TY - JOUR
AU - Ghetti,, C
AB - Abstract We investigated the performances of two computed tomography (CT) systems produced by the same manufacturers (Somatom Flash and Edge Siemens) with different detector technologies (Ultrafast Ceramic and Stellar) and different generation of iterative reconstruction (IR) algorithms (SAFIRE and ADMIRE). A homemade phantom was scanned and the images were reconstructed with filtered back-projection (FBP) and IR algorithms. In terms of image quality, the performances of the systems were checked using the low-contrast detectability, evaluated by a Channelized Hotelling Observer (CHO), and the noise power spectrum (NPS). The analysis with CHO showed the best performance of Edge respect to Flash system for both FBP and IR algorithms. This better behavior, which reaches 20%, has been ascribed to the Stellar detector. From the NPS analysis, the noise reduction due to Stellar detector was 57%, moreover ADMIRE algorithm preserves a more traditional CT image texture appearance versus SAFIRE due to a lower NPS peak shift. INTRODUCTION Evaluation of image quality (IQ) in computed tomography (CT) is important to ensure that clinical questions are correctly answered, whilst keeping patient radiation dose as low as is reasonably possible(1). This issue is more crucial when a new technology, as a new type of detector, is introduced in clinical practice or when a new reconstruction algorithm is implemented, and it is necessary to evaluate their effect on clinical images. Objective assessment of parameters that influence IQ is often made using physical metrics specified in either the spatial or spatial frequency such as the modulation transfer function (MTF), the contrast to noise ratio (CNR) and the noise power spectrum (NPS)(2). However, the mutual connections among these factors have not been clearly established yet, especially with regard to the new reconstruction techniques involving iterative methods for which some physical quantities cannot be properly defined. Moreover, the main limitations of this approach are the not immediate application of results to clinical practice. For these reasons, task-based approach(3) considering IQ in terms of the ability of an observer to extract the desired information has been widely studied and implemented using mathematical model observer (MO). These methods, based on statistical decision theory(4), have gained popularity in recent years to characterize IQ in CT in a quantitative way(5–8) and are not intended to be alternative to physical characterization but are complementary, whenever possible. Some of the applied MO operate in the spatial frequency domain(9–12) and others, primarily the channelized Hotelling observers (CHO), operate in the spatial domain(5,13–15). The spatial domain CHO is the most appropriate for evaluating CT images reconstructed by both filtered-back-projection (FBP) and iterative reconstruction (IR) algorithms(14,16,17). The performance of CHO has been successfully validated in previous studies using low-contrast object detection, localization and classification tasks(5,8,13). In addition, the use of a traditional metric as NPS has been proved to be useful in studying how the image texture can be modified by iterative reconstruction and to predict if clinical images have a familiar visual appearance for radiologists or if they show a plastic-like, blurry and over-smoothed aspect(18). In this study, the performances of two CT systems produced by the same manufacturer with different detector technologies and different generation of reconstruction algorithms were evaluated. Their performances were investigated in terms of low-contrast detectability using a CHO model observer and in terms of noise reduction and texture preservation with NPS assessment. MATERIALS AND METHODS A homemade phantom A NEMA IEC PET Body (NU2-2007) phantom, without its inserts and filled with water and iodinated contrast medium (Iomeron® 300 mg/ml, Bracco Imaging S.p.A., Italy), was used to simulate an average-sized patient (Figure 1). The phantom contains a cylindrical insert of 6 mm diameter, placed on the bottom of the center region to simulate a lesion. The insert has been created using 3D printer model Ultimaker 2+(19) with polyhydroxyalkanoates (PHA) and poly(lactic acid) (PLA) bioplastic material. The signal to background contrast was easily controlled by varying the concentration of the solution injected into the phantom. In this study, we reached about −15 HU contrast at 100 kV between the signal and the background. Figure 1 Open in new tabDownload slide On the left, the homemade phantom containing a low-contrast insert. On the right, the original axial image (512px × 512px) with a signal_present ROI. Figure 1 Open in new tabDownload slide On the left, the homemade phantom containing a low-contrast insert. On the right, the original axial image (512px × 512px) with a signal_present ROI. Multidetector CT image acquisition Images were acquired on two different CT scanner Siemens named Somatom Definition Flash and Somatom Definition Edge with similar thorax low-dose protocol. The CT Somatom Definition Flash is equipped with ultra-fast ceramic (UFC) detector(20) instead the CT Somatom Definition Edge is equipped with a new Stellar detector(21). On this last detector, engineering progress has reduced the problems with electronic noise during image acquisition integrating analogic-digital converters (ADC) on the same silicon chip(22). The Stellar Detector of the Edge system is the first third-generation detector that combines the photodiode and the ADC in one application specific integrated circuit (ASIC), reducing the path of the signal, electronic noise, power consumption and heat dissipation. We used the same clinical thorax protocol on both scanners with the following acquisition parameters: 128  ×  0.6-mm collimation, 1.5-mm slice thickness, 1.0 pitch, tube voltage fixed to 100 kV, 90-mAs tube current (without CARE Dose4D), 1-s rotation time. Automated exposure control (CAREDose 4D) was turned off to standardize across scans and to exclude the confounding effect of automated exposure control on image. The CT dose indexes (CTDIvol), determined for a 32-cm-diameter (polymethyl methacrylate) reference phantom, were retrieved from reports available in the CT workstation at the end of the acquisitions and result 3.5 mGy for Flash and Edge, respectively. A good agreement, within 5%, between recorded and measured values of CTDIvol was obtained on both CT scanners using a calibrated dose meter (RaySafe™ X2 CT Sensor). To ensure statistical robustness of the results, the phantom was scanned five times on each CT units without changing its position between the different acquisitions in order to obtain enough number of images for analysis with CHO. Images were reconstructed with FBP by using a medium smooth kernel named B30s and Br32 for Flash and Edge, respectively, available on each system and usually used in clinical practice. Unfortunately, it was not possible to use the same kernel exactly because the whole package of new reconstruction filters on the CT Edge was imported from the CT Siemens Somatom Force, and it is not available on Flash scanner(23). However, the kernel B30s used on CT Edge is the matching available to the kernel Br32 on CT Flash and it is also the kernel proposed by default on the protocol used. Moreover, the images were reconstructed with Sinogram-Affirmed Iterative Reconstruction named Siemens Healthcare, Erlangen, Germany-2010 (SAFIRE) for Flash system and with Advanced Modeled Iterative Reconstruction named ADMIRE (Siemens Healthcare, Forchheim, Germany-2013) for Edge system(23–25). The kernels used in IR algorithms were the corresponding ones with the filters used in FBP. SAFIRE is a hybrid iterative reconstruction technique incorporating a raw data-based iterative reconstruction algorithm and an image space iteration algorithm. The SAFIRE performs an initial reconstruction using a weighted FBP, following which, two different correction loops are introduced into the reconstruction process. In the first loop, the data are re-projected into the raw data space (sinogram data) to correct imperfections and remove any artefacts from the data. For each iteration, a dynamic raw-data based noise model is applied for reduction noise without noticeable loss of sharpness. In the second correction, the noise is removed from the image through a statistical optimization process in image space. Noise can be locally estimated and removed by using a dynamic raw-database noise model that, during each iteration, predicts the variance of the image noise in different directions in each image pixel and adjusts the space-variant regularization function correspondingly. Noise reduction occurs almost solely in image space, thus reducing the requirement to return to raw data space. The corrected image is compared with the original, and the process is repeated a number of times depending on the examination type(26). The new algorithm ADMIRE is a model-based iterative reconstruction algorithm that implements a statistical model for both the raw projection data and the image data, as well as a system model for the forward projection. Compared with SAFIRE, the analysis incorporates not only nearest-neighbor data but also a larger area. An improved statistical modeling applied to raw data projection, an enlarged voxel analysis and the use of a weighted FBP in the iterative loop perform a better preservation of the CT noise texture and artefact suppression(27). For both SAFIRE and ADMIRE, it is possible for the user to choose among five different strengths of iterative reconstruction (S1-S5), the effect of noise reduction is increased when the strength is higher but also the texture of the image could change going towards a more plastic aspect. Generating signal-absent and signal-present images The acquired images were prepared using a homemade GUI in MATLAB R2018a (Mathworks, Natick, USA), programming language to be analyzed by MO and human observers. Images were cropped with two 85 × 85 px ROIs (50 × 50 mm2) centered on the low-contrast insert and on the homogeneous background region in order to generate signal-present and signal-absent images, respectively. Overall, 100 signal-present and 100 signal-absent images were finally generated to be presented to human observers and used for evaluation with MO. CHO and internal noise In a signal detection task, an MO should decide whether an image, denoted by the vector g, belongs to the signal-present or the signal-absent image class. To make a decision, it computes a scalar variable λ, called decision variable, representing the probability that g belongs to a given class. Among the available model observers, in this work, the choice was for CHO, which was described and successfully used in a similar framework in previous studies where it was described in detail(5,13–15). Here, it is reminded that the decision variable is generated by a weighted linear combination of the channel responses using Equation (1): $$\begin{equation} {\lambda}_{CHO}={\omega}_{CHO}^T\cdot \left({V}^T\cdot g\right) \end{equation}$$(1) where ωCHO is the CHO template and VT is the transposed channel matrix. CHO implanted in this work uses 40 Gabor channels. The general form of Gabor function can be expressed using Equation (2): $${\begin{eqnarray}&& Ch\left(x,y\right)=\exp \left[-\frac{4\ln (2)\left({\left(x-x0\right)}^2+{\left(y-y0\right)}^2\right)}{w_s^2}\right]\nonumber\\ &&\qquad\times\, \cos \left[2\ \pi{f}_c\Big(\left(x-x0\right)\cos \theta +\left(y-y0\right)\sin \theta \right)+\,\varepsilon \Big] \end{eqnarray}}$$(2) These functions consist of a Gaussian modulated by a cosine function. In equation, fc denotes the center frequency of the channel, ws is the spatial width of the channel, the point (x0, y0) is the center of the channel, θ is the channel orientation and ε is a phase factor. We considered four channel passbands, given by [1/64, 1/32], [1/32, 1/16], [1/16, 1/8] and [1/8, 1/4] cycles/pixel. The center frequencies are thus fc = 3/128, 3/64, 3/32 and 3/16 cycles/pixel. In addition, we use five orientations and two phases for each passband, so that the total number of channels is 40 (4 frequency bands × 5 orientations × 2 phases). The five orientations are θ = 0, 2π/5, 4π/5, 6π/5 and 8π/5 radians and the two phases are ε = 0 and π/2. With respect to an MO, humans show lower performances in classification tasks and are not exactly reproducible as they generally give slightly different responses when they review the same images. In order to reproduce the suboptimal performances of human observers, noise was added to the decision variable. In MO literature, it was known as internal noise(13). Indicating with σb the standard deviation of the signal absent image, the final decision variable is given by Equation (3): $$\begin{equation} \lambda \left(\alpha \right)={\lambda}_{CHO}+\alpha \cdot u\cdot{\sigma}_b \end{equation}$$(3) where α is an adjustable weighting factor and u is a random number in the range (−1,1). According to(13, 15), it is reasonable to fix the amount of noise in a given condition and use it to evaluate images acquired in slightly different conditions (in terms of dose and reconstruction kernels). In our study, the weighting factor α is determined by tuning the CHO performances to match the human observer for the evaluation of FBP images on both scanners as described in the following paragraph. Human observer The human observer performance was evaluated by considering the responses of three experienced health professionals that evaluated the images at workstation calibrated to the DICOM Grayscale Standard Display Function(28). Observers were requested to perform a 2-alternative forced choice (2AFC) lesion-detection tasks with signal-present and signal-absent image combinations, with the aim of identifying which of two images contained the signal. To expert reader, 100 combinations of signal-present and signal-absent images were presented, prepared according to section 2.3 procedure. Signal was presented in random position, unknown to the observers, assigned by a binary number extracted with Gaussian probability. The signal-present and signal-absent image combinations were displayed on 1.3 mega pixel (1280 × 1024), 480 mm diagonal, secondary quality liquid crystal display (LCD) monitor RaidForce MX191 (EIZO, Shinagawa, Japan). All the images were presented to observers with the same display window (75-225 HU). The reading was performed in a room with an ambient light of about 10 lux. Observers were at a fixed distance of 50 cm from the screen and no feedback about whether their decision was correct was given to the observers. No time limit was imposed. The observer was requested to identify the quadrant in which he thought of seeing the low-contrast insert. At the end of the test, the percentage of correct response (PCR) in a 2-AFC test(29) was calculated for each observer. The results obtained by different observers were finally averaged. The 2-AFC task was performed on the FBP images for both scanners, chosen as a reference data set for the subsequent evaluations of IR algorithms and CHO. CHO evaluation and comparison with human observer The FOM (figure of merit) generally used to quantify the MO’s performances is the area under the ROC curve (AUC)(30). For a 2AFC detection task, AUC values span in the range from 0.5 (pure guessing) to 1 (absolute certainty) and it corresponds to PCR(31). First, the degree of agreement between CHO and human observer was evaluated with respect to reference data set. In order to define the degree of internal noise (α) for which CHO reflects human performance, the AUC obtained on FBP images by varying α was compared with those obtained with 2-AFC detection task executed by the three human readers. The internal noise parameter α was set to the value that best matches the CHO performances to the average of the human readers. Once set the α parameter, we calculated the AUCs using the CHO on images reconstructed with SAFIRE and ADMIRE (set at different strengths). The AUC results were then compared to evaluate the performance of each algorithm. NPS evaluation To objectively evaluate the quality of images obtained with IR algorithms, the common image quality indexes (the standard deviation of CT numbers and contrast-to noise ratio) are not sufficient because these algorithms present non-linearity and non-stationary properties that change the noise texture, leading to change in image-quality assessment. It is more appropriate to perform this evaluation using the NPS metric that gives a complete description of the noise by plotting the noise magnitude according to the frequency of the image, which is known as noise texture (e.g. image smoothing). The magnitude of the NPS reflects the degree of randomness at each spatial frequency and the integral of the NPS yields the variance of CT numbers(32). The shape and the peak of the NPS reveals where the noise is concentrated in frequency space: low-frequency noise concentration means that the noise will have a coarse graininess and the image appears blurry, blotchy and plastic, while high-frequency noise power concentration results in a finer graininess(26,33). NPS was calculated in a square ROI of 300 × 300 pixels (Figure 2) by using the method described by Ghetti et al.(34,35). Figure 2 Open in new tabDownload slide Image of the homogeneous region of the phantom used for NPS evaluation. Figure 2 Open in new tabDownload slide Image of the homogeneous region of the phantom used for NPS evaluation. ROIs were drawn, in the center of the phantom, on 10 consecutive images of the homogeneous region of the phantom where the low contrast insert was not present. NPS was then calculated on images reconstructed with FPB and iterative reconstructions (SAFIRE and ADMIRE) at 3 different strengths(2–3–4). NPS shapes, in particular the peak frequency, and integrals obtained on reconstructed images were finally compared to evaluate differences in noise texture. Results Determination of the internal noise α The results obtained with CHO on the reference data set, consisting in the FBP images from two scanners, by gradually varying α are reported in Figure 3. As expected, the MO performance degrades by adding the internal noise: AUC lowers up to 22 and 37% with Edge and Flash CTs, respectively when α rises from 1 to 10. Figure 3 Open in new tabDownload slide Dependency of MO performance from internal noise parameter α. Dashed lines indicate the human observer performance (the PCR). Figure 3 Open in new tabDownload slide Dependency of MO performance from internal noise parameter α. Dashed lines indicate the human observer performance (the PCR). Human observer performance obtained with 2-AFC task is also reported in Figure 3: the average PCR obtained by the three observers on training data acquired with Edge and Flash CTs was 0.87 ± 0.01 and 0.73 ± 0.01, respectively. The comparison with the average result obtained from 2-AFC tests performed by human observers defines α for which MO get closer to the human ones. It results that the best agreement between MO and human observer over the chosen training data acquired with Edge and Flash was reached for α = 5.8 ± 0.1 and α = 5.7 ± 0.2, respectively. The round value equal to α = 6 will then be used in the following to evaluate the performance on the images reconstructed with different IR algorithms. CHO evaluation Once set, the degree of internal noise at α = 6 to reproduce the performance of human observer, CHO was used to evaluate low-contrast insert detectability on images reconstructed with SAFIRE and ADMIRE. The effect of different strengths applied to IR algorithms was also evaluated. The improvement of AUC on Edge CT was 19.4% with FBP, 21.6% with IR strength 2, 21.3% with IR strength 3 and 21.1% with IR strength 4 (Figure 4). Figure 4 Open in new tabDownload slide Dependency of absolute AUC obtained from analysis of images reconstructed with FBP and IR (at different strengths) with CHO set at α = 6. Figure 4 Open in new tabDownload slide Dependency of absolute AUC obtained from analysis of images reconstructed with FBP and IR (at different strengths) with CHO set at α = 6. Moreover, the IR algorithms improve slightly the detectability of the signal in the similar manner for both scanners as seen from the parallel curve on the same graphic (Figure 4). Increasing the strength of IR algorithms, an improvement, not more than 8%, was obtained with respect to the images reconstructed with FBP in both the systems. NPS evaluation The obtained NPS allows to thoroughly characterize the effects of detectors and reconstruction algorithms on the structure of noise and total noise. Looking at the values of NPS areas, in terms of 1-D NPS integral, which is representative of standard deviation of CT numbers, the noise reduction obtained with Edge CT respect to Flash CT was −58% with FBP reconstruction. This reduction is fairly the same even if we compare NPS area calculated on IR algorithms, indicated as S2, S3, S4 for SAFIRE and A2, A3, A4 for ADMIRE, with the same strength (Table 1). Table 1 NPS integral and peak frequency obtained with different CT systems and reconstruction algorithms. Reconstruction algorithm . NPS area (HU) . % of reduction . NPS peak frequency (mm−1) . Flash . Edge . Edge vs Flash . Flash . Edge . FBP 48.9 20.6 58 0.18 0.14 Strength 2 IR 40.1 17.2 57 0.16 0.11 Strength 3 IR 35.8 15.6 56 0.14 0.11 Strength 4 IR 31.7 13.8 56 0.10 0.08 Reconstruction algorithm . NPS area (HU) . % of reduction . NPS peak frequency (mm−1) . Flash . Edge . Edge vs Flash . Flash . Edge . FBP 48.9 20.6 58 0.18 0.14 Strength 2 IR 40.1 17.2 57 0.16 0.11 Strength 3 IR 35.8 15.6 56 0.14 0.11 Strength 4 IR 31.7 13.8 56 0.10 0.08 Open in new tab Table 1 NPS integral and peak frequency obtained with different CT systems and reconstruction algorithms. Reconstruction algorithm . NPS area (HU) . % of reduction . NPS peak frequency (mm−1) . Flash . Edge . Edge vs Flash . Flash . Edge . FBP 48.9 20.6 58 0.18 0.14 Strength 2 IR 40.1 17.2 57 0.16 0.11 Strength 3 IR 35.8 15.6 56 0.14 0.11 Strength 4 IR 31.7 13.8 56 0.10 0.08 Reconstruction algorithm . NPS area (HU) . % of reduction . NPS peak frequency (mm−1) . Flash . Edge . Edge vs Flash . Flash . Edge . FBP 48.9 20.6 58 0.18 0.14 Strength 2 IR 40.1 17.2 57 0.16 0.11 Strength 3 IR 35.8 15.6 56 0.14 0.11 Strength 4 IR 31.7 13.8 56 0.10 0.08 Open in new tab It is also evident that the use of iterative reconstruction decreases noise with the increase of the strength applied in a similar manner with SAFIRE and ADMIRE even if the baseline point defined with FBP reconstruction for Edge is reduced by more than half (Figure 5). Figure 5 Open in new tabDownload slide Noise power spectra obtained on the uniform region of the phantom reconstructed through FBP and SAFIRE/ADMIRE iterative algorithms at different strengths. Figure 5 Open in new tabDownload slide Noise power spectra obtained on the uniform region of the phantom reconstructed through FBP and SAFIRE/ADMIRE iterative algorithms at different strengths. The change of noise texture with IR strength is more pronounced on CT Flash (Figure 6) with SAFIRE algorithm: the NPS peak frequency shift was 0.06 mm−1 with increasing the strength from 2 to 4 (Table 1). Figure 6 Open in new tabDownload slide The NPS normalized to maximum value obtained for Flash CT. Figure 6 Open in new tabDownload slide The NPS normalized to maximum value obtained for Flash CT. With ADMIRE algorithm, this shift was only 0.03 mm−1 increasing the strength from 2 to 4 and noise texture was overall maintained (Figure 7). Figure 7 Open in new tabDownload slide The NPS normalized to maximum value obtained for Edge CT. Figure 7 Open in new tabDownload slide The NPS normalized to maximum value obtained for Edge CT. The difference in NPS peak position with FBP reconstruction between Edge and Flash can be explained considering that the used kernel for Edge is slightly smoother than that the one used on Flash (Br32 vs B30s)(18,33,36). DISCUSSIONS In this study, the performances of two CT systems with different detector technologies and reconstruction algorithms were evaluated. Their performances were investigated in terms of low-contrast detectability and noise reduction and image texture assessment. The low-contrast detectability was evaluated by means of a CHO, after the addition of a tunable internal noise, which was chosen to make the CHO’s performances quite similar to the HO’s ones at least on a reference data set. It resulted that the internal noise to be added is substantially the same for the two scanners, indicating that it is reasonable to use a predetermined noise level for evaluating images acquired in different conditions, as well. The tuned CHO was then used to investigate the signal detectability with different iterative algorithms: SAFIRE and ADMIRE on Flash and Edge CT, respectively. Figure 4 shows that, independently from the used reconstruction kernels and algorithms, the EDGE CT performs quite better with respect to the FLASH. The observed difference can be ascribed to the Stellar detectors with respect to UFC detectors. Probably, the improved efficiency of the Stellar detector produces a better signal (less noisy) on input to the reconstruction tools, which in turn, produce better-quality images. The best performance in signal detectability was obtained with Edge CT applying ADMIRE IR with strength 4. In our study, the Stellar detector have reduced considerably NPS area improving the signal detectability of about 20% with respect to the UFC detector; this result are consistent with those reported by Christe et al.(22) in a phantom study and by Edner et al. in a clinical study(37). It means that if we maintain the image quality of Flash scanner on Edge scanner, it is possible to reduce the patient dose of about 20%. A further improvement of signal detectability (8%) was obtained by increasing the strength of IR algorithms in both systems as reported in literature(37). In conclusion, the higher efficiency of Stellar detector over the UFC detector and the better quality of IR images over the FBP ones was clearly highlighted by CHO. It is known that noise texture affects human detection performance; thus, images with equal noise magnitude but with different noise texture would not necessarily result in equal detection performance(27,33,38,39). The IR algorithms allows, at the same dose level, a reduction from 10 to 60% of noise within the image with respect to the FBP(26). However, it is also known that IR strength change the noise texture within the images(23). For this reason, the analysis of NPS allowed to investigate the effect of both algorithms on the noise texture. In addition to an high noise reduction due to the Stellar detector, NPSs have highlighted an important feature of two IR algorithms: the NPS peak shift towards lower spatial frequencies due to the increase of strength was less prominent with ADMIRE than with SAFIRE, yielding better preservation of noise texture limiting the plastic image aspect(23,38). The image evaluation metrics used in this study, i.e. low-contrast detectability and NPS, are two sides of the same coin: they influence each other because a different texture and a lower noise in images have a deep impact in the detection of a low-contrast object; in fact, several studies have demonstrated how the IR algorithms have improved the low-contrast visibility(40,41). The main limitation of this study was a very simple detection task, i.e. detecting a known symmetric object placed on a uniform background, which is very far from clinical condition. Furthermore, the study was conducted on the thorax protocol using only smooth reconstruction kernel. Larger differences could be observed when sharp reconstruction kernels were applied(18, 40). Moreover, the different kernels available on the two CTs (B30s vs Br32) represent a further index of variability: although the comparison of the results obtained with FBP and IR were in agreement with those reported in the literature(22,23,27,35,38,40), the comparison between the two detectors (UFC vs Stellar) and IRs (SAFIRE vs ADMIRE) is affected by the different kernels. CONCLUSIONS Stellar detector with integrated electronics developed to decrease electronic noise and ADMIRE IR implemented on Siemens Somatom Edge CT allow an overall improvement in noise control and in low-contrast detectability performance estimated with a CHO approach. Both IR algorithms, SAFIRE and ADMIRE, slightly improve the low-contrast detectability of the signal similarly. 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TI - CHARACTERIZATION OF TWO CT SYSTEMS USING A CHANNELIZED HOTELLING OBSERVER AND NPS METRIC
JF - Radiation Protection Dosimetry
DO - 10.1093/rpd/ncaa034
DA - 2020-07-13
UR - https://www.deepdyve.com/lp/oxford-university-press/characterization-of-two-ct-systems-using-a-channelized-hotelling-OmUpZVhyL3
SP - 224
EP - 233
VL - 189
IS - 2
DP - DeepDyve
ER -