Shaojie Tang

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT—Noise power spectrum NPS(k)

PURPOSE The differential phase contrast CT is emerging as a new technology to improve the contrast sensitivity of the conventional CT. Via system analysis, modeling, and computer simulation, the authors study the noise power spectrum (NPS)-an imaging performance indicator-of the differential phase contrast CT and compare it with that of the conventional CT. METHODS The differential phase contrast CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated with Fourier analysis and Fresnel analysis. To avoid any interference caused by scatter and beam hardening, a monochromatic x-ray source (30 keV) is assumed, which irradiates the object to be imaged by 360° so that no weighting scheme is needed. A 20-fold up-sampling is assumed to simulate x-ray beams propagation through the gratingsG1 and G2 with periods 8 and 4 μm, respectively, while the intergrating distance is 193.6 mm (1/16 of the Tabolt distance). The dimension of the detector cell for data acquisition ranges from 32 × 32 to 128 × 128 μm2 , while the field of view in data acquisition is 40.96 × 40.96 mm2 . A uniform water phantom with a diameter 37.68 mm is employed to study the NPS, with its complex refraction coefficient n = 1 - δ + iβ = 1 - 2.5604 × 10-7  + i1.2353 × 10-10 . The x-ray flux ranges from 106 to 108 photon/cm2 ·projection and observes the Poisson distribution, which is consistent with that of micro-CT in preclinical applications. The image matrix of reconstructed water phantom is 1280 × 1280, and a total of 180 regions at 128 × 128 matrix are used for NPS calculation via 2D Fourier Transform in which adequate zero padding is applied to avoid aliasing. RESULTS The preliminary data show that the differential phase contrast CT manifests its NPS with a 1/|k| trait, while the distribution of the conventional CTs NPS observes |k|. This accounts for the significant difference in their noise granularity and the differential phase contrast CTs substantial advantage in noise over the conventional CT, particularly, in the situations where the detector cell size for data acquisition is smaller than 100 μm. CONCLUSIONS The differential phase contrast CT detects the projection of refractive coefficients derivative and uses the Hilbert filter for image reconstruction, which leads to the radical difference in its NPS and the advantage in noise in comparison to that of the conventional CT.

Characterization of imaging performance in differential phase contrast CT compared with the conventional CT: Spectrum of noise equivalent quanta NEQ(k)

PURPOSE Differential phase contrast CT (DPC-CT) is emerging as a new technology to improve the contrast sensitivity of conventional attenuation-based CT. The noise equivalent quanta as a function over spatial frequency, i.e., the spectrum of noise equivalent quanta NEQ(k), is a decisive indicator of the signal and noise transfer properties of an imaging system. In this work, we derive the functional form of NEQ(k) in DPC-CT. Via system modeling, analysis, and computer simulation, we evaluate and verify the derived NEQ(k) and compare it with that of the conventional attenuation-based CT. METHODS The DPC-CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated through Fresnel and Fourier analysis. A monochromatic x-ray source (30 keV) is assumed to exclude any system imperfection and interference caused by scatter and beam hardening, while a 360° full scan is carried out in data acquisition to avoid any weighting scheme that may disrupt noise randomness. Adequate upsampling is implemented to simulate the x-ray beams propagation through the gratings G(1) and G(2) with periods 8 and 4 μm, respectively, while the intergrating distance is 193.6 mm (1∕16 of the Talbot distance). The dimensions of the detector cell for data acquisition are 32 × 32, 64 × 64, 96 × 96, and 128 × 128 μm(2), respectively, corresponding to a 40.96 × 40.96 mm(2) field of view in data acquisition. An air phantom is employed to obtain the noise power spectrum NPS(k), spectrum of noise equivalent quanta NEQ(k), and detective quantum efficiency DQE(k). A cylindrical water phantom at 5.1 mm diameter and complex refraction coefficient n = 1 - δ + iβ = 1 -2.5604 × 10(-7) + i1.2353 × 10(-10) is placed in air to measure the edge transfer function, line spread function and then modulation transfer function MTF(k), of both DPC-CT and the conventional attenuation-based CT. The x-ray flux is set at 5 × 10(6) photon∕cm(2) per projection and observes the Poisson distribution, which is consistent with that of a micro-CT for preclinical applications. Approximately 360 regions, each at 128 × 128 matrix, are used to calculate the NPS(k) via 2D Fourier transform, in which adequate zero padding is carried out to avoid aliasing in noise. RESULTS The preliminary data show that the DPC-CT possesses a signal transfer property [MTF(k)] comparable to that of the conventional attenuation-based CT. Meanwhile, though there exists a radical difference in their noise power spectrum NPS(k) (trait 1∕|k| in DPC-CT but |k| in the conventional attenuation-based CT) the NEQ(k) and DQE(k) of DPC-CT and the conventional attenuation-based CT are in principle identical. CONCLUSIONS Under the framework of ideal observer study, the joint signal and noise transfer property NEQ(k) and detective quantum efficiency DQE(k) of DPC-CT are essentially the same as those of the conventional attenuation-based CT. The findings reported in this paper may provide insightful guidelines on the research, development, and performance optimization of DPC-CT for extensive preclinical and clinical applications in the future.PURPOSE Differential phase contrast CT (DPC-CT) is emerging as a new technology to improve the contrast sensitivity of conventional attenuation-based CT. The noise equivalent quanta as a function over spatial frequency, i.e., the spectrum of noise equivalent quanta NEQ(k), is a decisive indicator of the signal and noise transfer properties of an imaging system. In this work, we derive the functional form of NEQ(k) in DPC-CT. Via system modeling, analysis, and computer simulation, we evaluate and verify the derived NEQ(k) and compare it with that of the conventional attenuation-based CT. METHODS The DPC-CT is implemented with x-ray tube and gratings. The x-ray propagation and data acquisition are modeled and simulated through Fresnel and Fourier analysis. A monochromatic x-ray source (30 keV) is assumed to exclude any system imperfection and interference caused by scatter and beam hardening, while a 360° full scan is carried out in data acquisition to avoid any weighting scheme that may disrupt noise randomness. Adequate upsampling is implemented to simulate the x-ray beams propagation through the gratingsG1 and G2 with periods 8 and 4 μm, respectively, while the intergrating distance is 193.6 mm (1/16 of the Talbot distance). The dimensions of the detector cell for data acquisition are 32 × 32, 64 × 64, 96 × 96, and 128 × 128 μm2 , respectively, corresponding to a 40.96 × 40.96 mm2 field of view in data acquisition. An air phantom is employed to obtain the noise power spectrum NPS(k), spectrum of noise equivalent quanta NEQ(k), and detective quantum efficiency DQE(k). A cylindrical water phantom at 5.1 mm diameter and complex refraction coefficient n = 1 - δ + iβ = 1 -2.5604 × 10-7 + i1.2353 × 10-10 is placed in air to measure the edge transfer function, line spread function and then modulation transfer function MTF(k), of both DPC-CT and the conventional attenuation-based CT. The x-ray flux is set at 5 × 106 photon/cm2 per projection and observes the Poisson distribution, which is consistent with that of a micro-CT for preclinical applications. Approximately 360 regions, each at 128 × 128 matrix, are used to calculate the NPS(k) via 2D Fourier transform, in which adequate zero padding is carried out to avoid aliasing in noise. RESULTS The preliminary data show that the DPC-CT possesses a signal transfer property [MTF(k)] comparable to that of the conventional attenuation-based CT. Meanwhile, though there exists a radical difference in their noise power spectrum NPS(k) (trait 1/|k| in DPC-CT but |k| in the conventional attenuation-based CT) the NEQ(k) and DQE(k) of DPC-CT and the conventional attenuation-based CT are in principle identical. CONCLUSIONS Under the framework of ideal observer study, the joint signal and noise transfer property NEQ(k) and detective quantum efficiency DQE(k) of DPC-CT are essentially the same as those of the conventional attenuation-based CT. The findings reported in this paper may provide insightful guidelines on the research, development, and performance optimization of DPC-CT for extensive preclinical and clinical applications in the future.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area

PURPOSES Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. METHODS We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner. RESULTS The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy. CONCLUSIONS In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small round areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori knowledge in a small round area is more feasible in clinical and preclinical practice.

Radial differential interior tomography and its image reconstruction with differentiated backprojection and projection onto convex sets.

PURPOSE Interior tomography has been recognized as one of the most effective approaches in computed tomography (CT) to reduce radiation dose rendered to patients. In this work, the authors propose and evaluate an imaging method of radial differential interior tomography. METHODS In interior tomography, an x-ray beam is collimated to only irradiate the region of interest (ROI) with suspected lesions while the surrounding area∕volume of normal tissues∕organs is spared. In the proposed imaging method of radial differential interior tomography, the outcome is a ROI image that has gone through a radial differential filtering. The image reconstruction algorithm for the radial differential interior tomography is kept in the fashion of differentiated backprojection and projection onto convex sets, but the required a priori knowledge in a small round area becomes zero and may be more readily available in practice. RESULTS Using the projection data simulated by computer and acquired by CT scanner, the authors evaluate and verify the performance of the proposed radial differential interior tomography method and its associated image reconstruction algorithm. The preliminary results show that the proposed imaging method can generate an image that is the radial differentiation of a conventional tomographic image and is robust over noise that inevitably exist in practice. CONCLUSIONS It is believed that the proposed imaging method may find its utility in advanced clinical applications wherein a ROI-based image processing and analysis is required for lesion visualization, characterization, and diagnosis.

Interior tomography with radial Hilbert filtering and a priori information in a small circular area

Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori information within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori information is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering (namely radial DBP-POCS method henceforth). We implement the radial DBP-POCS method, and thus the small area with the a priori information can be roughly circular (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation. The performance of the radial DBP-POCS method with the a priori information in a small circular area is evaluated with projection data of the standard Shepp-Logan phantom simulated by computer. The preliminary performance study shows that, if the a priori information in a small circular area is available, the radial DBP-POCS method can solve the interior tomography problem in a much more practical way at high accuracy. In comparison to the implementations of DBP-POCS method demanding the a priori information in horizontal or vertical strip, the radial DBP-POCS method requires the a priori information within a small circular area only. Such a relaxed requirement on the availability of a priori information can be readily met in practice, because a variety of small circular areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori information in a small circular area is feasible in clinical and preclinical practice.

X-ray phase Computed Tomography for nanoparticulated imaging probes and therapeutics - Preliminary feasibility study

With the scientific progress in cancer biology, pharmacology and biomedical engineering, the nano-biotechnology based imaging probes and therapeutical agents (namely probes/agents) - a form of theranostics - are among the strategic solutions bearing the hope for the cure of cancer. The key feature distinguishing the nanoparticulated probes/agents from their conventional counterparts is their targeting capability. A large surface-to-volume ratio in nanoparticulated probes/agents enables the accommodation of multiple targeting, imaging and therapeutic components to cope with the intra- and inter-tumor heterogeneity. Most nanoparticulated probes/agents are synthesized with low atomic number materials and thus their x-ray attenuation are very similar to biological tissues. However, their microscopic structures are very different, which may result in significant differences in their refractive properties. Recently, the investigation in the x-ray grating-based differential phase contrast (DPC) CT has demonstrated its advantages in differentiating low-atomic materials over the conventional attenuation-based CT. We believe that a synergy of x-ray grating-based DPC CT and nanoparticulated imaging probes and therapeutic agents may play a significant role in extensive preclinical and clinical applications, or even become a modality for molecular imaging. Hence, we propose to image the refractive property of nanoparticulated imaging probes and therapeutical agents using x-ray grating-based DPC CT. In this work, we conduct a preliminary feasibility study with a focus to characterize the contrast-to-noise ratio (CNR) and contrast-detail behavior of the x-ray grating-based DPC CT. The obtained data may be instructive to the architecture design and performance optimization of the x-ray grating-based DPC CT for imaging biomarker-targeted imaging probes and therapeutic agents, and even informative to the translation of preclinical research in theranostics into clinical applications.

Imaging performance in differential phase contrast CT compared with the conventional CT-noise equivalent quanta NEQ(k)

The grating-based x-ray differential phase contrast (DPC) CT is emerging as a new technology with the potential for extensive preclinical and clinical applications. In general, the performance of an imaging system is jointly determined by its signal property (modulation transfer function-MTF(k)) and noise property (noise power spectrum-NPS(k)), which is characterized by its spectrum of noise equivalent quanta. As reported by us previously, owing to an adoption of the Hilbert filtering for image reconstruction in the fashion of filtered backprojection (FBP), the noise property of DPC-CT characterized by its NPS(k) differs drastically from that of the conventional attenuation-based CT (1/|k| trait vs. |k| trait). In this work, via system analysis, modeling and simulated phantom study, we initially investigate the signal property of DPC-CT characterized by its MTF(k) and compare it with that of the conventional CT. In addition, we investigate the DPC-CTs spectrum of noise equivalent quanta NEQ(k) - the most important figure of merit (FOM) in the assessment of an imaging systems performance - by taking the MTF(k) and NPS(k) jointly into account. Through such a thorough investigation into both the signal and noise properties, the imaging performance of DPC-CT and its potential over the conventional attenuation-based CT can be fully understood and appreciated.

X-ray tube-based phase CT: spectrum polychromatics and imaging performance

Owing to its advantages in differentiating low-atomic materials over the conventional attenuation-based CT, the x-ray refraction-based phase contrast CT implemented with grating interferometer (namely grating-based differential phase contrast CT) has drawn increasing attention recently. Through the Talbot-effect, the phase variation of an object is retrieved and reconstructed to characterize the objects refraction property. The Talbot-effect is wavelength dependent, and a quantitative investigation into the influence of x-ray source spectrum polychromatics on the imaging performance of the grating-based differential phase contrast CT can provide guidelines on its architecture design and performance optimization. In this work, we conduct a computer simulation study of the x-ray grating-based differential phase contrast CT imaging under the condition of both monochromatic and polychromatic x-ray sources. The preliminary data shows that, the modulation transfer function (MTF) of a grating-based differential phase contrast CT with polychromatic source changes little in comparison to that with a monochromatic one. Furthermore, it is shown that the spectrum polychromatics leads to a remarkable improvement in the contrast-to-noise ratio of a grating-based differential phase contrast CT, which implies that a commercially available x-ray tube can be well suited to build a differential phase contrast CT with a grating-based interferometer to image the refractive property of an object.

Content-oriented sparse representation (COSR) for CT denoising with preservation of texture and edge

PURPOSE Denoising has been a challenging research subject in medical imaging, since the suppression of noise conflicts with the preservation of texture and edges. To address this challenge, we develop a content-oriented sparse representation (COSR) method for denoising in computed tomography (CT). METHODS An image is segmented into a number of content areas and each of them consists of similar material. Having been ex-painted, each content area is sparsely coded using the dictionary learnt from patches extracted from the corresponding content area. By constraining sparsity, noise is suppressed and the final image is formed by aggregating all denoised content areas. The performance of COSR method is examined with images simulated by computer and generated by multidetector row CT (MDCT), cone beam CT (CBCT), and micro-CT, in which water phantom, anthropomorphic phantom, a human subject, and a small animal are engaged, using the figures of merit, such as standard division (SD), contrast to noise ratio (CNR), and thresholded edge keeping index (EKIth ) and structural similarity index (SSIM). In addition, the optimization of performance by parameter tuning is also investigated. RESULTS Quantitatively gauged by metrics of noise, EKIth and SSIM, the performance evaluation shows that the proposed COSR method is effective in denoising (>50% reduction in noise) while it outperforms the conventional sparse representation method in preservation of texture and edge by ~20% (gauged by SSIM). It has also been shown that the COSR method is tolerable to inaccuracy in content area segmentation and variation in dictionary learning. Moreover, the computational efficiency of COSR can be substantially improved using prelearnt dictionaries. CONCLUSIONS The COSR method would find its utility in clinical and preclinical applications, such as low-dose CT, image segmentation, registration, and computer-aided diagnosis. The proposal of COSR denoising is of innovation and significance in the theory and practice of denoising in medical imaging. A demonstration code package is available at https://github.com/xiehq/COSR.

Axial 3D region of interest reconstruction using weighted cone beam BPF/DBPF algorithm cascaded with adequately oriented orthogonal butterfly filtering

Axial cone beam (CB) computed tomography (CT) reconstruction is still the most desirable in clinical applications. As the potential candidates with analytic form for the task, the back projection-filtration (BPF) and the derivative backprojection filtered (DBPF) algorithms, in which Hilbert filtering is the common algorithmic feature, are originally derived for exact helical and axial reconstruction from CB and fan beam projection data, respectively. These two algorithms have been heuristically extended for axial CB reconstruction via adoption of virtual PI-line segments. Unfortunately, however, streak artifacts are induced along the Hilbert filtering direction, since these algorithms are no longer accurate on the virtual PI-line segments. We have proposed to cascade the extended BPF/DBPF algorithm with orthogonal butterfly filtering for image reconstruction (namely axial CB-BPP/DBPF cascaded with orthogonal butterfly filtering), in which the orientation-specific artifacts caused by post-BP Hilbert transform can be eliminated, at a possible expense of losing the BPF/DBPF’s capability of dealing with projection data truncation. Our preliminary results have shown that this is not the case in practice. Hence, in this work, we carry out an algorithmic analysis and experimental study to investigate the performance of the axial CB-BPP/DBPF cascaded with adequately oriented orthogonal butterfly filtering for three-dimensional (3D) reconstruction in region of interest (ROI).