Data fusion in X-ray computed tomography using a superiorization approach

Abstract

X-ray computed tomography (CT) is an important and widespread inspection technique in industrial non-destructive testing. However, large-sized and heavily absorbing objects cause artifacts due to either the lack of penetration of the specimen in specific directions or by having data from only a limited angular range of views. In such cases, valuable information about the specimen is not revealed by the CT measurements alone. Further imaging modalities, such as optical scanning and ultrasonic testing, are able to provide data (such as an edge map) that are complementary to the CT acquisition. In this paper, a superiorization approach (a newly developed method for constrained optimization) is used to incorporate the complementary data into the CT reconstruction; this allows precise localization of edges that are not resolvable from the CT data by itself. Superiorization, as presented in this paper, exploits the fact that the simultaneous algebraic reconstruction technique (SART), often used for CT reconstruction, is resilient to perturbations; i.e., it can be modified to produce an output that is as consistent with the CT measurements as the output of unmodified SART, but is more consistent with the complementary data. The application of this superiorized SART method to measured data of a turbine blade demonstrates a clear improvement in the quality of the reconstructed image.

Blob parameter selection for image representation

“…The empty cells in the table correspond to r 1 ; r 2 pairs leading to complex values for the blob parameter α Eq. (20). Clearly, using the pair 1; 4 reduces the error better than using any other pair.…”

“…(19)] and α [Eq. (20)]. We complete this section by a discussion of the justification of choosing the so-called standard values for a and α (already referred to in Section 1) that were proposed by Matej and Lewitt [6] and have been adopted by others since; see, for example, [13,14].…”

“…In this case we may recommend blob parameters obtained from low zerocrossing orders (even the pairs j 1 , j 2 or j 1 , j 3 in Table 2, which may outperform the standard parameters with regard to preservation the edges); but if the uniform parts of the object are meaningful for the application, we may recommend blob parameters obtained from high zero-crossing orders. A relevant application for the latter is industrial computerized tomography (see, for example, [20]) for the detection of undesirable inhomogeneities in manufactured machine parts.…”

Can linear superiorization be useful for linear optimization problems?

“…In particular, [26] and [9] are reviews of interest. Recent research includes a variety of reports ranging from new applications in industrial x-ray computed tomography [39] to new mathematical results on the foundation of superiorization such as strict Fejér monotonicity by superiorization of feasibility-seeking projection methods [18]. A recent detailed description of previous work related to superiorization can be found in [15, Section 3].…”

Perturbation resilience of proximal gradient algorithm for composite objectives

“…This point will have a low cost function value and hence it will be superior to other points. This heuristic method is usually less time consuming that makes it applicable to some important practical problems such as medical image recovery [9,16], computed tomography [20], intensity-modulated radiation therapy [8], and so on.…”