Rainer Grimmer

Cone-beam CT image reconstruction with extended z range.

In circular cone-beam CT the Feldkamp [Feldkamp-Davis-Kress (FDK)] algorithm is the most prominent image reconstruction algorithm. For example, in radiation oncology images reconstructed with the Feldkamp algorithm are used for accurate patient positioning. The scan and reconstruction volumes are limited by the size of the flat panel detector. Flat panel detectors, however, are expensive and difficult to manufacture in large size. For numerous treatment techniques, extending this scan volume would be very beneficial. In most applications, data from 360° or more are available. However, usually only those slices are reconstructed where each pixel is seen under the full 360° range. Yet for a 360° scan there are regions that are seen by less than 360°, namely, those that lie further off the plane of the circular source trajectory. Performing a reconstruction also for those slices where all voxels are seen at least by 180° will extend the z range and therefore increase the dose usage. In this work a new method is presented that reconstructs also those slices where some or all pixels receive less than 360° but at least 180° of the data. The procedure significantly increases the longitudinal range of the reconstructed volume. As opposed to the existing techniques, the proposed method does not necessitate any multiple convolutions or multiple backprojections, lending itself therefore for a very efficient implementation. To validate the abilities of the extended reconstruction, the authors performed an evaluation of the image quality by using simulated and measured CT data. The method shows good image quality on simulated phantom data as well as on clinical patient scans. Image noise and spatial resolution behave as expected. This means that the noise equals FDK values in the normal region and increases in the extended region due to reduced data redundancies. The extended Feldkamp demonstrates its ability to extend the reconstructable z range and appears to be useful in clinical practice.

Assessment of spatial resolution in CT

To quantify spatial resolution in CT one typically performs separate measurements for the lateral and the longitudinal point spread function (PSF). Many procedures further require reconstructions with very small voxel sizes, e.g. when wire phantoms are scanned. This, however, may already change the shape of the PSF. For example, this is the case when Moiré filters are applied or when iterative image reconstruction algorithms are used. Aiming at assessing the point spread function (PSF) and the modulation transfer function (MTF) of a CT scanner using a single measurement we propose to measure a sphere, perform a standard image reconstruction and evaluate profiles through the sphere surface. The radial symmetry of CT scanners allows to reduce the dimensionality of the PSF and the MTF from three to two by radial averaging. It is shown that the resulting two-dimensional profiles can be decomposed into a radial and into a longitudinal component by two-dimensional parallel-beam filtered backprojection. Our method was assessed using simulated and measured data of a homogeneous sphere. The measurements were performed with the capable in-vivo cone-beam micro-CT scanner VAMP TomoScope 30s. The longitudinal and radial PSFs, and the corresponding MTFs, highly agree with those obtained with conventional methods, for both the simulations and the measurements. Figures of merit extracted from the curves, such as the full width at half maximum of the PSF or the 10% value of the MTF, differ by less than 5% between the new method and the conventional approaches. Therewith it gives a technique which requires only one, easy to handle, measurement of a sphere to calculate radial and longitudinal PSF and therefrom obtain the corresponding MTFs. Furthermore it does not require a dedicated reconstruction with very small voxels. Therefore it appears superior to existing methods.

Empirical Cupping Correction for CT Scanners with Primary Modulation (ECCP)

X-ray CT measures the attenuation of polychromatic x-rays through an object. The rawdata acquired, which are the negative logarithm of the relative x-ray intensity behind the patient, must undergo water precorrection to linearize the measurement and to convert them into line integrals that are ready for reconstruction. The function to linearize the measured projection data depends on the detected spectrum of the ray. This spectrum may vary as a function of the detector position, e.g. in cases where the heel effect becomes relevant, or where a bow-tie filter introduces channel-dependent beam hardening, or in cases where a primary modulator is used to modulate the primary intensity of the spectrum. We propose a new approach that allows to handle these effects. Our empirical cupping correction for primary modulation (ECCP) corrects for artifacts, such as cupping artifacts or ring artifacts, that are induced by non-linearities in the projection data due to spatially varying pre- or post filtration of the x-rays. To do so, ECCP requires nothing but a simple scan of a homogeneous phantom of nearly arbitrary shape. Based on this information, coefficients of a polynomial series are calculated and stored for later use. Numerical examples and physical measurements are shown to demonstrate the quality of the precorrection. ECCP achieves to remove the cupping artifacts and to obtain well-calibrated CT-values even in cases of strong primary modulation. A combination of ECCP with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.

A new method for cupping and scatter precorrection for flat detector CT

Scatter and beam hardening are prominent artifacts in x-ray CT. Currently, there is no precorrection method that inherently accounts for tube voltage modulation and shaped prefiltration. We generalized a method for self-calibration based on binary tomography of homogeneous objects to use this information to preprocess scans of other, non-binary objects, e.g. to reduce artifacts in medical CT applications. Further on we extended the method to handle not only beam hardening but also scatter and to allow for detector pixel-specific precorrections. This implies that our calibration technique handles varying tube voltage and shaped prefiltration. We propose a method that models the beam hardening correction by using a rational function while the scatter component is modeled using the pep-model. A smoothness constraint is applied to the parameter space to regularize the underdetermined system of non-linear equations. The parameters determined are then used to precorrect CT scans. Our algorithm was evaluated using simulated data of a flat panel cone-beam CT scanner with tube voltage variation and bow-tie prefiltration and real data of a flat detector cone-beam CT scanner. In simulation studies our correction model proved to be nearly perfect and the algorithm showed its abilities by correcting the beam hardening and scatter effects. Reconstructions of measured data showed significantly less artifacts than the standard reconstruction.

Dual energy CT material decomposition from inconsistent rays (MDIR)

In dual energy CT (DECT) the object is scanned with two different detected spectra in order to provide material-selective or energy-selective images of the object. Thereby, generally a higher order correction of beam hardening artifacts than it can be applied to usual single energy scans is possible. All known methods to do that need to combine the sinograms in rawdata space before image reconstruction. Therefore, a precondition of those methods is that geometrically identical rays are measured for each sinogram (consistent rays). However, most CT scanners actually acquire inconsistent rays in the sense that geometrically different rays are measured for each spectrum. Then the possibility of higher order beam hardening corrections remains unused and the resulting dual energy specific images show significantly reduced quality. We propose an iterative algorithm for material decomposition from inconsistent rays (MDIR) that allows even in the case of inconsistent rays to reconstruct material-selective or energy-selective images that are almost free of beam hardening artifacts. The algorithm is assessed using simulated data without noise (to enhance the visibility of beam hardening artifacts) and a micro CT scan of a mouse. The simulation studies find that the method is able to completely remove beam hardening caused image quality degradation after few (two to four) iterations. For the mouse scan an improvement in image quality can be noticed. In any case MDIR succeeds in reducing image artifacts that origin from beam hardening considerably while the image noise remains constant.

Cone-beam CT sequence scan reconstruction with improved dose usage and scan coverage

For circular cone-beam CT often one scan covers not the complete z-range of interest. If this is the case two or more circle scans are made. These sequence scans are typically reconstructed by separately reconstructing each circle scan followed by combining the resulting partial volumes. This image-based concatenation method uses only those data that are needed for each partial volume, the contribution of rays to neighboring volumes are ignored, redundancies are not used, and dose is wasted. Therefore an algorithm that uses all rays that run through a voxel by appropriately weighting the rays followed by filtered backprojection was developed and evaluated. This leads to improved dose usage and increases the overlap region of neighboring volumes, potentially leading to reduced artifacts in this region. Alternatively, our approach allows to increase the table increment between adjacent circle acquisitions, and thereby the scan coverage, without impairing image quality or increasing dose. To evaluate our method we use the geometry of the Varian OBI flat panel detector CT scanner. Simulated and measured data are processed at varying table increment values and an evaluation of image noise, spatial resolution and artifacts has been performed. The method shows good image quality on simulated phantom data as well as on clinical patient data. In this paper the algorithm demonstrates its ability to extend the z-range of sequence scans and to improve the image quality in the overlap region and turns out to be usable on devices in the clinical practice.

Comparison and classification of 3D objects surface point clouds on the example of feet

One of the main tasks of shoe manufacturing is the production of well fitting shoes for different specialized markets. The key to conduct this properly is the analysis of the factors that influence the variations of the foot shape. In this paper methods and results of clustering and analysis of 3D foot surfaces are presented. The data were collected from a study with more than 12,000 feet that have been laser-scanned. The database contains point clouds acquired from persons coming from different regions of the world. Furthermore, additional personal data were collected. Two different methods for quantifying the similarity of 3D surface point clouds are therefore developed. The first method generally works on nearly arbitrary 3D surface point clouds, while the second one is specialized on foot data sets. These similarity measures were used on the data sets of the foot-shape study, together with clustering and feature quality evaluation methods. The purpose was to obtain information about the impact of, and the relationship among, the different factors influencing the shape of a foot. Through the observations of the experiments presented here it was possible to build up a hierarchy of different levels of feature-groups determined by their impact on the foot shape. Furthermore, an investigation of the quality and amount of impact of the features, according to their ability to separate specific subgroups of persons, is shown. Based on these results it was possible to select those features, which result in the largest effect when designing shoes for e.g. the Asian versus European markets.

Frequency-combined extended 3D reconstruction for multiple circular cone-beam CT scans

In circular cone-beam CT a single circle scan often does not cover the complete z-range of interest. If this is the case, two or more circle scans are acquired. The standard combination of the separate reconstructions has two disadvantages: 1) The reconstructable volume is smaller than possible, thus dose remains unused and the noise level is higher than necessary. 2) The cone-beam artifacts are increased at the edges of the partial volumes which have a large distance to the midplanes. To overcome these disadvantages we developed a method that simultaneously reconstructs all circle scans and thereby is able to reconstruct larger segments from each circle scan on the one hand and that reduces cone-beam artifacts by combining the segments in frequency domain on the other hand. The proposed method was evaluated using a simulation study as well as measured data from different flat-panel cone-beam CT scanners, as for example the Varian OBI scanner. In the example geometry we used the maximal reconstructable z-range can be increased by 25% and our approach additionally leads to a noise reduction of about 40% in the overlap region. Regarding the cone-beam artifacts, we were able to reduce the artifact level to a value as low as achievable by more complex algorithms that perform a voxel-wise weighted backprojection to favor voxels seen under small cone-angles. This paper demonstrates that the proposed algorithm is able to significantly improve the reconstruction of sequence scans while the reconstruction time is kept equivalent to the standard approach. We further demonstrate that the method can be used in clinical practice.

Empirical cupping correction for CT scanners with primary modulation (ECCP)

X-ray CT measures the attenuation of polychromatic x-rays through an object. The rawdata acquired, which are the negative logarithm of the relative x-ray intensity behind the patient, must undergo water precorrection to linearize the measurement and to convert them into line integrals that are ready for reconstruction. The function to linearize the measured projection data depends on the detected spectrum of the ray. This spectrum may vary as a function of the detector position, e.g. in cases where the heel effect becomes relevant, or where a bow-tie filter introduces channel-dependent beam hardening, or in cases where a primary modulator is used to modulate the primary intensity of the spectrum. We propose a new approach that allows to handle these effects. Our empirical cupping correction for primary modulation (ECCP) corrects for artifacts, such as cupping artifacts or ring artifacts, that are induced by non-linearities in the projection data due to spatially varying pre- or post filtration of the x-rays. To do so, ECCP requires nothing but a simple scan of a homogeneous phantom of nearly arbitrary shape. Based on this information, coefficients of a polynomial series are calculated and stored for later use. Numerical examples and physical measurements are shown to demonstrate the quality of the precorrection. ECCP achieves to remove the cupping artifacts and to obtain well-calibrated CT-values even in cases of strong primary modulation. A combination of ECCP with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.

Material decomposition with inconsistent rays (MDIR) for cone-beam dual energy CT

Dual energy CT (DECT) provides material-selective CT images by acquiring the object of interest with two different x-ray spectra, a low and a high energy spectrum. Today, two techniques to process the rawdata are in use: Image-based DECT reconstructs the low and the high energy data separately and then performs a linear combination of the images to yield the desired material-selective images. This method can only provide a first order approximation of the true material decomposition and it will not be able to remove higher order beam hardening artifacts from the images. By contrast, rawdata-based DECT naturally deals with higher order effects and is therefore the better way to go. However, rawdata-based DECT requires the same line integrals to be available for both scans (consistent scans). This requirement may not be met for CT scanners that are available today. To handle the material decomposition of DECT from inconsistent scans (i.e. non-overlapping rays for each measured spectrum) a material decomposition algorithm (MDIR) that allows for different scan trajectories and scan geometries for the low and the high energy scan was developed and evaluated. The results of our iterative algorithm are comparable to those obtained by a rawdata-based approach. However, conventional rawdata-based approaches are often not applicable since inconsistent rays are acquired. It should be noted that MDIR can be extended to scans with more than two different spectra and to decompositions into more than two basis functions in a straightforward way.