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.

Purpose: In the last decade, C-arm-based cone-beam CT became a widely used modality for intraoperative imaging. Typically a C-arm CT scan is performed using a circular or elliptical trajectory around a region of interest. Therefore, an angular range of at least 180• plus fan angle must be covered to ensure a completely sampled data set. However, mobile C-arms designed with a focus on classical 2D applications like fluoroscopy may be limited to a mechanical rotation range of less than 180• to improve handling and usability. The method proposed in this paper allows for the acquisition of a fully sampled data set with a system limited to a mechanical rotation range of at least 180• minus fan angle using a new trajectory design. This enables CT like 3D imaging with a wide range of C-arm devices which are mainly designed for 2D imaging. Methods: The proposed trajectory extends the mechanical rotation range of the C-arm system with two additional linear shifts. Due to the divergent character of the fan-beam geometry, these two shifts lead to an additional angular range of half of the fan angle. Combining one shift at the beginning of the scan followed by a rotation and a second shift, the resulting rotate-plus-shift trajectory enables the acquisition of a completely sampled data set using only 180• minus fan angle of rotation. The shifts can be performed using, e.g., the two orthogonal positioning axes of a fully motorized C-arm system. The trajectory was evaluated in phantom and cadaver examinations using two prototype C-arm systems. Results: The proposed trajectory leads to reconstructions without limited angle artifacts. Compared to the limited angle reconstructions of 180• minus fan angle, image quality increased dramatically. Details in the rotate-plus-shift reconstructions were clearly depicted, whereas they are dominated by artifacts in the limited angle scan. Conclusions: The method proposed here employs 3D imaging using C-arms with less than 180• rotation range adding full 3D functionality to a C-arm device retaining both handling comfort and the usability of 2D imaging. This method has a clear potential for clinical use especially to meet the increasing demand for an intraoperative 3D imaging. C 2016 American Association of Physicists in Medicine. [http://dx

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.

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 ℓ1norm of the image after it has been transformed by a sparsifying transformation. This yields to an inequalityconstrained 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 eld 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 rawdata are mostly removed without introducing new eects like staircasing. All scenarios are compared to an existing implementation of the ASDPOCS algorithm, which realizes the stepsize adaption in a dierent way. Additional prior information as proposed by the PICCS algorithm can be incorporated easily into the optimization process.

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