Object shape dependency of in-plane resolution for iterative reconstruction of computed tomography

The present study aimed to investigate whether the in-plane resolution property of iterative reconstruction (IR) of computed tomography (CT) data is object shape-dependent by testing columnar shapes with diameters of 3, 7, and 10 cm (circular edge method) and a cubic shape with 5-cm side lengths (linear edge method). For each shape, objects were constructed of acrylic (contrast in Hounsfield units [ΔHU] = 120) as well as a soft tissue equivalent material (ΔHU = 50). For each shape, we measured the modulation transfer functions (MTFs) of IR and filtered back projection (FBP) using two multi-slice CT scanners at scan doses of 5 and 10 mGy. In addition, we evaluated a thin metal wire using the conventional method at 10 mGy. For FBP images, the MTF results of the tested objects and the wire method showed substantial agreement, thus demonstrating the validity of our analysis technique. For IR images, the MTF results of different shapes were nearly identical for each object contrast and dose combination, and we did not observe shape-dependent effects of the resolution properties of either tested IR. We conclude that both the circular edge method and linear edge method are equally useful for evaluating the resolution properties of IRs.     

Objective assessment of low-contrast computed tomography images with iterative reconstruction

ObjectiveThis study aims to assess low-contrast image quality using a low-contrast object specific contrast-to-noise ratio (CNR_LO) analysis for iterative reconstruction (IR) computed tomography (CT) images.MethodsA phantom composed of low-contrast rods placed in a uniform material was used in this study. Images were reconstructed using filtered back projection (FBP) and IR (Adaptive Iterative Dose Reduction 3D). Scans were performed at six dose levels: 1.0, 1.8, 3.1, 4.6, 7.1 and 13.3 mGy. Objective image quality was assessed by comparing CNR_LO with CNR using a human observer test.ResultsCompared with FBP, IR yielded increased CNR at the same dose levels. The results of CNR_LO and observer tests showed similarities or only marginal differences between FBP and IR at the same dose levels. The coefficient of determination for CNR_LO was significantly better (R² = 0.86) than that of CNR (R² = 0.47).ConclusionFor IR, CNR_LO could potentially serve as an objective index reflective of a human observer assessment. The results of CNR_LO test indicated that the IR algorithm was not superior to FBP in terms of low-contrast detectability at the same radiation doses.     

Image quality comparison of a nonlinear image-based noise reduction technique with a hybrid-type iterative reconstruction for pediatric computed tomography

PurposeTo compare computed tomography (CT) image properties between a vendor-independent image-based noise reduction technique, Image-space Noise Reduction (iNoir) and a hybrid-type iterative reconstruction technique, Adaptive Statistical Iterative Reconstruction (ASIR).MethodsA cylindrical water phantom, corresponding to pediatric body size, containing soft-tissue-equivalent rod and 12-mg iodine/ml rod was scanned at size-specific dose estimates of 8.4 and 16.7 mGy. For assessments of image quality and noise texture change, task-based system performance function (SPF) and peak frequency difference (PFD) were compared, respectively, among filtered back projection (FBP), IR image with 50%-blending rate (50%ASIR), 100%ASIR, 50%iNoir, and 100%iNoir. Human observer test for pediatric CT images was performed by radiologists.ResultsFor the soft-tissue contrast, SPF² of 100%iNoir was the highest. The average SPF² between 0.1 and 0.5 cycles/mm for 100%iNoir increased by approximately 70% compared with FBP, while ASIR indicted slight increases in the frequency region of >0.2 cycles/mm. For the iodine contrast, 100%iNoir indicated highest values at the spatial frequencies corresponding pediatric artery diameters. The PFDs of iNoir were negligible and lower than that of ASIR. The results of human observer test supported results of SPF² and PFD.ConclusionsCompared with ASIR, iNoir provided better image quality for pediatric abdominal CT without compromising noise texture change.     

Evaluation of a commercial Model Based Iterative reconstruction algorithm in computed tomography

IntroductionIterative reconstruction algorithms have been introduced in clinical practice to obtain dose reduction without compromising the diagnostic performance.PurposeTo investigate the commercial Model Based IMR algorithm by means of patient dose and image quality, with standard Fourier and alternative metrics.Materials and methodsA Catphan phantom, a commercial density phantom and a cylindrical water filled phantom were scanned both varying CTDI_vol and reconstruction thickness. Images were then reconstructed with Filtered Back Projection and both statistical (iDose) and Model Based (IMR) Iterative reconstruction algorithms.Spatial resolution was evaluated with Modulation Transfer Function and Target Transfer Function. Noise reduction was investigated with Standard Deviation. Furthermore, its behaviour was analysed with 3D and 2D Noise Power Spectrum. Blur and Low Contrast Detectability were investigated.Patient dose indexes were collected and analysed.ResultsAll results, related to image quality, have been compared to FBP standard reconstructions.Model Based IMR significantly improves Modulation Transfer Function with an increase between 12% and 64%. Target Transfer Function curves confirm this trend for high density objects, while Blur presents a sharpness reduction for low density details.Model Based IMR underlines a noise reduction between 44% and 66% and a variation in noise power spectrum behaviour. Low Contrast Detectability curves underline an averaged improvement of 35–45%; these results are compatible with an achievable reduction of 50% of CTDI_vol.A dose reduction between 25% and 35% is confirmed by median values of CTDI_vol.ConclusionIMR produces an improvement in image quality and dose reduction.     

Assessment of temporal resolution of multi-detector row computed tomography in helical acquisition mode using the impulse method

The purpose of this study was to propose a method for assessing the temporal resolution (TR) of multi-detector row computed tomography (CT) (MDCT) in the helical acquisition mode using temporal impulse signals generated by a metal ball passing through the acquisition plane. An 11-mm diameter metal ball was shot along the central axis at approximately 5 m/s during a helical acquisition, and the temporal sensitivity profile (TSP) was measured from the streak image intensities in the reconstructed helical CT images. To assess the validity, we compared the measured and theoretical TSPs for the 4-channel modes of two MDCT systems. A 64-channel MDCT system was used to compare TSPs and image quality of a motion phantom for the pitch factors P of 0.6, 0.8, 1.0 and 1.2 with a rotation time R of 0.5 s, and for two R/P combinations of 0.5/1.2 and 0.33/0.8. Moreover, the temporal transfer functions (TFs) were calculated from the obtained TSPs. The measured and theoretical TSPs showed perfect agreement. The TSP narrowed with an increase in the pitch factor. The image sharpness of the 0.33/0.8 combination was inferior to that of the 0.5/1.2 combination, despite their almost identical full width at tenth maximum values. The temporal TFs quantitatively confirmed these differences. The TSP results demonstrated that the TR in the helical acquisition mode significantly depended on the pitch factor as well as the rotation time, and the pitch factor and reconstruction algorithm affected the TSP shape.     

Iterative image reconstruction using modified non-local means filtering for limited-angle computed tomography

PurposeLimited-angle CT imaging is an effective technique to reduce radiation. However, existing image reconstruction methods can effectively reduce streak artifacts but fail to suppress those artifacts around edges due to incomplete projection data. Thus, a modified NLM (mNLM) based reconstruction method is proposed.MethodsSince the artifacts around edges mainly exist in local position, it is possible to restore the true pixels in artifacts using pixels located in artifacts-free regions. In each iteration, mNLM is performed on image reconstructed by ART followed by positivity constraint. To solve the problem caused by ART-mNLM that there is undesirable information that may appear in the image, ART-TV is then utilized in the following iterative process after ART-mNLM iterates for a number of iterations. The proposed algorithm is named as ART-mNLM/TV.ResultsSimulation experiments are performed to validate the feasibility of algorithm. When the scanning range is [0, 150°], our algorithm outperforms the ART-NLM and ART-TV with more than 40% and 29% improvement in terms of SNR and with more than 58% and 49% reduction in terms of MAE. Consistently, reconstructed images from real projection data also demonstrate the effectiveness of presented algorithm.ConclusionThis paper uses mNLM which benefits from redundancy of information across the whole image, to recover the true value of pixels in artifacts region by utilizing pixels from artifact-free regions, and artifacts around the edges can be mitigated effectively. Experiments show that the proposed ART-mNLM/TV is able to achieve better performances compared to traditional methods.     

Cone-beam breast computed tomography using ultra-fast image reconstruction with constrained,total-variation minimization for suppression of artifacts

Compressed sensing based iterative reconstruction algorithms for computed tomography such as adaptive steepest descent-projection on convex sets (ASD-POCS) are attractive due to their applicability in incomplete datasets such as sparse-view data and can reduce radiation dose to the patients while preserving image quality. Although IR algorithms reduce image noise compared to analytical Feldkamp-Davis-Kress (FDK) algorithm, they may generate artifacts, particularly along the periphery of the object. One popular solution is to use finer image-grid followed by down-sampling. This approach is computationally intensive but may be compensated by reducing the field of view. Our proposed solution is to replace the algebraic reconstruction technique within the original ASD-POCS by ordered subsets-simultaneous algebraic reconstruction technique (OS-SART) and with initialization using FDK image. We refer to this method as Fast, Iterative, TV-Regularized, Statistical reconstruction Technique (FIRST). In this study, we investigate FIRST for cone-beam dedicated breast CT with large image matrix. The signal-difference to noise ratio (SDNR), the difference of the mean value and the variance of adipose and fibroglandular tissues for both FDK and FIRST reconstructions were determined. With FDK serving as the reference, the root-mean-square error (RMSE), bias, and the full-width at half-maximum (FWHM) of microcalcifications in two orthogonal directions were also computed. Our results suggest that FIRST is competitive to the finer image-grid method with shorter reconstruction time. Images reconstructed using the FIRST do not exhibit artifacts and outperformed FDK in terms of image noise. This suggests the potential of this approach for radiation dose reduction in cone-beam breast CT.     

Optimization-based region-of-interest reconstruction for X-ray computed tomography based on total variation and data derivative

Region-of-interest (ROI) and interior reconstructions for computed tomography (CT) have drawn much attention and can be of practical value for potential applications in reducing radiation dose and hardware cost. The conventional wisdom is that the exact reconstruction of an interior ROI is very difficult to be obtained by only using data associated with lines through the ROI. In this study, we propose and investigate optimization-based methods for ROI and interior reconstructions based on total variation (TV) and data derivative. Objective functions are built by the image TV term plus the data finite difference term. Different data terms in the forms of L1-norm, L2-norm, and Kullback–Leibler divergence are incorporated and investigated in the optimizations. Efficient algorithms are developed using the proximal alternating direction method of multipliers (ADMM) for each program. All sub-problems of ADMM are solved by using closed-form solutions with high efficiency. The customized optimizations and algorithms based on the TV and derivative-based data terms can serve as a powerful tool for interior reconstructions. Simulations and real-data experiments indicate that the proposed methods can be of practical value for CT imaging applications.     

Real time evaluation of overranging in helical computed tomography

Overranging or overscanning increases the dose delivered to patients undergoing helical Computed Tomography examinations. In order to reduce it, nowadays most of the multidetector tomographs close the X-ray beam aperture at the scan extremes. This technical innovation, usually referred to as dynamic or adaptive collimation, also influences the overranging assessment methods. In particular, the film free approach proposed in previous studies is not suitable for these modern tomographs. The present study aims to introduce a new method of estimating overranging with real time dosimetry, even suitable for tomographs equipped with adaptive collimation. The approach proposed is very easy to implement and time saving because only a pencil chamber is required. It is also equivalent in precision and in accuracy to the film based one, considered an absolute benchmark.     

Application of computed tomography for the evaluation of obstetrically relevant pelvic parameters in German Holstein-Friesian cows

The aim of this study was to use computed tomography for the evaluation of the suitability of external pelvimetry to determine obstetrically relevant parameters. External pelvimetric measurements obtained in vivo using calipers and internal pelvimetric measurements obtained in vitro using computed tomography were taken in 30 German Holstein-Friesian cows (Bos taurus). All measurements were highly reproducible with intraclass correlation coefficients ≥98%. Hip width was the external variable with the highest correlation to internal variables, particularly pelvic inlet area and circumference, pelvic volume, medial horizontal diameter of the pelvic inlet, and the narrowest horizontal diameter of the midpelvis (r² > 0.60, P < 0.0001). The pelvic inlet area and circumference, the pelvic volume, and the diagonal diameter of the pelvis were sufficiently predicted with the aid of external pelvic measurements and age (r²≥ 0.80, P < 0.0001). The results of this study show that external pelvimetry yields reliable information about the size of the pelvis when the age of the cow is considered.     

High-resolution computed tomography for the comparative study of fossil and extant bone

Special methods have been developed to use computed tomography (CT) for 3-dimensional imaging of both fossil and extant bones. Most commercial CT scanners cannot display the internal structure of fossils because the very high density is beyond the upper limits of the normal CT number scale (Hounsfield scale) of the scanners. X-ray projections from CT scans of fossils were modified by scaling the data to provide an expanded CT number scale, allowing the internal structure of highly fossilized objects to be visualized. These images were compared with state-of-the-art, high-resolution CT images of extant bone. Special image reformatting software was used to provide qualitative and quantitative 3-dimensional imaging. The recent rapid advances in CT technology have made this imaging modality the procedure of choice in much of diagnostic radiology. Use of this tool in paleoanthropology has been limited in the past by restricted access to scanners. However, new developments in CT will make this technique available to many researchers in the near future.     

Opportunities for biomineralization research using multiscale computed X-ray tomography as exemplified by bone imaging

Biominerals typically have complex hierarchical structures traversing many length scales. This makes their structural characterization complicated, since it requires 3D techniques that can probe full specimens at down to nanometer-resolution, a combination that is difficult – if not impossible – to achieve simultaneously. One challenging example is bone, a mineralized tissue with a highly complex architecture that is replete with a network of cells. X-ray computed tomography techniques enable multiscale structural characterization through the combination of various equipment and emerge as promising tools for characterizing biominerals. Using bone as an example, we discuss how combining different X-ray imaging instruments allow characterizing bone structures from the nano- to the organ-scale. In particular, we compare and contrast human and rodent bone, emphasize the importance of the osteocyte lacuno-canalicular network in bone, and finally illustrate how combining synchrotron X-ray imaging with laboratory instrumentation for computed tomography is especially helpful for multiscale characterization of biominerals.     

A patient-specific approach for quantitative and automatic analysis of computed tomography images in lung disease: Application to COVID-19 patients

PurposeQuantitative metrics in lung computed tomography (CT) images have been widely used, often without a clear connection with physiology. This work proposes a patient-independent model for the estimation of well-aerated volume of lungs in CT images (WAVE).MethodsA Gaussian fit, with mean (Mu.f) and width (Sigma.f) values, was applied to the lower CT histogram data points of the lung to provide the estimation of the well-aerated lung volume (WAVE.f). Independence from CT reconstruction parameters and respiratory cycle was analysed using healthy lung CT images and 4DCT acquisitions. The Gaussian metrics and first order radiomic features calculated for a third cohort of COVID-19 patients were compared with those relative to healthy lungs. Each lung was further segmented in 24 subregions and a new biomarker derived from Gaussian fit parameter Mu.f was proposed to represent the local density changes.ResultsWAVE.f resulted independent from the respiratory motion in 80% of the cases. Differences of 1%, 2% and up to 14% resulted comparing a moderate iterative strength and FBP algorithm, 1 and 3 mm of slice thickness and different reconstruction kernel. Healthy subjects were significantly different from COVID-19 patients for all the metrics calculated. Graphical representation of the local biomarker provides spatial and quantitative information in a single 2D picture.ConclusionsUnlike other metrics based on fixed histogram thresholds, this model is able to consider the inter- and intra-subject variability. In addition, it defines a local biomarker to quantify the severity of the disease, independently of the observer.     

Split-bolus computed tomography urography (CTU) achieves more than half of radiation dose reduction in females and overweight patients than conventional single-bolus computed tomography urography

ObjectiveTo compare radiation dose between single-bolus and split-bolus computed tomography urography (CTU).Materials and methodsWe prospectively enrolled patients undergoing single-bolus and split-bolus CTU from 2019 June to 2020 June. The age, sex and body mass index (BMI) of each patient was recorded and categorized into BMI classes. The radiation dose indices including volumetric computed dose index, size-specific dose estimate, dose length product and effective dose of each patient were compared between 2 CTU groups with calculation of dose reduction proportions (DRPs).ResultsSeventy-six patients underwent single-bolus (n = 39) and split-bolus (n = 37) CTU. Single-bolus CTU had higher radiation doses than split-bolus CTU and there were statistically significant differences of all radiation dose indices between two CTU groups without and with stratification by sex and BMI classes. The DRPs of volumetric computed dose index, size-specific dose estimate, dose length product and effective dose using split-bolus CTU were 49%, 49%. 50%, and 45%, respectively. Multiple linear regression with an effect size (f²) as 2.24 showed females (p = 0.027) and higher BMI classes (p = 2.38 *10⁻⁹) were associated with higher effective doses; and split-bolus CTU, lower effective doses (p = 5.40 *10⁻¹⁵). Using split-bolus CTU, females had consistently higher DRP of all radiation dose indices than males (54–55% versus 40–42%). Overweight patients had the largest DRP as 55% of effective dose.ConclusionsSplit-bolus CTU could be preferred by its significant radiation dose reduction effect in regard to single-bolus CTU, which was most profound in females and overweight patients.     

In-vivo range of motion of the subtalar joint using computed tomography

Understanding in vivo subtalar joint kinematics is important for evaluation of subtalar joint instability, the design of a subtalar prosthesis and for analysing surgical procedures of the ankle and hindfoot. No accurate data are available on the normal range of subtalar joint motion. The purpose of this study was to introduce a method that enables the quantification of the extremes of the range of motion of the subtalar joint in a loaded state using multidetector computed tomography (CT) imaging. In 20 subjects, an external load was applied to a footplate and forced the otherwise unconstrained foot in eight extreme positions. These extreme positions were foot dorsiflexion, plantarflexion, eversion, inversion and four extreme positions in between the before mentioned positions. CT images were acquired in a neutral foot position and each extreme position separately. After bone segmentation and contour matching of the CT data sets, the helical axes were determined for the motion of the calcaneus relative to the talus between four pairs of opposite extreme foot positions. The helical axis was represented in a coordinate system based on the geometric principal axes of the subjects’ talus. The greatest relative motion between the calcaneus and the talus was calculated for foot motion from extreme eversion to extreme inversion (mean rotation about the helical axis of 37.3±5.9°, mean translation of 2.3±1.1 mm). A consistent pattern of range of subtalar joint motion was found for motion of the foot with a considerable eversion and inversion component.     

Deep learning for predicting subtype classification and survival of lung adenocarcinoma on computed tomography

ObjectivesThe subtype classification of lung adenocarcinoma is important for treatment decision. This study aimed to investigate the deep learning and radiomics networks for predicting histologic subtype classification and survival of lung adenocarcinoma diagnosed through computed tomography (CT) images.MethodsA dataset of 1222 patients with lung adenocarcinoma were retrospectively enrolled from three medical institutions. The anonymised preoperative CT images and pathological labels of atypical adenomatous hyperplasia, adenocarcinoma in situ, minimally invasive adenocarcinoma, invasive adenocarcinoma (IAC) with five predominant components were obtained. These pathological labels were divided into 2-category classification (IAC; non-IAC), 3-category and 8-category. We modeled the classification task of histological subtypes based on modified ResNet-34 deep learning network, radiomics strategies and deep radiomics combined algorithm. Then we established the prognostic models in lung adenocarcinoma patients with survival outcomes. The accuracy (ACC), area under ROC curves (AUCs) and C-index were primarily performed to evaluate the algorithms.ResultsThis study included a training set (n = 802) and two validation cohorts (internal, n = 196; external, n = 224). The ACC of deep radiomics algorithm in internal validation achieved 0.8776, 0.8061 in the 2-category, 3-category classification, respectively. Even in 8 classifications, the AUC ranged from 0.739 to 0.940 in internal set. Further, we constructed a prognosis model that C-index was 0.892(95% CI: 0.846–0.937) in internal validation set.ConclusionsThe automated deep radiomics based triage system has achieved the great performance in the subtype classification and survival predictability in patients with CT-detected lung adenocarcinoma nodules, providing the clinical guide for treatment strategies.     

Task-based characterization of a deep learning image reconstruction and comparison with filtered back-projection and a partial model-based iterative reconstruction in abdominal CT: A phantom study

PurposeWe aimed to thoroughly characterize image quality of a novel deep learning image reconstruction (DLIR), and investigate its potential for dose reduction in abdominal CT in comparison with filtered back-projection (FBP) and a partial model-based iterative reconstruction (ASiR-V).MethodsWe scanned a phantom at three dose levels: regular (7 mGy), low (3 mGy) and ultra-low (1 mGy). Images were reconstructed using DLIR (low, medium and high levels) and ASiR-V (0% = FBP, 50% and 100%). Noise and contrast-dependent spatial resolution were characterized by computing noise power spectra and target transfer functions, respectively. Detectability indexes of simulated acute appendicitis or colonic diverticulitis (low contrast), and calcium-containing urinary stones (high contrast) (|ΔHU| = 50 and 500, respectively) were calculated using the nonprewhitening with eye filter model observer.ResultsAt all dose levels, increasing DLIR and ASiR-V levels both markedly decreased noise magnitude compared with FBP, with DLIR low and medium maintaining noise texture overall. For both low- and high-contrast spatial resolution, DLIR not only maintained, but even slightly enhanced spatial resolution in comparison with FBP across all dose levels. Conversely, increasing ASiR-V impaired low-contrast spatial resolution compared with FBP. Overall, DLIR outperformed ASiR-V in all simulated clinical scenarios. For both low- and high-contrast diagnostic tasks, increasing DLIR substantially enhanced detectability at any dose and contrast levels for any simulated lesion size.ConclusionsUnlike ASiR-V, DLIR substantially reduces noise while maintaining noise texture and slightly enhancing spatial resolution overall. DLIR outperforms ASiR-V by enabling higher detectability of both low- and high-contrast simulated abdominal lesions across all investigated dose levels.     

The naso-frontal joint in snakes as revealed by high-resolution X-ray computed tomography of intact and complete skulls

The naso-frontal joint of snakes is described on the basis of high-resolution X-ray computed tomography scans of single individuals of spirit-preserved snake specimens. The suspension of the snout unit from the braincase at the naso-frontal joint shows some broad evolutionary trends among snakes with potential phylogenetic implications, such as sutured or fused medial frontal flanges formed by the medial frontal pillars and the frontal subolfactory processes (in alethinophidians), the restriction of the usually extended dorsoventral contact of the medial nasal flange with the medial frontal flanges to a dorsal or ventral contact (in macrostomatans), and the transfer of the main element of snout suspension from the nasal to the septomaxilla (in colubroids). Some phylogenetic implications of the morphological characters identified in this study are outlined and discussed.     

Method for determining the half-value layer in computed tomography scans using a real-time dosimeter: Application to dual-source dual-energy acquisition

PurposeWe have proposed a method for determining the half-value layers (HVL) in dual-source dual-energy computed tomography (DS-DECT) scans without the need for the X-ray tubes to be fixed.MethodsA custom-made lead-covered case and an ionizing chamber connected with a multi-function digitizer module (a real-time dosimeter) were used. The chamber was placed in the center of the case, and aluminum or copper filters were placed in front of the aperture. The HVL was measured using aperture widths of 1.0, 2.0, and 3.0 cm for tube potentials of 80, 120, and 150 kV in single-source single-energy CT (SS-SECT) scans and was calculated from the peak air kerma rate (peak method) and the integrated air kerma rate (integrating method); the obtained values were compared with those from a conventional non-rotating method performed using the same procedure. The HVL was then measured using an aperture width of 1.0 cm for tube potential combinations of 70/Sn150 kV and 100/Sn150 kV in DS-DECT scans using the peak method.ResultsIn the SS-SECT scans, the combination of a 1.0-cm aperture and the peak method was adequate due to the small differences in the HVL values obtained for the conventional non-rotating method. The method was also found to be applicable for the DS-DECT scans.ConclusionsOur proposed method can determine the HVL in SS-SE and DS-DECT scans to a good level of accuracy without the need for the X-ray tubes to be fixed. The combination of a 1.0-cm aperture and the peak method was adequate.     

Quantitative study on exact reconstruction sampling condition by verifying solution uniqueness in limited-view CT

In limited-view computed tomography reconstruction, iterative image reconstruction with sparsity-exploiting methods, such as total variation (TV) minimization, inspired by compressive sensing, potentially claims large reductions in sampling requirements. However, a quantitative notion of this claim is non-trivial because of the ill-defined reduction in sampling achieved by the sparsity-exploiting method. In this paper, exact reconstruction sampling condition for limited-view problem is studied by verifying the uniqueness of solution in TV minimization model. Uniqueness is tested by solving a convex optimization problem derived from the sufficient and necessary condition of solution uniqueness. Through this method, the sufficient sampling number of exact reconstruction is quantified for any fixed phantom and settled geometrical parameter in the limited-view problem. This paper provides a reference to quantify the sampling condition. Three phantoms are tested to study the sampling condition of limited view exact reconstruction in this paper. The experiment results show the quantified sampling number and indicate that an object would be accurately reconstructed as the scanning range becomes narrower by increasing sampling number. The increased samplings compensate for the deficiency of the projection angle. However, the lower bound of the scanning range corresponding to three different phantoms are presented, in which an exact reconstruction cannot be obtained once the projection angular is narrowed to this extent no matter how to increase sampling.