Effect of iterative sparse-view CT reconstruction with task-specific projection angles on dimensional measurements

X-ray computed tomography based on a small number of radiographic projections (sparse-view CT) is relevant for several application cases in industry, where reducing the measurement time plays a major role (e.g. for in-line CT). Because of low data quality of sparse-view CT scans due to insufficient sampling, new concepts are needed to reduce measurement uncertainties for dimensional metrology. Iterative image reconstruction techniques provide a promising opportunity for this purpose as they are in principle able to handle limited data or noise well and give the possibility to select specific projection angles (i.e. perspective views) for circular scan trajectories. In this paper, the influence of task-specific projection angles on dimensional measurements is discussed using algebraic and statistical iterative reconstruction of simulated and experimentally obtained sparse-view scans. It is shown that measurement deviations for specific dimensional measurands can be reduced by selecting projection angles which are expected to have a high contribution to a good imaging of relevant geometric features.


Introduction
Reducing the measurement time is an important demand for industrial in-line CT.While there are concepts for industrial devices which use a conveyor belt and a CT setup with rotating source and detector similar to clinical devices [1], another realised possibility is to use conventional industrial micro-CT devices extended by robotic part placement.The most common setup for micro-CT devices consists of a fixed frame with X-ray source (cone beam) and flat panel detector, and a stage for the measurement object to perform a 360 • -scan for the acquisition of single radiographic transmission images (projections).The acquisition time for this circular cone beam CT can in principle be reduced using a low number of projections (sparse-view CT), but the quality of volume data suffers from insufficient sampling.For industrial devices, filtered backprojection approaches like the widely used FDK algorithm (according to Feldkamp, Davis and Kress [2]) are commonly used for reconstructing a three-dimensional gray value data set out of the measured projections.Algebraic and statistical iterative reconstruction techniques could be a promising alternative especially for sparse-view scans because they have the general advantage that physical models can be integrated, e.g. for better noise handling, and that prior information can be used to improve results even for limited projection data [3].The use of iterative techniques was mainly inhibited in the past because of the orders of magnitude higher computational expense.However, increasing performance of graphics processing units (GPUs) makes iterative methods more and more feasible for current and future applications.While for medical research, there is comprehensive work dealing with the development and effects of iterative reconstruction techniques for sparse-view CT (see e.g.[4]), little research exists in the field of dimensional metrology.Jones and Huthwaite showed that the number of projections can significantly be reduced for dimensional measurements if iterative algorithms with prior information are used [5].However, the results were dependant on the experimental setup and part complexity.In contrast to the FDK algorithm, iterative reconstruction techniques allow customised scan trajectories in a straightforward way, because a change of the projection geometry for a single projection can be taken into account by modifying the system matrix of the underlying mathematical description, which in the case of algebraic techniques is purely based on solving a linear system of equations.Therefore, it is possible to adapt the projection angles of a circular scan, which are usually distributed equally.There exist current approaches that make an adaption of the scan trajectory also possible for filtered backprojection techniques [6], but no profound work exists for dimensional applications.Varga et al. investigated the influence of the angle choice for binary iterative reconstrutcion of two-dimensional phantoms [7].They found that certain projection angles contribute more to a high quality of the reconstructed image than others and compared different optimization algorithms for the angle selection.The methods used could in principle be transferred to more realistic and application-orientated cases.Other research activities do not deal with the described circular trajectory (axial CT) but consider more complex non-standard scan trajectories.Based on simulations, Fischer et al. investigated, how a nearly free three-dimensional scan trajectory can be optimised with regard to dimensional measurement tasks for a low number of projections [8].The work focused mainly on simulations as the practical implementation was limited with regard to the part positioning.Further approaches for complex trajectories exist in form of robotic systems, where either source and detector [9] or the measurement object [10] is positioned with a robot arm.In the first case, a complete circular trajectory is not even possible because of the movement restrictions of the robots.
9th Conference on Industrial Computed Tomography, Padova, Italy (iCT 2019) In this work, only circular trajectories are considered.These can in principle be realised using standard industrial devices, if access to the control system is given.The relevance for a variety of users is given in this way.The effect of a task-specific selection of certain projection angles for a sparse-view scan was investigated for two exemplary cases.The concept common for all investigations was to use sets with a high number of radiographic projections, which were then thinned out to artificially create sparse-view scans with equally distributed or user defined projection angles.In this way, deviations caused by changing measurement conditions can be avoided and results with a different number of projections can directly be compared.For benchmarking of the different reconstruction techniques, a simulated projection stack of a virtual test specimen with exactly known dimensions (used as reference) was used.Furthermore, projections from a real CT scan of an aluminium test piece were used to test the effect for a simple application case.Results will be compared in a qualitative way based on cross section images and quantitatively by evaluating measurement deviations for selected dimensional measurement tasks.

Methods 2.1 Virtual test specimen
The first projection stack investigated was generated using a radiographic simulation (cone beam setup) of a virtual test specimen.The part and its position and orientation in relation to the detector and the vertical rotation axis can be seen in Figure 1a).The specimen consists of two parts: A cuboid (green) of size 14 mm × 3 mm × 3 mm including cavities with a cross-sectional area of 3 mm × 1.5 mm, which the actual dimensional measurement tasks were defined on, and a baseplate with four cylinders (purple) with a diameter of 6 mm as outer frame.This outer frame is not fully captured by the detector screen and was added to induce additional, angle dependent artefacts.The measurement setup was therefore chosen to simulate a measurement task for which problems arise when applying a conventional circular CT scan with FDK reconstruction, especially in the case of a sparse-view scan.The software aRTist (version 2.8.3) from the Bundesanstalt für Materialforschung und -prüfung (BAM) was used for simulation.The properties of the X-ray source and the detector were set according to former work at the Institute of Manufacturing Metrology [11] to match the characteristics of the cone beam CT scanner Tomocheck 200 3D (Werth).Scattering as well as a drift of the position or orientation of the specimen was not considered.Iron was chosen as material for the specimen.The detector size was 960 × 960 pixels with a pixel size of 50 µm.The magnification was approximately 2.8, leading to a voxel size of 18 µm.The software was set to simulate a tube voltage of 130 kV, a tube current of 275 µA, the usage of a steel prefilter with a thickness of 0.5 mm, exposure time of the detector of 0.75 s and an averaging of three single images per projection.N = 800 projections (equally distributed between 0 • and 360 • ) were generated and stored as images encoded with 16 bit unsigned integers.Parallel planes with identical size were defined with the evaluation software (see chapter 2.4) for the lower and middle cavity of the cuboid part of the specimen.The fit points used for the least squares plane fits were restricted to a minimum edge distance of 0.2 mm.They can be seen in Figure 1b).Unidirectional lengths d i (see Figure 1c) and bidirectional lengths t i (wall thickness) were defined for both cavities as distances between the center positions of the fit planes, projected onto the relevant part axis.All in all, eight measurands are defined in this way, with four of which respectively having an identical nominal value.The two considered cavities are orientated perpendicular to each other and symmetrical with respect to the rotation axis.For scans with a sufficient number of projections, it is therefore expected that the measurement deviations for measurands with the same nominal value coincide.In the case of sparse-view scans, the symmetry breaking due to undersampling could lead on the other hand to different deviations.

Aluminium test part
An aluminium part designed at the Institute of Manufacturing Metrology was chosen as test piece for a real CT measurement using the cone beam CT device Metrotom 1500 (Zeiss).A three-dimensional representation and the dimensions of the part can be seen in Figure 2. The bidirectional length features which are labelled in Figure 2b) and 2c) were used as measurement tasks.The distances are based on planes which were fit with least squares to touch points with a minimum edge distance of 1 mm for the top side and 0.75 mm for the smaller planes of the bottom (inner) side.All measurands are evaluated as distances between the center positions of the planes, projected onto the respective part axis.The part was placed bottom up (referring to Figure 2a) in styrofoam for a CT scan with N = 2500 projections.As the detector (2048 x 2048 pixels) was operated in 2x2 binning mode, the sampling is comparatively high, considering that the number of projections is typically chosen roughly equal to the width of the measurement object in detector pixels.On the other hand, the high number gives a greater freedom when artificially creating sparse-view scans based on the measured projection stack.A tube voltage of 150 kV, tube current of 350 µA, detector gain of 8 and an integration time of 2 s were applied.No prefilter and no image averaging were used.The magnification was 6.5, corresponding to a voxel size of 61 µm.The flat field corrected projections were cropped to a pixel size of 839 × 424 to only contain the measurement object and clamping material and afterwards used as input for the reconstruction software.To be able to evaluate measurement deviations separated from manufacturing inaccuracies, tactile reference measurements were performed using the coordinate measurement machine (CMM) UPMC 1200 CARAT S-ACC (Zeiss).The reference values were obtained as average from two single measurement series.Measurement uncertainties were determined using Monte Carlo simulations (virtual CMM according to guideline VDI/VDE 2617 part 7) and are ≤ 3.4 µm (coverage factor k = 2).The measurement of the outer dimensions (top side) were repeated once again with a different clamping process of the part.Differences in measurement values were ≤ 1.2 µm.

Reconstruction
The application programming interface of Cera 3.0 (Siemens Healthcare) was used for the development of reconstruction programs in C++.Three different reconstruction algorithms were used for the investigations: The standard FDK reconstruction as well as the algebraic and statistical reconstruction algorithms (hereinafter abbreviated as "ITR algebraic" and "ITR statistical") of the iterative CT reconstruction module of Cera.The detailed underlying mathematical descriptions for the algorithms are not publicly accessible, but according to the supplier ITR algebraic is similar to the simultaneous algebraic reconstruction technique (SART) [12] and ITR statistical is based on the expectation maximization (EM) method [13].Specific parameters like the number of iterations or the relaxation factor can be varied for the iterative algorithms.The FDK algorithm was applied with Shepp-Logan filter and without further artefact reduction techniques or truncation correction.The possibility to input projections from known specific projection angles on a circular trajectory was implemented for iterative reconstruction.The selection of projection angles was done manually considering the orientation of the planes which define the dimensional measurands.For the algebraic algorithm, the order of projection input was programmed in a way that the angle difference of two subsequent projections is as near as possible to 90 • .In the case of the projection data from real CT measurement, ordered subsets with four projections (again as near as possible to 90 • ) per subset were applied for the statistical reconstruction to accelerate the convergence behaviour.The number of iterations was set manually based on preliminary work, as it is not clear in advance how a stop criterion with regard to optimised dimensional measurement output should be chosen.The number of iterations in some cases can have a significant influence on the measurement results, which will be discussed in detail in the results chapter.The relaxation factor was set to the default value.For all iterative reconstruction runs, all voxels of the volume were initialised with a constant value of 0.01.The reconstruction programs were run on a workstation using the GPU Tesla K40 (Nvidia).

Surface determination
The software VGStudio Max 3.2 (Volume Graphics) was used in batch mode for surface determination and dimensional measurements which were finally used to evaluate the results.A common approach for surface determination is to start from a skin model (contour) which is defined by the iso-50% value of the gray level histogram.Based on this starting skin model, an advanced iterative surface determination can be performed, which is locally adapting the skin.If this procedure is applied for sparse-view scans with FDK reconstruction, strong artefacts result in incorrectly detected material areas.This is shown in Figure 3a) for the aluminium part.In contrast, the surface of the statistically reconstructed part could be analysed using the iso-50% value (see Figure 3b).As the artefacts make it impossible to perform dimensional measurements on the sparse-view scans with FDK reconstruction, an alternative approach was used to be able to compare results from different reconstruction algorithms.Instead of the iso-50% value, the triangulated surface of the underlying CAD (stl files) was chosen as starting skin model.With regard to in-line applications, for which sparse-view scans are mainly relevant and for which the geometric model typically is given, this is seen as justifiable method.A drawback of this approach is that the searching distance for the iterative surface determination can influence the measurement results.But as the searching distance was kept constant for all evaluations of the same part, the comparability of the results is still given.For the aluminium test part, the searching distance was set to 0.24 mm.In case of the virtual test specimen, the maximal reasonable value (regarding the wall thickness) of 0.35 mm was used, which is more than 19 times the voxel size.For this reason, the influence of the searching distance can be neglected for this part.The effect of the used approach can be seen in the lower row of Figure 3.For CT scans with a high number of projections, the choice of the starting skin has a negligible effect on the dimensional measurement values.For FDK reconstruction of the aluminium part with N = 2500, the differences between dimensional measurement values for the two different strategies were ≤ 1 µm.To be able to use the surface from CAD as starting skin model, the measured parts have to be registered in the CAD coordinate system first.In case of the virtual test specimen, this was done by directly applying the correct transformation rules as the transition between CAD coordinate system and coordinate system of the simulation software is exactly known.In this way, influences of the registration on the dimensional measurements can be excluded.In case of the aluminium part, a conventional surface determination was done first, followed by a best fit registration to the CAD reference.After this step, the described surface determination method (starting skin model based on CAD) was applied.The best fit registration was repeated one more time, as the improved quality of the surface can lead to a different transformation rule.

Virtual test specimen
Figure 4 shows a qualitative comparison of the results in form of horizontal cross sections through the middle cavity.The first two columns were obtained with equally distributed projection angles (360 • scan).Due to beam hardening originating from the cuboid and the four cylinders of the outer frame (not visible in the cross sections), artefacts are already visible for the FDK reconstruction with N = 800.With N = 25, additional strong artefacts from undersampling can be seen.For N = 800, the solution of ITR algebraic is nearly identical to the FDK solution.For N = 25, the material transitions and streaks from undersampling are more blurred.The number of iterations from left to right was 800, 10, 1 and 10 for ITR algebraic and 10, 7, 2 and 3 for ITR statistical.The numbers were chosen according to optimised qualitative and quantitative results.The statistical iterative reconstruction shows a good handling of beam hardening and sampling artefacts, but edges are not correctly reproduced.The third and fourth column show results, when task-specific projection angles are used for the iterative reconstruction techniques.The angles were chosen in a way such that transmission directions are close to tangential views to the part surface (45 • , 135 • , ...).For the first projection set ("task-specific angles 1"), the angle range of single projections around the tangential directions was roughly 4 • with linearly increasing angle increment.For the second projection set, the range was from 22 • to 30 • with angle increment increasing quadratic with the distance to the tangential view.For both projection sets, it can be seen that beam hardening artefacts are widely avoided, due to the fact that the disturbing cylinders of the outer frame (compare Figure 1 a) do not superimpose the part of interest for the used projections.Because of the orthogonal arrangement, the material of the part is blurred in these directions, especially for the first set.The nature of the algebraic algorithm, which is based on solving a linear system of equations can very clearly be retraced.For a more detailed analysis, Figure 5 shows line profiles with normalised gray values which were recorded along the dashed lines in Figure 4.While the FDK reconstruction with N = 800 shows sharp edges with a high gradient, the background level is  not constant because of the mentioned artefacts.The sampling artefacts for FDK with N = 25 cause strong disturbances, which do not occur in the case of the statistical iterative reconstruction.On the other hand, the material transitions are blurred for the statistically reconstructed volume.The statistical reconstruction with N = 25 and task-specific projection angles (first set) in contrast shows a sharp transition similar to FDK with 800 projections, but with constant background level along the line.Still, problems for the surface determination in the edge regions (right angle in cross sections) due to the different gray value levels in the whole cross section are observed and material transitions are not reproduced properly in this edge regions, but as for the plane fitting a minimum edge distance of 0.2 mm was applied, the corner areas do not contribute to the dimensional measurement.
For the different reconstructed volumes listed in Figure 4, a quantitative comparison is shown in Figure 6 and Figure 7 for the defined length features.In case of the statistical reconstruction, a strong dependence of the measurement deviations of bidirectional measurements on the number of iterations was observed (see Figure 7b)).Therefore, the values from ITR statistical can not properly be compared to results from other algorithms and are therefore not plotted in Figure 7a).For all other results, there were only minor and no clear systematic differences when varying the number of iterations.
For both unidirectional and bidirectional measurands, it can be seen that for a conventional CT scan with equally distributed projection angles the iterative techniques have no advantage regarding this simulated application case.The deviations for statistical reconstruction in fact are the highest.However, when applying the task-specific projection angles, the deviations can significantly be reduced because of the sharper imaging of the material transitions.While for the unidirectional measurands the results become better than those from FDK reconstruction with the same number of projections, for the wall thicknesses a clear improvement is only obtained with the second projection set.
In general, with higher sampling the investigated method could be an alternative to region of interest CT [14] for parts which contain disturbing objects at few certain angular views.Figure 7: a) Measurement deviations (reference CAD) for the evaluated wall thicknesses t i (compare Figure 1c) of the virtual test specimen.Values from statistical iterative reconstruction are not listed in a) due to their strong dependence on the chosen number of iterations, which is shown in b) for one wall thickness (equally distributed projection angles).

Aluminium test part
Horizontal cross sections of the reconstructed volumes of the measured aluminium part can be seen in Figure 8.The number of iterations for ITR algebraic were from left to right 500, 800 and 100 respectively and for ITR statistical 10, 20 and 20 (ordered subsets used).It was checked that a higher number of iterations did not yield superior results.The FDK reconstruction with 2500 equally distributed projections shows a good quality and only minor artefacts at the right angles corners of the part.For N = 25, streaks from insufficient sampling and a worse contrast can be seen.Like for the virtual test specimen, the algebraic reconstructed volume with N = 2500 is nearly identical to the FDK solution.For N = 25, the material transitions are again less sharp than for FDK.The statistical reconstruction shows nearly fully noise removal, but also inhomogeneous gray values inside the part.As only length features along the two horizontal axes of the part were defined as measurement tasks, the angles for task-specific projection angles were chosen with higher sampling around the axes directions.While planes along this directions appear more sharp, round features like the three drills are skewed.
The results from dimensional measurements are plotted in Figure 9 with equally distributed projection angles for iterative As both outer and inner length features are included, a systematic error from surface determination would result in positive as well as negative deviations.This can approximately be seen for the high quality FDK reconstruction.Outer length features have positive deviation values from 14 µm to 24 µm, while the deviations of all but one inner lengths are negative, albeit with lower absolute values < 14 µm.For FDK and ITR algebraic with N = 25, the trend is the same, but with higher absolute deviations.
Values from statistical reconstruction with low projection number show different behaviour with positive deviations for all but two values.Like for the virtual test specimen, the dimensional results depend on the number of iterations, but the influence is lower.If the number of iterations is increased from 20 to 800, the mean absolute deviation is increasing by 6 µm.A direct comparison of single values is therefore difficult, but the outcome that the iterative reconstruction techniques do not lead to higher accuracy for the sparse-view scan with equally distributed projection angles in comparison to FDK reconstruction is still valid when a different number of iterations is used.When the task-specific projection angle set (see right column of Figure 8) is applied, the measurement deviations for both statistical and algebraic reconstruction are reduced significantly in average.For ITR algebraic, the mean absolute deviation is reduced by 77 % from roughly 59 µm to 14 µm and the maximum absolute deviation is reduced by 62 % to 53 µm.In case of ITR statistical, the mean absolute deviation is reduced by 87 % from roughly 58 µm to 7 µm and the maximum absolute deviation is reduced by 82 % to 23 µm.In comparison to the FDK reconstruction of the sparse-view scan, the results from iterative reconstruction with task-specific projection angles show a clear improvement.The results are even comparable to the high quality FDK reconstruction with 2500 projections.

Time aspect
The reconstruction time is an important factor when considering the practical application of iterative algorithms for measurement purposes.The dependencies for the reconstruction time t for the used algorithms can roughly be described in the following form: where N It is the number of iterations and V is the number of voxels for the reconstructed volume.V was kept constant for each part respectively.So the duration for reconstruction only differed because of the different number of projections and iterations.
In the following, examples are given which were obtained with the used graphics card (4.29 Tflops single precision performance, 2880 CUDA cores).The time for algebraic reconstruction of the virtual test specimen (V = 960 3 ) with N = 800 and N It = 800 was 55.5 h, while for the sparse-view scan with N = 25 and N It = 10, reconstruction was completed after 80 s.The reconstruction times for ITR statistical was in the same order of magnitude for all sparse-view scans of the two parts and even the reconstruction with high N was below one hour for both parts because of the low number of iterations.FDK reconstruction needed ≤ 20 s for all investigations.
All in all, iterative reconstruction times are practicable for sparse-view scans, especially when considering the reduction of machine time.In case of the measured aluminium part, the complete scan process took two hours and fifty minutes.A sparse view scan with 25 projections could be performed in roughly 2 minutes.Hence, the advantage regarding machine time reduction outweighs the disadvantage of a higher computational runtime, particularly when regarding operating costs.

Conclusion
The effect of algebraic and statistical iterative reconstruction with task-specific projection angles on qualitative and quantitative measurement results was investigated for simulated and experimentally obtained sparse-view CT scans for two different measurement objects.As projections from thinned out stacks of identical scans were used, the results could directly be compared with results from FDK reconstruction with a high or low number of equally distributed projections.
In the case of a homogeneous angle distribution, especially the statistical iterative reconstruction showed good qualitative results with low noise and reduced artefacts.However, the measurement accuracy was not improved for the investigated case that prior information from CAD data was used for surface determination.Additionally, some measurands were not properly evaluable due to a strong dependence on the number of iterations.When applying task-specific projection angles for the sparse-view scans in a way that tangential views of planes relevant for the defined measurement tasks were covered, measurement deviations were significantly decreased for both investigated cases and a clear advantage for the iterative reconstruction techniques in comparison to FDK reconstruction with the same number of projections could be observed, especially for the experimentally obtained data from an aluminium part.The results show that the investigated method is promising with regard to in-line applications.
In future, further extended investigations on additional measurement objects and using statistical evaluations of repeated measurements are needed to obtain more general statements.Future work will also focus on developing a systematic, simulation based procedure to choose optimal scan angles for a given measurement task and number of projections.

Figure 1 :
Figure 1: Geometry and measurement tasks for the virtual test specimen.a) Radiographic setup in the software aRTist 2. b) Least squares fitted planes (green fit points) defining the evaluated distance measures.c) Cross section of middle cavity with schematically indicated unidirectional distances d i and wall thicknesses t i which are based on the fitted planes.

Figure 2 :
Figure 2: aluminium test part.a) 3D rendering of a high quality measurement.b) Top view with evaluated outer distances.c) Bottom view with evaluated inner distances.

Figure
Figure Differences in surface determination when using the iso-50% value as starting skin model (a,b) or the triangulated surface data from CAD (c,d).

Figure 4 :
Figure 4: Detail view of cross sections (contrast stretched to maximum range) through reconstructed volumes of the virtual test specimen when using 800 or 25 projections.Modified angles for the two different sets of scans with task-specific projection angles are indicated by the black arrows of the inserts.Gray value profiles along the dashed lines are evaluated in Figure 5.

Figure 5 :
Figure 5: Line profiles (see dashed lines in Figure4) for the virtual test specimen.The gray values were normalised to a range from 0 (minimum gray value along line) to 1 (maximum value along line).

Figure 6 :
Figure 6: Measurement deviations (reference CAD) for the unidirectional measurands d i (compare Figure 1c) of the virtual test specimen.

Figure 8 :
Figure 8: Cross sections through reconstructed volumes of the aluminium test part for N = 2500 and N = 25 projections.Modified task-specific projection angles are indicated by the black arrows of the insert.reconstructionand in Figure10with the task-specific distribution.The results from FDK reconstruction are added in both plots for comparison.Results from iterative reconstruction with N = 2500 are not added in the plots as the values lie in the same range as those from FDK with high N. Values from statistical reconstruction show in average even lower deviation values.As both outer and inner length features are included, a systematic error from surface determination would result in positive as well as negative deviations.This can approximately be seen for the high quality FDK reconstruction.Outer length features have positive deviation values from 14 µm to 24 µm, while the deviations of all but one inner lengths are negative, albeit with lower absolute values < 14 µm.For FDK and ITR algebraic with N = 25, the trend is the same, but with higher absolute deviations.Values from statistical reconstruction with low projection number show different behaviour with positive deviations for all but two values.Like for the virtual test specimen, the dimensional results depend on the number of iterations, but the influence is lower.If the number of iterations is increased from 20 to 800, the mean absolute deviation is increasing by 6 µm.A direct comparison of single values is therefore difficult, but the outcome that the iterative reconstruction techniques do not lead to higher accuracy for the sparse-view scan with equally distributed projection angles in comparison to FDK reconstruction is still valid when a different number of iterations is used.When the task-specific projection angle set (see right column of Figure8) is applied, the measurement deviations for both statistical and algebraic reconstruction are reduced significantly in average.For ITR algebraic, the mean absolute deviation is reduced by 77 % from roughly 59 µm to 14 µm and the maximum absolute deviation is reduced by 62 % to 53 µm.In case of ITR statistical, the mean absolute deviation is reduced by 87 % from roughly 58 µm to 7 µm and the maximum absolute deviation is reduced by 82 % to 23 µm.In comparison to the FDK reconstruction of the sparse-view scan, the results from iterative reconstruction with task-specific projection angles show a clear improvement.The results are even comparable to the high quality FDK reconstruction with 2500 projections.

Figure 9 :
Figure 9: Length measurement deviations (reference tactile measurement) of different reconstructed sparse-view scans with equally distributed projection angles.The results from FDK reconstruction with N = 2500 are included for comparison.

Figure 10 :
Figure 10: Length measurement deviations (reference tactile measurement) when using task-specific projection angles in comparison to FDK reconstruction with equally distributed angles.