Computed Tomography Reconstruction Method Research Articles

An interactive method based on multi-objective optimization for limited-angle CT reconstruction

Objective. Limited-angle x-ray computed tomography (CT) is a typical ill-posed inverse problem, leading to artifacts in the reconstructed image due to the incomplete projection data. Most iteration CT reconstruction methods involve optimization for a single object. This paper explores a multi-objective optimization model and an interactive method based on multi-objective optimization to suppress the artifacts of limited-angle CT. Approach. The model includes two objective functions on the dual domain within the data consistency constraint. In the interactive method, the structural similarity index measure (SSIM) is regarded as the value function of the decision maker (DM) firstly. Secondly, the DM arranges the objective functions of the multi-objective optimization model to be optimized according to their absolute importance. Finally, the SSIM and the simulated annealing (SA) method help the DM choose the desirable reconstruction image by improving the SSIM value during the iteration process. Main results. Simulation and real data experiments demonstrate that the artifacts can be suppressed by the proposed method, and the results were superior to those reconstructed by the other three reconstruction methods in preserving the edge structure of the image. Significance. The proposed interactive method based on multi-objective optimization shows some potential advantages over classical single object optimization methods.

A dual-energy CT reconstruction method based on anchor network from dual quarter scans.

Compared with conventional single-energy computed tomography (CT), dual-energy CT (DECT) provides better material differentiation but most DECT imaging systems require dual full-angle projection data at different X-ray spectra. Relaxing the requirement of data acquisition is an attractive research to promote the applications of DECT in wide range areas and reduce the radiation dose as low as reasonably achievable. In this work, we design a novel DECT imaging scheme with dual quarter scans and propose an efficient method to reconstruct the desired DECT images from the dual limited-angle projection data. We first study the characteristics of limited-angle artifacts under dual quarter scans scheme, and find that the negative and positive artifacts of DECT images are complementarily distributed in image domain because the corresponding X-rays of high- and low-energy scans are symmetric. Inspired by this finding, a fusion CT image is generated by integrating the limited-angle DECT images of dual quarter scans. This strategy enhances the true image information and suppresses the limited-angle artifacts, thereby restoring the image edges and inner structures. Utilizing the capability of neural network in the modeling of nonlinear problem, a novel Anchor network with single-entry double-out architecture is designed in this work to yield the desired DECT images from the generated fusion CT image. Experimental results on the simulated and real data verify the effectiveness of the proposed method. This work enables DECT on imaging configurations with half-scan and largely reduces scanning angles and radiation doses.

A non-local total generalized variation regularization reconstruction method for sparse-view x-ray CT

Sparse-view x-ray computed tomography (CT) reconstruction, employing total generalized variation (TGV), effectively mitigates the stepwise artifacts associated with total variation (TV) regularization while preserving structural features within transitional regions of the reconstructed image. Despite TGV surpassing TV in reconstruction quality, it neglects the non-local self-similarity prior, recognized for its efficacy in restoring details during CT reconstruction. This study introduces a non-local TGV (NLTGV) to address the limitation of TGV regularization method. Specifically, we propose an NLTGV-regularized method for sparse-view CT reconstruction, utilizing non-local high-order derivative information to maintain image features and non-local self-similarity for detail recovery. Owing to the non-differentiability of the NLTGV regularized, we employ an alternating direction method of multipliers optimization method, facilitating an efficient solution by decomposing the reconstruction model into sub-problems. The proposed method undergoes evaluation using both simulated and real-world projection data. Simulation and experimental results demonstrate the efficacy of the proposed approach in enhancing the quality of reconstructed images compared to other competitive variational reconstruction methods. In conclusion, the simultaneous incorporation of sparsity priors of high-order TV and non-local similarity proves advantageous for structural detail recovery in sparse-view CT reconstruction.

A Bayesian approach for CT reconstruction with defect detection for subsea pipelines

Subsea pipelines can be inspected via 2D cross-sectional x-ray computed tomography (CT). Traditional reconstruction methods produce an image of the pipe’s interior that can be post-processed for detection of possible defects. In this paper we propose a novel Bayesian CT reconstruction method with built-in defect detection. We decompose the reconstruction into a sum of two images; one containing the overall pipe structure, and one containing defects, and infer the images simultaneously in a Gibbs scheme. Our method requires that prior information about the two images is very distinct, i.e. the first image should contain the large-scale and layered pipe structure, and the second image should contain small, coherent defects. We demonstrate our methodology with numerical experiments using synthetic and real CT data from scans of subsea pipes in cases with full and limited data. Experiments demonstrate the effectiveness of the proposed method in various data settings, with reconstruction quality comparable to existing techniques, while also providing defect detection with uncertainty quantification.

Two-and-a-half order score-based model for solving 3D ill-posed inverse problems

Computed Tomography (CT) and Magnetic Resonance Imaging (MRI) are crucial technologies in the field of medical imaging. Score-based models demonstrated effectiveness in addressing different inverse problems encountered in the field of CT and MRI, such as sparse-view CT and fast MRI reconstruction. However, these models face challenges in achieving accurate three dimensional (3D) volumetric reconstruction. The existing score-based models predominantly concentrate on reconstructing two-dimensional (2D) data distributions, resulting in inconsistencies between adjacent slices in the reconstructed 3D volumetric images. To overcome this limitation, we propose a novel two-and-a-half order score-based model (TOSM). During the training phase, our TOSM learns data distributions in 2D space, simplifying the training process compared to working directly on 3D volumes. However, during the reconstruction phase, the TOSM utilizes complementary scores along three directions (sagittal, coronal, and transaxial) to achieve a more precise reconstruction. The development of TOSM is built on robust theoretical principles, ensuring its reliability and efficacy. Through extensive experimentation on large-scale sparse-view CT and fast MRI datasets, our method achieved state-of-the-art (SOTA) results in solving 3D ill-posed inverse problems, averaging a 1.56 dB peak signal-to-noise ratio (PSNR) improvement over existing sparse-view CT reconstruction methods across 29 views and 0.87 dB PSNR improvement over existing fast MRI reconstruction methods with × 2 acceleration. In summary, TOSM significantly addresses the issue of inconsistency in 3D ill-posed problems by modeling the distribution of 3D data rather than 2D distribution which has achieved remarkable results in both CT and MRI reconstruction tasks.

A Locally Weighted Linear Regression Look-Up Table-Based Iterative Reconstruction Method for Dual Spectral CT.

Compared with traditional computed tomography (CT), dual spectral CT (DSCT) exhibits superior material distinguishability and thus has broad prospects in industrial and medical fields. In iterative DSCT algorithms, accurately modeling forward-projection functions is crucial, but it is very difficult to analytically provide accurate functions. In this article, we propose a locally weighted linear regression look-up table-based (LWLR-LUT) iterative reconstruction method for DSCT. First, the proposed method uses LWLR to establish LUTs for the forward-projection functions through calibration phantoms, achieving good local information calibration. Second, the reconstructed images can be iteratively obtained through the established LUTs. The proposed method not only does not require knowledge of the X-ray spectra and the attenuation coefficients, but also implicitly accounts for some scattered radiation while fitting locally the forward-projection functions in the calibration space. Both numerical simulations and real data experiments demonstrate that the proposed method can achieve highly accurate polychromatic forward-projection functions and greatly improve the quality of the images reconstructed from scattering-free and scattering projections. The proposed method is simple and practical, and achieves good material decomposition effects for objects with different complex structures through simple calibration phantoms.

Deep residual unfolding: A novel sparse computed tomography reconstruction method leveraging iterative learning and neural networks

Addressing the challenge of compromised imaging quality in sparse Computed Tomography (CT) reconstructions—a significant issue due to the inherent sparsity of CT scan data—we present a novel method grounded in both iterative unfolding and deep learning techniques. This sparse CT reconstruction method involves constructing and minimizing an energy model, which comprises both a data fidelity term and a regularization term. Unlike traditional methods that rely on sparse variation operators like Total Variation (TV), our approach employs a deep learning model instantiated as a Residual Convolutional Neural Network. Enhanced with Group Normalization and the Swish activation function, this network iteratively unfolds the energy model to improve reconstruction quality. Our method's efficacy is validated through metrics such as Peak Signal Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Root Mean Square Error (RMSE) on a specific CT dataset. Overall, this work contributes to the advancement of sparse CT reconstructions, with significant potential implications for medical imaging applications.

Photon-counting spectral CT reconstruction with sparse and double low-rank components fusion

ObjectivePhoton-counting CT (computed tomography) has aroused more attention. The relatively high dose of X-ray increases concerns about radiation, dose reduction can mitigate radiation risk, however, projection data within energy channel suffers from strong noise, leading to degraded results. Besides, there is high correlation among channels since the multi-channel data is captured from the same object, which should be utilized to improve reconstruction quality. To suppress noise while preserving details in reconstruction and improve material decomposition accuracy, we proposed a novel optimization-based spectral CT reconstruction method with a fusion framework. MethodsTwo results were obtained by implementing two iterative reconstructions with different constraints and can be treated as complementary components. The first constraint is sparsity, the second constraint is double low-rank, moreover, a heuristic strategy is designed to solve double low-rank constrained optimization. We developed a guided filter based fusion framework to fuse sparse component and double low-rank component. ResultsExperimental results showed that our method achieved satisfying visualization, higher values of PSNR (peak signal-to-noise ratio) and SSIM (structure similarity), moreover, lower material decomposition error in this work.Conclusion.Our method can well perform spectral CT reconstruction under low-signal-to-ratio situation and it has decent performance in noise suppression, edge preserving and material discrimination.

A cascading l0 regularization reconstruction method in nonsubsampled contourlet domain for limited-angle CT

In some computed tomography (CT) practical applications, the projection data is incomplete, which makes some limited-angle artifacts presented in the reconstructed image. Total variation (TV) regularization method is used to suppress the artifacts, but the edge of reconstructed image is distorted or some tiny details are missed. To preserve the edge of reconstructed image, a cascading ℓ0 regularization-based reconstruction model in nonsubsampled contourlet transform (NSCT) domain is proposed, which considers both the directional peculiarity of artifacts and the smooth of low frequency of the reconstructed image. In the proposed reconstruction model, a ℓ0 regularization term in the high frequency is used to suppress the artifacts and noise, and a ℓ0 regularization of gradient image in low frequency is used to suppress the limited-angle artifacts, to preserve the edge of object and to smooth the reconstructed image. To solve the proposed model, a proximal alternating linearized Peaceman–Rachford splitting method (PAL-PRSM) is proposed, which uses the Peaceman–Rachford splitting method that updates the Lagrange multiplier twice, one after each minimization of the subproblem, to deal with the optimization problem firstly, and then the proximal linearization is used to avoid computing the inverse of a huge system matrix. In addition, to compensate the proximal linearization, we add an additional term into Lagrange multiplier updating. Real data experiments are investigated to demonstrate the effectiveness of PAL-PRSM method, and the results show that the proposed method outperforms two other CT reconstruction methods on preserving the edge of reconstructed image. On the whole, the proposed method is a compromise between denoising and preserving the edge of reconstructed image.

A total variation prior unrolling approach for computed tomography reconstruction.

With the rapid development of deep learning technology, deep neural networks can effectively enhance the performance of computed tomography (CT) reconstructions. One kind of commonly used method to construct CT reconstruction networks is to unroll the conventional iterative reconstruction (IR) methods to convolutional neural networks (CNNs). However, most unrolling methods primarily unroll the fidelity term of IR methods to CNNs, without unrolling the prior terms. The prior terms are always directly replaced by neural networks. In conventional IR methods, the prior terms play a vital role in improving the visual quality of reconstructed images. Unrolling the hand-crafted prior terms to CNNs may provide a more specialized unrolling approach to further improve the performance of CT reconstruction. In this work, a primal-dual network (PD-Net) was proposed by unrolling both the data fidelity term and the total variation (TV) prior term, which effectively preserves the image edges and textures in the reconstructed images. By further deriving the Chambolle-Pock (CP) algorithm instance for CT reconstruction, we discovered that the TV prior updates the reconstructed images with its divergences in each iteration of the solution process. Based on this discovery, CNNs were applied to yield the divergences of the feature maps for the reconstructed image generated in each iteration. Additionally, a loss function was applied to the predicted divergences of the reconstructed image to guarantee that the CNNs' results were the divergences of the corresponding feature maps in the iteration. In this manner, the proposed CNNs seem to play the same roles in the PD-Net as the TV prior in the IR methods. Thus, the TV prior in the CP algorithm instance can be directly unrolled to CNNs. The datasets from the Low-Dose CT Image and Projection Data and the Piglet dataset were employed to assess the effectiveness of our proposed PD-Net. Compared with conventional CT reconstruction methods, our proposed method effectively preserves the structural and textural information in reference to ground truth. The experimental results show that our proposed PD-Net framework is feasible for the implementation of CT reconstruction tasks. Owing to the promising results yielded by our proposed neural network, this study is intended to inspire further development of unrolling approaches by enabling the direct unrolling of hand-crafted prior terms to CNNs.

A Bayesian approach to CT reconstruction with uncertain geometry

ABSTRACT Computed tomography (CT) is a method for synthesizing volumetric or cross-sectional images of an object from a collection of projections. Popular reconstruction methods for CT are based on the assumption that the projection geometry, which describes the relative location and orientation of the radiation source, object, and detector for each projection, is exactly known. However, in practice, these geometric parameters are estimated quantities with uncertainty. A failure to accurately estimate the geometry may lead to reconstructions with severe misalignment artifacts that significantly decrease their scientific or diagnostic value. We propose a novel reconstruction method that jointly estimates the reconstruction and the center-of-rotation offset for fan-beam tomography. The reconstruction method is based on a Bayesian approach that yields a point estimate for the reconstruction and center-of-rotation offset and, in addition, provides valuable information regarding their uncertainty. This is achieved by approximately sampling from the joint posterior distribution of the reconstruction and center-of-rotation offset using a hierarchical Gibbs sampler. Our methodology is highly flexible and can be adapted to other geometric parameters and/or scan modes. Through numerical experiments based on real tomographic data, we compare the proposed Bayesian method to two existing approaches to the problem of correcting the geometry and demonstrate that our method achieves comparable or better results under challenging conditions.

Noise Characteristics Modeled Unsupervised Network for Robust CT Image Reconstruction.

Deep learning (DL)-based methods show great potential in computed tomography (CT) imaging field. The DL-based reconstruction methods are usually evaluated on the training and testing datasets which are obtained from the same distribution, i.e., the same CT scan protocol (i.e., the region setting, kVp, mAs, etc.). In this work, we focus on analyzing the robustness of the DL-based methods against protocol-specific distribution shifts (i.e., the training and testing datasets are from different region settings, different kVp settings, or different mAs settings, respectively). The results show that the DL-based reconstruction methods are sensitive to the protocol-specific perturbations which can be attributed to the noise distribution shift between the training and testing datasets. Based on these findings, we presented a low-dose CT reconstruction method using an unsupervised strategy with the consideration of noise distribution to address the issue of protocol-specific perturbations. Specifically, unpaired sinogram data is enrolled into the network training, which represents unique information for specific imaging protocol, and a Gaussian mixture model (GMM) is introduced to characterize the noise distribution in CT images. It can be termed as GMM based unsupervised CT reconstruction network (GMM-unNet) method. Moreover, an expectation-maximization algorithm is designed to optimize the presented GMM-unNet method. Extensive experiments are performed on three datasets from different scan protocols, which demonstrate that the presented GMM-unNet method outperforms the competing methods both qualitatively and quantitatively.

Image reconstruction method for limited-angle CT based on total variation minimization using guided image filtering.

Radiation is harmful to the human body, which is coupled with the fact that scanning conditions pose a number of restrictions. As a result, the projection data of a scanned object are generally acquired within a limited-angle range in practical computed tomography (CT) applications. Under this circumstance, classical image reconstruction methods cannot obtain high-quality images, and limited-angle artifacts appear in the reconstructed image. In recent years, the l1 norm of a gradient image-based total variation minimization (TVL1) image reconstruction method has often been used to deal with the image reconstruction problem from undersampling projection data, but limited-angle artifacts have been encountered near the edges for limited-angle CT. The l0 norm of a gradient image-based total variation minimization (TVL0) image reconstruction method can better preserve the edges, but it cannot obtain acceptable results when the scanning angle range is further reduced. Inspired by the advantages of guided image filtering (GIF), which can better smooth an image and preserve its structure, we used it to improve the reconstructed image quality for limited-angle CT by transferring reconstructed results of the TVL1 method to those of the TVL0 method. Simulation experiments show that the proposed method can better preserve structures and suppress limited-angle artifacts and noise than several related reconstruction methods.

Accuracy of the doses computed by the Eclipse treatment planning system near and inside metal elements

Metal artefacts degrade clinical image quality which decreases the confidence of using computed tomography (CT) for the delineation of key structures for treatment planning and leads to dose errors in affected areas. In this work, we investigated accuracy of doses computed by the Eclipse treatment planning system near and inside metallic elements for two different computation algorithms. An impact of CT metal artefact reduction methods on the resulting calculated doses has also been assessed. A water phantom including Gafchromic film and metal inserts was irradiated (max dose 5 Gy) using a 6 MV photon beam. Three materials were tested: titanium, alloy 600, and tungsten. The phantom CT images were obtained with the pseudo-monoenergetic reconstruction (PMR) and the iterative metal artefact reduction (iMAR). Image sets were used for dose calculation using an Eclipse treatment planning station (TPS). Monte Carlo (MC) simulations were used to predict the true dose distribution in the phantom allowing for comparison with doses measured by film and calculated by TPS. Measured and simulated percentage depth doses (PDDs) were not statistically different (p > 0.618). Regional differences were observed at edges of metallic objects (max 8% difference). However, PDDs simulated with and without film were statistically different (p < 0.002). PDDs calculated by the Acuros XB algorithm based on the dose-to-medium approach best matched the MC reference regardless of the CT reconstruction methods and inserts used (p > 0.078). PDDs obtained using other algorithms significantly differ from the MC values (p < 0.011). The Acuros XB algorithm with a dose-to-medium approach provides reliable dose calculation in all metal regions when using the Varian system. The inability of the AAA algorithm to model backscatter dose significantly limits its clinical application in the presence of metal. No significant impact on the dose calculation was found for a range of metal artefact reduction strategies.

A Limited-View CT Reconstruction Framework Based on Hybrid Domains and Spatial Correlation.

Limited-view Computed Tomography (CT) can be used to efficaciously reduce radiation dose in clinical diagnosis, it is also adopted when encountering inevitable mechanical and physical limitation in industrial inspection. Nevertheless, limited-view CT leads to severe artifacts in its imaging, which turns out to be a major issue in the low dose protocol. Thus, how to exploit the limited prior information to obtain high-quality CT images becomes a crucial issue. We notice that almost all existing methods solely focus on a single CT image while neglecting the solid fact that, the scanned objects are always highly spatially correlated. Consequently, there lies bountiful spatial information between these acquired consecutive CT images, which is still largely left to be exploited. In this paper, we propose a novel hybrid-domain structure composed of fully convolutional networks that groundbreakingly explores the three-dimensional neighborhood and works in a “coarse-to-fine” manner. We first conduct data completion in the Radon domain, and transform the obtained full-view Radon data into images through FBP. Subsequently, we employ the spatial correlation between continuous CT images to productively restore them and then refine the image texture to finally receive the ideal high-quality CT images, achieving PSNR of 40.209 and SSIM of 0.943. Besides, unlike other current limited-view CT reconstruction methods, we adopt FBP (and implement it on GPUs) instead of SART-TV to significantly accelerate the overall procedure and realize it in an end-to-end manner.

A content-adaptive unstructured grid based regularized CT reconstruction method with a SART-type preconditioned fixed-point proximity algorithm

The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.

Reconstruction of High-Resolution Computed Tomography Image in Sinogram Space

An important part of any computed tomography (CT) system is the reconstruction method, which transforms the measured data into images. Reconstruction methods for CT can be either analytical or iterative. The analytical methods can be exact, by exact projector inversion, or non-exact based on Back projection (BP). The BP methods are attractive because of thier simplicity and low computational cost. But they produce suboptimal images with respect to artifacts, resolution, and noise. This paper deals with improve of the image quality of BP by using super-resolution technique. Super-resolution can be beneficial in improving the image quality of many medical imaging systems without the need for significant hardware alternation. In this paper, we propose to reconstruct a high-resolution image from the measured signals in Sinogram space instead of reconstructing low-resolution images and then post-process these images to get higher resolution image.

Free trajectory cone beam computed tomography reconstruction method for synchronous scanning of geometric calibration phantom and imaging object

In order to suppress the geometrical artifacts caused by random jitter in ray source scanning, and to achieve flexible ray source scanning trajectory and meet the requirements of task-driven scanning imaging, a method of free trajectory cone-beam computed tomography (CBCT) reconstruction is proposed in this paper. This method proposed a geometric calibration method of two-dimensional plane. Based on this method, the geometric calibration phantom and the imaging object could be simultaneously imaged. Then, the geometric parameters could be obtained by online calibration method, and then combined with the geometric parameters, the alternating direction multiplier method (ADMM) was used for image iterative reconstruction. Experimental results showed that this method obtained high quality reconstruction image with high contrast and clear feature edge. The root mean square errors (RMSE) of the simulation results were rather small, and the structural similarity (SSIM) values were all above 0.99. The experimental results showed that it had lower image information entropy (IE) and higher contrast noise ratio (CNR). This method provides some practical value for CBCT to realize trajectory freedom and obtain high quality reconstructed image.

Physics-based iterative reconstruction for dual-source and flying focal spot computed tomography.

For single-source helical Computed Tomography (CT), both Filtered-Back Projection (FBP) and statistical iterative reconstruction have been investigated. However, for dual-source CT with flying focal spot (DS-FFS CT), a statistical iterative reconstruction that accurately models the scanner geometry and acquisition physics remains unknown to researchers. Therefore, our purpose is to present a novel physics-based iterative reconstruction method for DS-FFS CT and assess its image quality. Our algorithm uses precise physics models to reconstruct from the native cone-beam geometry and interleaved dual-source helical trajectory of a DS-FFS CT. To do so, we construct a noise physics model to represent data acquisition noise and a prior image model to represent image noise and texture. In addition, we design forward system models to compute the locations of deflected focal spots, the dimension, and sensitivity of voxels and detector units, as well as the length of intersection between x-rays and voxels. The forward system models further represent the coordinated movement between the dual sources by computing their x-ray coverage gaps and overlaps at an arbitrary helical pitch. With the above models, we reconstruct images by an advanced Consensus Equilibrium (CE) numerical method to compute the maximum a posteriori estimate to a joint optimization problem that simultaneously fits all models. We compared our reconstruction with Siemens ADMIRE, which is the clinical standard hybrid iterative reconstruction (IR) method for DS-FFS CT, in terms of spatial resolution, noise profile, and image artifacts through both phantoms and clinical scan datasets. Experiments show that our reconstruction has a higher spatial resolution, with a Task-Based Modulation Transfer Function (MTFtask ) consistently higher than the clinical standard hybrid IR. In addition, our reconstruction shows a reduced magnitude of image undersampling artifacts than the clinical standard. By modeling a precise geometry and avoiding data rebinning or interpolation, our physics-based reconstruction achieves a higher spatial resolution and fewer image artifacts with smaller magnitude than the clinical standard hybrid IR.

A fast image reconstruction method for planar objects CT inspired by differentiation property of Fourier transform (DPFT)

In planar objects computed tomography (CT), restricted to the scanning environment, projections can only be collected from limited angles. Moreover, limited by the emitting power of the x-ray source, only a few photons penetrate the long side of the planar objects, which results in the noise increasing in projections. Planar objects CT reconstruction based on these two conditions is mathematically corresponding to solving an ill-posed inverse problem. Although several iterative reconstruction algorithms of limited-angle CT were proposed, high-quality planar objects CT reconstruction algorithms with fast convergence are still the goals of many researchers. In order to address the aforementioned problems, we proposed a new optimization model for planar objects CT reconstruction. Inspired by the theory of ‘visible boundary and invisible boundary’ in limited-angle CT and the differentiation property of Fourier transform, a new optimization objective function is proposed in this paper. Based on the statistical noise model of existing CT system, the convex set constraint of the optimization model is given. Besides, the optimization model is solved by convex set projection and Fourier transform differentiation property. The proposed algorithm was evaluated with both simulated data and real data. The experimental results show that the proposed algorithm can achieve the effect of noise suppression, limited-angle artifacts reduction, and fast structure reconstruction when it applies to planar objects CT.