and algorithm behaviors is discussed, and examples of application of various functionals are assessed. A scheme for incorporation of a priori geometry information in the variational reconstruction is demonstrated. It is shown that the minimal support functional is effective in reconstructing compact, high contrast features, and is therefore likely to be useful in applications such as dimensional analysis and the imaging of cracks. This paper presents a summary of the continuation of the work reported last year [1], hence concepts discussed in detail in ref. [1] will only be stated briefly in this writing.

Book Title

Review of Progress in Quantitative Nondestructive Evaluation

Volume

11A

Chapter

Chapter 3: Interpretive Signal Processing and Image Reconstruction

Section

Imaging and Inversion Techniques

Pages

749-756

DOI

10.1007/978-1-4615-3344-3_96

Language

en

File Format

application/pdf

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Jan 1st, 12:00 AM

Limited Data Tomography Using Support Minimization with a Priori Data

Brunswick, ME

This paper addresses the reconstruction of incomplete projection data such as obtained in limited angle X-ray tomography, including cases where a priori object geometry information is available. A variational approach is taken in which the missing projection data is determined through optimization of a functional measure of non-physical or undesirable solution (image) attributes. The focus of the research is on the prescription of appropriate functional measures, and in particular on the application of a functional which minimizes the support (i.e. area) of the solution image. The connection between functional attributes and algorithm behaviors is discussed, and examples of application of various functionals are assessed. A scheme for incorporation of a priori geometry information in the variational reconstruction is demonstrated. It is shown that the minimal support functional is effective in reconstructing compact, high contrast features, and is therefore likely to be useful in applications such as dimensional analysis and the imaging of cracks. This paper presents a summary of the continuation of the work reported last year [1], hence concepts discussed in detail in ref. [1] will only be stated briefly in this writing.