Location

Brunswick, ME

Start Date

1-1-1997 12:00 AM

Description

During the last few years some attempts were made to modify the approaches for 3D reconstruction algorithms, based mainly upon Radon theory, in case of extreme lack of data, i.e. limited number of projections and views. The inverse Radon transform is not applicable in this case because of the insufficiently filled Radon space. Then the interpolation of the data, which are absent in the unfilled back projection space, is unattainable. In this case, some kind of a priori knowledge or structural constraints is required to restrict the permissible solutions [1–4]. The classical regularization procedure, also known as Tichonov-Miller regularization [5–7], can be applied for the stated problem as used in some CT applications, e.g. [1], where the a priori knowledge is introduced by a special functional type, which allows to reduce the required number of projections to about 100.

Book Title

Review of Progress in Quantitative Nondestructive Evaluation

Volume

16A

Chapter

Chapter 1: Standard Techniques

Section

Radiation Techniques

Pages

317-323

DOI

10.1007/978-1-4615-5947-4_41

Language

en

File Format

application/pdf

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Jan 1st, 12:00 AM

Multi Step 3D X-Ray Tomography for a Limited Number of Projections and Views

Brunswick, ME

During the last few years some attempts were made to modify the approaches for 3D reconstruction algorithms, based mainly upon Radon theory, in case of extreme lack of data, i.e. limited number of projections and views. The inverse Radon transform is not applicable in this case because of the insufficiently filled Radon space. Then the interpolation of the data, which are absent in the unfilled back projection space, is unattainable. In this case, some kind of a priori knowledge or structural constraints is required to restrict the permissible solutions [1–4]. The classical regularization procedure, also known as Tichonov-Miller regularization [5–7], can be applied for the stated problem as used in some CT applications, e.g. [1], where the a priori knowledge is introduced by a special functional type, which allows to reduce the required number of projections to about 100.