Task-Specific Acquisition Trajectories optimized using Observer Models

Abstract

Scan time is a crucial factor in industrial computed tomography (CT). With modern computers performing reconstructions in seconds or minutes, the duration for the projection acquisition, which is often in the order of hours, becomes the limiting factor. Therefore, it is desirable to reduce the number of projections in order to cut costs or allow for new applications, such as inline CT. So far, many different approaches mostly targeting the reconstruction method have been performed to optimize the outcome for undersampled data, but only few work has been conducted concerning the scan planing. Nevertheless, the commonly used circular standard-trajectories for image acquisition are highly inefficient since they do not consider the geometry of the inspected objects. It has already been shown that using workpiece-tailored instead of conventional circular trajectories can shorten scan times significantly. In this work we present an observer model based algorithm that has previously been applied in medical and industrial studies and extend it in several aspects. Subsequently, we focus on comparing different observer models that have not been used for this optimization yet and evaluate their performance for identifying valuable projections that contribute most to the reconstructed image.

Selection and evaluation of spherical acquisition trajectories for industrial computed tomography

“…The test artefact for our investigation serves the part shown in figure 2 that we have already used in previous investigations [44] and which is based on the bat phantom of a similar work [45]. It comprises a main body with a cylinder and a sphere as relevant local features (i.e.…”

“…Consequently, at least some of the valuable projections (with respect to the SNR) are supposed to be located with their X-ray path pointing through these windows. Unlike in earlier work [44], all materials were set to be elementary iron. The test part features a rather flat shape, a certain degree of symmetry and clearly defined edges and holes that can also be found at practically relevant parts and industrial items.…”

“…until 72 projections, then in steps of 10 from 80 to 200 and at last with a step size of 100 from 300 to 2400, resulting in 53 sampling points. The finer step size for lower projection numbers was selected since the fastest rate of quality change is expected to be in this lower region, like shown in earlier works [41,42,44,49] (see also §4). Since the scope of this work lies in the investigation of this few-projection range, we will focus on it in the following discussions even though results for all samples are provided.…”

“…The natural first choice is the typically commercially used design, which is a planar equiangular circle trajectory (PC). Since it has been shown that the reconstruction result depends on the choice of the start angle in particular for few projections [44,50], we compute s circular trajectories for each number of projections n with starting angle α 0 (s) = 2π/s • n and angular increment α = 2π/n , where denotes the 'round towards zero' operator. The number of trajectories for each n is given by s = 72/n , i.e.…”

“…For higher n > 36, we restrict ourselves to only one projection since it is not clearly defined anymore what an equidistant trajectory set would be and the differences between the trajectories becoming reasonably small, as apparent in the graphs. By this sampling method, projections might be removed from the set with increasing n and fixed α 0 owing to the changing α, which typically results in fluctuations in image quality for small n (and therefore high α), which has been observed before [44]. In order to compensate for this, we average over all available reference trajectories for the same number of projections n to get a smooth and more reasonable benchmark trajectory (see example in last paragraph).…”