Purpose: Inverting the discrete x-ray transform (DXT) with the nonlinear partial volume (NLPV) effect, which we refer to as the NLPV DXT, remains of theoretical and practical interest. We propose an optimization-based algorithm for accurately and directly inverting the NLPV DXT.
Methods: Formulating the inversion of the NLPV DXT as a nonconvex optimization program, we propose an iterative algorithm, referred to as the nonconvex primal-dual (NCPD) algorithm, to solve the problem. We obtain the NCPD algorithm by modifying a first-order primal-dual algorithm to address the nonconvex optimization. Subsequently, we perform quantitative studies to verify and characterize the NCPD algorithm.
Results: In addition to proposing the NCPD algorithm, we perform numerical studies to verify that the NCPD algorithm can reach the devised numerically necessary convergence conditions and, under the study conditions considered, invert the NLPV DXT by yielding numerically accurate image reconstruction.
Conclusion: We have developed and verified with numerical studies the NCPD algorithm for accurate inversion of the NLPV DXT. The study and results may yield insights into the effective compensation for the NLPV artifacts in CT imaging and into the algorithm development for nonconvex optimization programs in CT and other tomographic imaging technologies.
In this work, we investigate and characterize optimization-based image reconstruction from list-mode TOFPET data collected by using a digital TOF-PET scanner with reduced detectors, while seeking possibly to maintain the image quality and volume coverage. In particular, we focused on two patterns of sparse configurations, in both of which the total number of crystals is reduced to 50% of the corresponding clinical TOF-PET scanner. The reconstruction problem from data of the two sparse configurations is formulated as the solution to an image-TV-constrained, data-KLminimization optimization problem, and the image is reconstructed by use of an algorithm tailored from a Chambolle and Pock (CP) algorithm through solving the optimization problem. The characteristics of each sparse configuration was investigated by assessing the corresponding reconstructions visually and quantitatively. Results of the study suggest that certain sparse TOF-PET configurations may yield images with quality and volume coverage comparable to that obtained with current clinical TOF-PET scanner that has densely populated detectors.
In a standard data model for CT, a single ray often is assumed between a detector bin and the X-ray focal spot even though they are of finite sizes. However, due to their finite sizes, each pair of detector bin and X-ray focal spot necessarily involves multiple rays, thus resulting in the non-linear partial volume (NLPV) effect. When an algorithm developed for a standard data model is applied to data with NLPV effect, it may engender NLPV artifacts in images reconstructed. In the presence of the NLPV effect, data necessarily relates non-linearly to the image of interest, and image reconstruction free of NLPV is thus tantamount to inverting appropriately the non-linear data model. In this work, we develop an optimization-based algorithm for solving the non-linear data model in which the NLPV effect is included, and use the algorithm to investigate the characteristics and reduction of the NLPV artifacts in images reconstructed. The algorithm, motivated by our previous experience in dealing with a non-linear data model in multispectral CT reconstruction, compensates for the NLPV effect by numerically inverting the non-linear data model through solving a non-convex optimization program. The algorithm, referred to as the non-convex Chambolle-Pock (ncCP) algorithm, is used in simulation studies for numerically characterizing the inversion of the non-linear data model and the compensation for the NLPV effect.
In this work, we investigate the non-linear partial volume (NLPV) effect caused by sub-detector sampling in CT. A non-linear log-sum of exponential data model is employed to describe the NLPV effect. Leveraging our previous work on multispectral CT reconstruction dealing with a similar non-linear data model, we propose an optimization-based reconstruction method for correcting the NLPV artifacts by numerically inverting the non-linear model through solving a non-convex optimization program. A non-convex Chambolle-Pock (ncCP) algorithm is developed and tailored to the non-linear data model. Simulation studies are carried out with both discrete and continuous FORBILD head phantom with one high-contrast ear section on the right side, based on a circular 2D fan-beam geometry. The results suggest that, under the data condition in this work, the proposed method can effectively reduce or eliminate the NLPV artifacts caused by the sub-detector ray integration.
Time-of-flight (TOF) positron emission tomography (PET) has gained remarkable development recently due to the advances in scintillator, silicon photomultipliers (SiPM), and fast electronics. However, current clinical reconstruction algorithms in TOF-PET are still based on ordered-subset-expectation-maximization (OSEM) and its variants, which may face challenges in non-conventional imaging applications, such as fast imaging within short scan time. In this work, we propose an image-TV constrained optimization problem, and tailor a primal- dual algorithm for solving the problem and reconstructing images. We collect list-mode data of a Jaszczak phantom with a prototype digital TOF-PET scanner. We focus on investigating image reconstruction from data collected within reduced scan time, and thus of lower count levels. Results of the study indicate that our proposed algorithm can 1) yield image reconstruction with suppressed noise, extended axial volume coverage, and improved spatial resolution over that obtained in conventional reconstructions, and 2) yield reconstructions with potential clinical utility from data collected within shorter scan time.
Cone-beam artifact may be observed in the images reconstructed from circular trajectory data by use of the FDK algorithm or its variants for an imaged subject with longitudinally strong contrast variation in advanced diagnostic CT with a large number of detector rows. Existing algorithms have limited success in correcting for the effect of the cone-beam artifacts especially on the reconstruction of low-contrast soft-tissue. In the work, we investigate and develop optimization-based reconstruction algorithms to compensate for the cone-beam artifacts in the reconstruction of low-contrast anatomies. Specifically, we investigate the impact of optimization-based reconstruction design based upon different data-fidelity terms on the artifact correction by using the Chambolle- Pock (CP) algorithm tailored to each of the specific data-fidelity terms considered. We performed numerical studies with real data collected with the 320-slice Canon Medical System CT scanner, demonstrated the effectiveness of the optimization-based reconstruction design, and identified the optimization-based reconstruction that corrects most effectively for the cone-beam artifacts.
Photon counting x-ray detectors (PCD) offer a great potential for energy-resolved imaging that would allow for promising applications such as low-dose imaging, quantitative contrast-enhanced imaging, as well as spectral tissue decomposition. However, physical processes in photon counting detectors produce undesirable effects like charge sharing and pulse-pile up that can adversely affect the imaging application. Existing detector response models for photon counting detectors have mainly used either X-ray fluorescence imaging or radionuclides to calibrate their detector and estimate the model parameters. The purpose of our work was to apply one such model to our photon counting detector and to determine the model parameters from transmission measurements. This model uses a polynomial fit to model the charge sharing response and energy resolution of the detector as well as an Aluminum filter to model the modification of the spectrum by the X-ray. Our experimental setup includes a Si-based photon counting detector to generate transmission spectra from multiple materials at varying thicknesses. Materials were selected so as to exhibit k-edges within the 15-35 keV region. We find that transmission measurements can be used to successfully model the detector response. Ultimately, this approach could be used for practical detector energy calibration. A fully validated detector response model will allow for exploration of imaging applications for a given detector.
There exists interest in designing a PET system with reduced detectors due to cost concerns, while not significantly compromising the PET utility. Recently developed optimization-based algorithms, which have demonstrated the potential clinical utility in image reconstruction from sparse CT data, may be used for enabling such design of innovative PET systems. In this work, we investigate a PET configuration with reduced number of detectors, and carry out preliminary studies from patient data collected by use of such sparse-PET configuration. We consider an optimization problem combining Kullback-Leibler (KL) data fidelity with an image TV constraint, and solve it by using a primal-dual optimization algorithm developed by Chambolle and Pock. Results show that advanced algorithms may enable the design of innovative PET configurations with reduced number of detectors, while yielding potential practical PET utilities.
We report on the development of silicon strip detectors for energy-resolved clinical mammography. Typically, X-ray integrating detectors based on scintillating cesium iodide CsI(Tl) or amorphous selenium (a-Se) are used in most commercial systems. Recently, mammography instrumentation has been introduced based on photon counting Si strip detectors. The required performance for mammography in terms of the output count rate, spatial resolution, and dynamic range must be obtained with sufficient field of view for the application, thus requiring the tiling of pixel arrays and particular scanning techniques. Room temperature Si strip detector, operating as direct conversion x-ray sensors, can provide the required speed when connected to application specific integrated circuits (ASICs) operating at fast peaking times with multiple fixed thresholds per pixel, provided that the sensors are designed for rapid signal formation across the X-ray energy ranges of the application. We present our methods and results from the optimization of Si-strip detectors for contrast enhanced spectral mammography. We describe the method being developed for quantifying iodine contrast using the energy-resolved detector with fixed thresholds. We demonstrate the feasibility of the method by scanning an iodine phantom with clinically relevant contrast levels.