Frank Bergner

Improved total variation-based CT image reconstruction applied to clinical data.

In computed tomography there are different situations where reconstruction has to be performed with limited raw data. In the past few years it has been shown that algorithms which are based on compressed sensing theory are able to handle incomplete datasets quite well. As a cost function these algorithms use the ℓ(1)-norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequality-constrained convex optimization problem. Due to the large size of the optimization problem some heuristic optimization algorithms have been proposed in the past few years. The most popular way is optimizing the raw data and sparsity cost functions separately in an alternating manner. In this paper we will follow this strategy and present a new method to adapt these optimization steps. Compared to existing methods which perform similarly, the proposed method needs no a priori knowledge about the raw data consistency. It is ensured that the algorithm converges to the lowest possible value of the raw data cost function, while holding the sparsity constraint at a low value. This is achieved by transferring the step-size determination of both optimization procedures into the raw data domain, where they are adapted to each other. To evaluate the algorithm, we process measured clinical datasets. To cover a wide field of possible applications, we focus on the problems of angular undersampling, data lost due to metal implants, limited view angle tomography and interior tomography. In all cases the presented method reaches convergence within less than 25 iteration steps, while using a constant set of algorithm control parameters. The image artifacts caused by incomplete raw data are mostly removed without introducing new effects like staircasing. All scenarios are compared to an existing implementation of the ASD-POCS algorithm, which realizes the step-size adaption in a different way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.

An investigation of 4D cone-beam CT algorithms for slowly rotating scanners

PURPOSEnTo evaluate several algorithms for 4D cone-beam computed tomography (4D CBCT) with slow rotating devices. 4D CBCT is used to perform phase-correlated (PC) reconstructions of moving objects, such as breathing patients, for example. Such motion phase-dependent reconstructions are especially useful for updating treatment plans in radiation therapy. The treatment plan can be registered more precisely to the motion of the tumor and, in consequence, the irradiation margins for the treatment, the so-called planning target volume, can be reduced significantly.nnnMETHODSnIn the study, several algorithms were evaluated for kilovoltage cone-beam CT units attached to linear particle accelerators. The reconstruction algorithms were the conventional PC reconstruction, the McKinnon-Bates (MKB) algorithm, the prior image constrained compressed sensing (PICCS) approach, a total variation minimization (ASD-POCS) algorithm, and the autoadaptive phase correlation (AAPC) algorithm. For each algorithm, the same motion-affected raw data were used, i.e., one simulated and one measured data set. The reconstruction results from the authors implementation of these algorithms were evaluated regarding their noise and artifact levels, their residual motion blur, and their computational complexity and convergence.nnnRESULTSnIn general, it turned out that the residual motion blur was lowest in those algorithms which exclusively use data from a single motion phase. Algorithms using the image from the full data set as initialization or as a reference for the reconstruction were not capable of fully removing the motion blurring. The iterative algorithms, especially approaches based on total variation minimization, showed lower noise and artifact levels but were computationally complex. The conventional methods based on a single filtered backprojection were computationally inexpensive but suffered from higher noise and streak artifacts which limit the usability. In contrast, these methods showed to be less demanding and more predictable in their outcome than the total variation minimization based approaches.nnnCONCLUSIONSnThe reconstruction algorithms including at least one iterative step can reduce the 4D CBCT specific artifacts. Nevertheless, the algorithms that use the full data set, at least for initialization, such as MKB and PICCS in the authors implementation, are only a trade-off and may not fully achieve the optimal temporal resolution. A predictable image quality as seen in conventional reconstruction methods, i.e., without total variation minimization, is a desirable property for reconstruction algorithms. Fast, iterative approaches such as the MKB can therefore be seen as a suitable tradeoff.

Autoadaptive phase-correlated (AAPC) reconstruction for 4D CBCT

PURPOSEnKilovoltage cone-beam computed tomography (CBCT) is widely used in image-guided radiation therapy for exact patient positioning prior to the treatment. However, producing time series of volumetric images (4D CBCT) of moving anatomical structures remains challenging. The presented work introduces a novel method, combining high temporal resolution inside anatomical regions with strong motion and image quality improvement in regions with little motion.nnnMETHODSnIn the proposed method, the projections are divided into regions that are subject to motion and regions at rest. The latter ones will be shared among phase bins, leading thus to an overall reduction in artifacts and noise. An algorithm based on the concept of optical flow was developed to analyze motion-induced changes between projections. The technique was optimized to distinguish patient motion and motion deriving from gantry rotation. The effectiveness of the method is shown in numerical simulations and patient data.nnnRESULTSnThe images reconstructed from the presented method yield an almost the same temporal resolution in the moving volume segments as a conventional phase-correlated reconstruction, while reducing the noise in the motionless regions down to the level of a standard reconstruction without phase correlation. The proposed simple motion segmentation scheme is yet limited to rotation speeds of less than3°∕s.nnnCONCLUSIONSnThe method reduces the noise in the reconstruction and increases the image quality. More data are introduced for each phase-correlated reconstruction, and therefore the applied dose is used more efficiently.

Low‐dose cardio‐respiratory phase‐correlated cone‐beam micro‐CT of small animals

PURPOSEnMicro-CT imaging of animal hearts typically requires a double gating procedure because scans during a breath-hold are not possible due to the long scan times and the high respiratory rates, Simultaneous respiratory and cardiac gating can either be done prospectively or retrospectively. True five-dimensional information can be either retrieved with retrospective gating or with prospective gating if several prospective gates are acquired. In any case, the amount of information available to reconstruct one volume for a given respiratory and cardiac phase is orders of magnitud lower than the total amount of information acquired. For example, the reconstruction of a volume from a 10% wide respiratory and a 20% wide cardiac window uses only 2% of the data acquired. Achieving a similar image quality as a nongated scan would therefore require to increase the amount of data and thereby the dose to the animal by up to a factor of 50.nnnMETHODSnTo achieve the goal of low-dose phase-correlated (LDPC) imaging, the authors propose to use a highly efficient combination of slightly modified existing algorithms. In particular, the authors developed a variant of the McKinnon-Bates image reconstruction algorithm and combined it with bilateral filtering in up to five dimensions to significantly reduce image noise without impairing spatial or temporal resolution.nnnRESULTSnThe preliminary results indicate that the proposed LDPC reconstruction method typically reduces image noise by a factor of up to 6 (e.g., from 170 to 30 HU), while the dose values lie in a range from 60 to 500 mGy. Compared to other publications that apply 250-1800 mGy for the same task [C. T. Badea et al., 4D micro-CT of the mouse heart, Mol. Imaging 4(2), 110-116 (2005); M. Drangova et al., Fast retrospectively gated quantitative four-dimensional (4D) cardiac micro computed tomography imaging of free-breathing mice, Invest. Radiol. 42(2), 85-94 (2007); S. H. Bartling et al., Retrospective motion gating in small animal CT of mice and rats, Invest. Radiol. 42(10), 704-714 (2007)], the authors LDPC approach therefore achieves a more than tenfold dose usage improvement.nnnCONCLUSIONSnThe LDPC reconstruction method improves phase-correlated imaging from highly undersampled data. Artifacts caused by sparse angular sampling are removed and the image noise is decreased, while spatial and temporal resolution are preserved. Thus, the administered dose per animal can be decreased allowing for long-term studies with reduced metabolic inference.

Normalized metal artifact reduction (NMAR) in computed tomography

Severe artifacts degrade the image quality and the diagnostic value of CT images if metal objects are present in the field of measurement. The standard method for metal artifact reduction (MAR) replaces affected projection data by interpolated data. Often, linear interpolation is used. However, sinogram interpolation introduces new artifacts and lacks accuracy close to metal objects even if more complex interpolation schemes are used. Recently, a method was presented, which uses a simple length normalization of the sinogram prior to interpolation in order to better preserve the contrast between air and water-equivalent objects. However, contrast between objects from different materials, water and bone, for example, is still impaired. We introduce a generalized normalization technique, which concisely preserves details of different materials. This normalization is performed based on a forward projection of a ternary image, which is obtained from a multi-threshold segmentation of the initial image. Simulations and measurements are performed to evaluate our normalized metal artifact reduction method (NMAR) in comparison to standard MAR with linear interpolation and MAR based on simple length normalization. We find considerable improvements in particular for bone structures with metal implants. The improvements are quantified by comparing profiles through images and sinograms for the different methods using simulated data. NMAR clearly outperforms both other methods. We also obtain promising results by applying NMAR to clinical data. This is demonstrated with a scan of a patient with two hip endoprostheses. NMAR is computationally inexpensive, as only parts of a forward projection need to be computed additional to the steps of a interpolation-based MAR. Therefore, our normalization technique can be used as an additional step in any conventional sinogram interpolation-based MAR method.

A new approach to limited angle tomography using the compressed sensing framework

The limited angle problem is a well-known problem in computed tomography. It is caused by missing data over a certain angle interval, which make an inverse Radon transform impossible. In daily routine this problem can arise for example in tomosynthesis, C-arm CT or dental CT. In the last years there has been a big development in the field of compressed sensing algorithms in computed tomography, which deal very good with incomplete data. The most popular way is to integrate a minimal total variation norm in form of a cost function into the iteration process. To find an exact solution of such a constrained minimization problem, computationally very demanding higher order algorithms should be used. Due to the non perfect sparsity of the total variation representation, reconstructions often show the so called staircase effect. The method proposed here uses the solutions of the iteration process as an estimation for the missing angle data. Compared to a pure compressed sensing-based algorithm we reached much better results within the same number of iterations and could eliminate the staircase effect. The algorithm is evaluated using measured clinical datasets.

Water calibration for CT scanners with tube voltage modulation

X-ray CT measures the attenuation of polychromatic x-rays through an object of interest. The CT data acquired are the negative logarithm of the relative x-ray intensity after absorption. These data must undergo water precorrection to linearize the measured data and convert them into line integrals through the patient that can be reconstructed to yield the final CT image. The function to linearize the measured projection data depends on the tube voltage U. In most circumstances, CT scans are carried out with a constant tube voltage. For those cases there are dozens of different techniques to carry out water precorrection. In our case the tube voltage is rather modulated as a function of the object. We propose an empirical cupping correction (ECCU) algorithm to correct for CT cupping artifacts that are induced by nonlinearities in the projection data. The method is rawdata based, empirical and requires neither knowledge of the x-ray spectrum nor of the attenuation coefficients. It aims at linearizing the attenuation data using a precorrection function of polynomial form in the polychromatic attenuation data q and in the tube voltage U. The coefficients of the polynomial are determined once using a calibration scan of a homogeneous phantom. The coefficients are computed in the image domain by fitting a series of basis images to a template image. The template image is obtained directly from the uncorrected phantom image and no assumptions on the phantom size or of its positioning are made. Rawdata are precorrected by passing them through the once-determined polynomial. Numerical examples are shown to demonstrate the quality of the precorrection. ECCU is achieved to remove the cupping artifacts and to obtain well-calibrated CT values. A combination of ECCU with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.

Cluster Dynamics Study of Neutron Irradiation Induced Defects in Fe-12.5at%Cr Alloy

Cluster dynamics (CD) is used to study the evolution of the size distributions of vacancy clusters (VC), self-interstitial atom (SIA) clusters(SIAC) and Cr precipitates in neutron irradiated Fe-12.5at%Cr alloys at T = 573 K with irradiation doses up to 12 dpa and a flux of 140 ndpa/s. Transmission electron microscopy (TEM) and small angle neutron scattering (SANS) data on the defect structure of this material irradiated at doses of 0.6 and 1.5 dpa are used to calibrate the model. A saturation behavior was found by CD for the free vacancy and free SIA concentrations as well as for the number density of the SIAC and the volume fraction of the Cr precipitates for neutron exposures above 0.006 dpa. The CD simulations also indicate the presence of VC with radii less than 0.5 nm and a strong SIAC peak with a mean diameter of about 0.5 nm, both invisible in SANS and TEM experiments. A specific surface tension of about 0.028 J/m2 between the a matrix and the Cr-rich a precipitate was found as best fit value for reproducing the long-term Cr evolution in the irradiated Fe-12.5%Cr alloys observed by SANS.

Improved sparsity-constrained image reconstruction applied to clinical CT data

Compresssed sensing seems to be very promising for image reconstruction in computed tomography. In the last years it has been shown, that these algorithms are able to handle incomplete data sets quite well. As cost function these algorithms use the ℓ1 — norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequality — constrained convex optimization problem. Due to the large size of the optimization problem some heuristic optimization algorithms have been proposed in the last years. The most popular way is optimizing the rawdata and sparsity cost functions separately in an alternating manner. In this paper we will follow this strategy. Thereby we present a new method to adapt these optimization steps. Compared to existing methods which perform similar, the proposed method needs no a priori knowledge about the rawdata consistency. It is ensured that the algorithm converges to the best possible value of the rawdata cost function, while holding the sparsity constraint at a low value. This is achieved by transferring both optimization procedures into the rawdata domain, where they are adapted to each other. To evaluate the algorithm, we process measured clinical datasets. To cover a wide field of possible applications, we focus on the problems of angular undersampling, data lost due to metal implants, limited view angle tomography and interior tomography. In all cases the presented method reaches convergence within less than 25 iteration steps, while using a constant set of algorithm control parameters. The image artifacts caused by incomplete raw-data are mostly removed without introducing new effects like staircasing. All scenarios are compared to an existing implementation of the ASD — POCS algorithm, which realizes the stepsize adaption in a different way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.

Empirical cupping correction for CT scanners with tube voltage modulation (ECCU)

X-ray CT measures the attenuation of polychromatic x-rays through an object of interest. The CT data aquired are the negative logarithm of the relative x- ray intensity behind the patient. These data must undergo water precorrection to linearize the measured data and convert them into line integrals through the patient that can be reconstructed to yield the final CT image. The function to linearize the measured projection data depends on the tube voltage U. In most circumstances, CT scans are carried out with a constant tube voltage. For those cases there are dozens of different techniques to carry out water precor-rection. In our case the tube voltage is rather modulated as a function of the object. We propose an empirical cupping correction (ECCU) algorithm to correct for CT cupping artifacts that are induced by non-linearities in the projection data. The method is rawdata-based, empirical and does neither require knowledge of the x-ray spectrum nor of the attenuation coefficients. It aims at linearizing the attenuation data using a precorrection function of polynomial form in the polychromatic attenuation data q and in the tube voltage U. The coefficients of the polynomial are determined once using a calibration scan of a homogeneous phantom. Computing the coefficients is done in image domain by fitting a series of basis images to a template image. The template image is obtained directly from the uncorrected phantom image and no assumptions on the phantom size or of its positioning are made. Rawdata are precorrected by passing them through the once-determined polynomial. Numerical examples are shown to demonstrate the quality of the precorrection. ECCU achieves to remove the cupping artifacts and to obtain well-calibrated CT-values. A combination of ECCU with analytical techniques yielding a hybrid cupping correction method is possible and allows for channel-dependent correction functions.