Monitored Reconstruction: Computed Tomography as an Anytime Algorithm

Abstract

Computed tomography is an important technique for non-destructive analysis of an object's internal structure, relevant for scientific studies, medical applications, and industry. Pressing challenges emerging in the field of tomographic imaging include speeding up reconstruction, reducing the time required to obtain the X-ray projections, and reducing the radiation dose imparted to the object. In this paper, we introduce a model of a monitored reconstruction process, in which the acquiring of projections is interspersed with image reconstruction. This model allows to examine the tomographic reconstruction process as an anytime algorithm and consider a problem of finding the optimal stopping point, corresponding to the required number of X-ray projections for the currently scanned object. We outline the theoretical framework for the monitored reconstruction, propose ways of constructing stopping rules for various reconstruction quality metrics and provide their experimental evaluation. Due to stopping at different times for different objects, the proposed approach allows to achieve a higher mean reconstruction quality for a given mean number of X-ray projections. Conversely, fewer projections on average are used to achieve the same mean reconstruction quality. INDEX TERMS Anytime algorithms, computed tomography, dose reduction, monitored reconstruction, optimal stopping, x-ray tomography.

Monitored Tomographic Reconstruction—An Advanced Tool to Study the 3D Morphology of Nanomaterials

“…It is normal practice that tomographic image reconstruction starts after the completion of the scan protocol, after which the recognition process can be started [14]. In this section, we turn to the monitored reconstruction approach introduced in [10] in order to explain how to look at the reconstruction as a process with the monitored result, i.e., we present a framework for monitored reconstruction. The fact that the quality of reconstruction depends not only on the number of projections but also on the sequence of their shooting was already shown in the 1990s [15].…”

“…Here, E n (•) is the conditional expectation of a random variable given that the first n observations are taken. If the stopping problem is monotonic, an optimal stopping rule can be found in form [10]:…”

“…To apply the stopping rules, we used the straightforward-estimation method [10], assuming that the looking distance is close to the distance between the two most recently obtained results:…”

“…This tomographic-reconstruction algorithm is empowered by sophisticated correction modules that autonomously estimate and effectively suppress artifacts and random errors using gradient descent and deep learning algorithms (examples see [8,9]). Another development to shorten the data acquisition time for XCT was reported by Bulatov et al [10]. A monitored reconstruction process was proposed that performs the reconstruction procedure not only after the completion of the measurement protocol.…”

X-ray tomography: the way from layer-by-layer radiography to computed tomography

“…Finally, we are going to comment on the approach to tomographic surveying proposed by the authors and known as "the reconstruction with monitoring". This approach makes it possible to decrease the radiation load on an object through replacing the fixed protocol of the projection surveying with the protocol with monitored reconstruction [2].…”