Regularization For Reconstruction Research Articles

Robust anomaly detection via adversarial counterfactual generation

AbstractThe capability to devise robust outlier and anomaly detection tools is an important research topic in machine learning and data mining. Recent techniques have been focusing on reinforcing detection with sophisticated data generation tools that successfully refine the learning process by generating variants of the data that expand the recognition capabilities of the outlier detector. In this paper, we propose $$\textrm{ARN}$$ ARN , a semi-supervised anomaly detection and generation method based on adversarial counterfactual reconstruction. $$\textrm{ARN}$$ ARN exploits a regularized autoencoder to optimize the reconstruction of variants of normal examples with minimal differences that are recognized as outliers. The combination of regularization and counterfactual reconstruction helps to stabilize the learning process, which results in both realistic outlier generation and substantially extended detection capability. In fact, the counterfactual generation enables a smart exploration of the search space by successfully relating small changes in all the actual samples from the true distribution to high anomaly scores. Experiments on several benchmark datasets show that our model improves the current state of the art by valuable margins because of its ability to model the true boundaries of the data manifold.

The Application of Piecewise Regularization Reconstruction to the Calibration of Strain Beams.

Standard beams are mainly used for the calibration of strain sensors using their load reconstruction models. However, as an ill-posed inverse problem, the solution to these models often fails to converge, especially when dealing with dynamic loads of different frequencies. To overcome this problem, a piecewise Tikhonov regularization method (PTR) is proposed to reconstruct dynamic loads. The transfer function matrix is built both using the denoised excitations and the corresponding responses. After singular value decomposition (SVD), the singular values are divided into submatrices of different sizes by utilizing a piecewise function. The regularization parameters are solved by optimizing the piecewise submatrices. The experimental result shows that the MREs of the PTR method are 6.20% at 70 Hz and 5.86% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits MREs of 28.44% and 29.61% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates MREs of 29.98% and 18.42% at the same frequencies. Furthermore, the PREs of the PTR method are 3.54% at 70 Hz and 3.73% at 80 Hz. The traditional Tikhonov regularization method based on GCV exhibits PREs of 27.01% and 26.88% at frequencies of 70 Hz and 80 Hz, respectively, whereas the L-curve-based approach demonstrates PREs of 29.50% and 15.56% at the same frequencies. All in all, the method proposed in this paper can be extensively applied to load reconstruction across different frequencies.

Accelerated free-breathing liver fat and quantification using multi-echo stack-of-radial MRI with motion-resolved multidimensional regularized reconstruction: Initial retrospective evaluation.

To improve image quality, mitigate quantification biases and variations for free-breathing liver proton density fat fraction (PDFF) and quantification accelerated by radial k-space undersampling. A free-breathing multi-echo stack-of-radial MRI method was developed with compressed sensing with multidimensional regularization. It was validated in motion phantoms with reference acquisitions without motion and in 11 subjects (6 patients with nonalcoholic fatty liver disease) with reference breath-hold Cartesian acquisitions. Images, PDFF, and maps were reconstructed using different radial view k-space sampling factors and reconstruction settings. Results were compared with reference-standard results using Bland-Altman analysis. Using linear mixed-effects model fitting (p < 0.05 considered significant), mean and SD were evaluated for biases and variations of PDFF and , respectively, and coefficient of variation on the first echo image was evaluated as a surrogate for image quality. Using the empirically determined optimal sampling factor of 0.25 in the accelerated in vivo protocols, mean differences and limits of agreement for the proposed method were [-0.5; -33.6, 32.7] s-1 for and [-1.0%; -5.8%, 3.8%] for PDFF, close to those of a previous self-gating method using fully sampled radial views: [-0.1; -27.1, 27.0] s-1 for and [-0.4%; -4.5%, 3.7%] for PDFF. The proposed method had significantly lower coefficient of variation than other methods (p < 0.001). Effective acquisition time of 64 s or 59 s was achieved, compared with 171 s or 153 s for two baseline protocols with different radial views corresponding to sampling factor of 1.0. This proposed method may allow accelerated free-breathing liver PDFF and mapping with reduced biases and variations.

Secure Low-complexity Compressive Sensing with Preconditioning Prior Regularization Reconstruction

Compressive sensing (CS), a breakthrough technology in image processing, provides a privacy-preserving layer and image reconstruction while performing sensing and recovery processes, respectively. Unfortunately, it still faces high-complexity, low-security, and low-quality reconstruction challenges during image processing. Therefore, this article presents a secure low-complexity CS scheme with preconditioning prior regularization reconstruction. More specifically, the original image is compressed by a low-complexity LFSR-based sparse circulant matrix to obtain measurements. It is worth noting that measurements achieve preliminary distribution equalization through the Tanh sequence to acquire processed measurements. Furthermore, the privacy-preserving edge processing for processed measurements can achieve high security. Finally, preconditioning prior regularization CS reconstruction is designed to improve reconstruction performance. Simulation results and analyses demonstrate that the proposed scheme can achieve low-complexity sampling, high security, and superior reconstruction performance.

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.

Nonlinear Dynamic Analysis of Seafloor Pressure Time Series with and without Internal Waves

Ocean internal wave as a nonlinear process oscillates within ocean interior rather than the surface. Internal waves have significant influences on the transport of material, energy and even global climate. The generation, transmission and attenuation of internal wave play a significant role in the ocean dynamics owing to the exchange of the energy within each process. In this paper, reduced complexity of seafloor pressure time series induced by internal wave in the southern Taiwan bank has been investigated using nonlinear dynamic analysis. Cao method has been used to distinguish between the pressure signal with internal wave and the random signal without internal wave. The reconstructed phase spaces and correlation dimensions of the time series with and without internal wave are compared. Internal wave leads the seafloor pressure time series to produce a more regular phase space reconstruction and more low dimensional dynamics. Our study suggests that nonlinear dynamic analysis could be a valuable and promising method in real-time ocean internal wave detection.

K-UNN: k-space interpolation with untrained neural network.

Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approaches lack the modeling of physical priors, resulting in poor performance in some common scenarios (e.g., partial Fourier (PF), regular sampling, etc.) and the lack of theoretical guarantees for reconstruction accuracy. To bridge this gap, we propose a safeguarded k-space interpolation method for MRI using a specially designed UNN with a tripled architecture driven by three physical priors of the MR images (or k-space data), including transform sparsity, coil sensitivity smoothness, and phase smoothness. We also prove that the proposed method guarantees tight bounds for interpolated k-space data accuracy. Finally, ablation experiments show that the proposed method can characterize the physical priors of MR images well. Additionally, experiments show that the proposed method consistently outperforms traditional parallel imaging methods and existing UNNs, and is even competitive against supervised-trained deep learning methods in PF and regular undersampling reconstruction.

Simultaneous off-the-grid regularization and reconstruction for 3D seismic data by a new combined sampling operator

Seismic samples are generally designed to be placed on perfect Cartesian coordinates, that is, on-the-grid. However, sampling geometry is disturbed by obstacles in field applications. Large obstacles result in missing samples. For small obstacles, geophones or sources are placed at an available off-the-grid location nearest to the designed grid. To achieve simultaneous off-the-grid regularization and missing data reconstruction for 3D seismic data, we develop a new mathematical model based on a new combined sampling operator, a 3D curvelet transform, and a fast projection onto convex sets (FPOCS) algorithm. The sampling operator is combined with a binary mask for on-the-grid samples reconstruction and a barycentric Lagrangian (BL) operator for off-the-grid samples regularization. A 2D BL operator is obtained using the tensor product of two 1D BL operators. The inversion problem is efficiently solved based on FPOCS. This method is tested on synthetic and field data sets. The reconstruction results outperform the methods based on the binary mask in terms of signal-to-noise ratio and visual effect.

Motion-compensated low-rank reconstruction for simultaneous structural and functional UTE lung MRI.

Three-dimensional UTE MRI has shown the ability to provide simultaneous structural and functional lung imaging, but it is limited by respiratory motion and relatively low lung parenchyma SNR. The purpose of this paper is to improve this imaging by using a respiratory phase-resolved reconstruction approach, named motion-compensated low-rank reconstruction (MoCoLoR), which directly incorporates motion compensation into a low-rank constrained reconstruction model for highly efficient use of the acquired data. The MoCoLoR reconstruction is formulated as an optimization problem that includes a low-rank constraint using estimated motion fields to reduce the rank, optimizing over both the motion fields and reconstructed images. The proposed reconstruction along with XD and motion state-weighted motion-compensation (MostMoCo) methods were applied to 18 lung MRI scans of pediatric and young adult patients. The data sets were acquired under free-breathing and without sedation with 3D radial UTE sequences in approximately 5 min. After reconstruction, they went through ventilation analyses. Performance across reconstruction regularization and motion-state parameters were also investigated. The in vivo experiments results showed that MoCoLoR made efficient use of the data, provided higher apparent SNR compared with state-of-the-art XD reconstruction and MostMoCo reconstructions, and yielded high-quality respiratory phase-resolved images for ventilation mapping. The method was effective across the range of patients scanned. The motion-compensated low-rank regularized reconstruction approach makes efficient use of acquired data and can improve simultaneous structural and functional lung imaging with 3D-UTE MRI. It enables the scanning of pediatric patients under free-breathing and without sedation.

Quality of latrines and willingness to improve them in rural Ethiopia

Abstract Ethiopia recorded the world's fastest increase in latrine coverage over the past two decades, but it was largely achieved by the adoption of latrines that do not meet basic hygienic standards. Therefore, this study aims to examine the quality of latrines and their upgrading at household level through a case study from the Loka Abaya district, South Ethiopia. Of the initially sampled 549 households, 422 (77%) had private latrines, and a survey was administered among them. The data were characterized descriptively, and correlates of the latrine quality and willingness to improve were analysed. The average latrine quality score in the sample was only 2.8 of the maximum six quality dimensions. Despite the low quality of latrines, 63% of respondents were satisfied with their sanitation situation. Both past improvements and plans to improve latrines were frequently reported. However, these reported changes mostly involved regular maintenance or reconstructions of collapsed latrines. No substantial upgrading of the functionality was identified. We identified inadequate awareness about the means of hygienic sanitation, implying the importance of community education. Demand for as well as supply of hygienic sanitation products are further constrained by the low purchasing power of households implying a need for sanitation subsidies.

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.

Data adaptive regularization with reference tissue constraints for liver quantitative susceptibility mapping.

To improve repeatability and reproducibility across acquisition parameters and reduce bias in quantitative susceptibility mapping (QSM) of the liver, through development of an optimized regularized reconstruction algorithm for abdominal QSM. An optimized approach to estimation of magnetic susceptibility distribution is formulated as a constrained reconstruction problem that incorporates estimates of the input data reliability and anatomical priors available from chemical shift-encoded imaging. The proposed data-adaptive method was evaluated with respect to bias, repeatability, and reproducibility in a patient population with a wide range of liver iron concentration (LIC). The proposed method was compared to the previously proposed and validated approach in liver QSM for two multi-echo spoiled gradient-recalled echo protocols with different acquisition parameters at 3T. Linear regression was used for evaluation of QSM methods against a reference FDA-approved -based LIC measure and measurements; repeatability/reproducibility were assessed by Bland-Altman analysis. The data-adaptive method produced susceptibility maps with higher subjective quality due to reduced shading artifacts. For both acquisition protocols, higher linear correlation with both - and -based measurements were observed for the data-adaptive method ( for , for ) than the standard method ( and ). For both protocols, the data-adaptive method enabled better test-retest repeatability (repeatability coefficients 0.19/0.30 ppm for the data-adaptive method, 0.38/0.47 ppm for the standard method) and reproducibility across protocols (reproducibility coefficient 0.28 vs. 0.53ppm) than the standard method. The proposed data-adaptive QSM algorithm may enable quantification of LIC with improved repeatability/reproducibility across different acquisition parameters as 3T.

Semiconductor superlattice physical unclonable function based two-dimensional compressive sensing cryptosystem and its application to image encryption

Most image encryption methods are symmetric cryptosystems, in which the encryptor and decryptor are required to share the same key. To reduce the risk of key generation and key distribution for image cipher scheme, in this paper, we present a novel scheme based on semiconductor superlattice physical unclonable function (SSL-PUF) and two-dimensional compressive sensing (2DCS). Distinguished from other existing CS-based cryptosystems, SSL-PUF with quantum tunneling induced chaos is utilized, in which the key distribution for the public channel can be achieved by a pair of matched SSL-PUF. First, the seed key generated from SSL-PUF is extended with the pseudo-random coupled map lattices (PRCML) module. Next, gradient-type alternating minimization approach is employed to solve the low coherence measurement matrix. Finally, compressing and encrypting can be implemented simultaneously by measuring the plain image bi-directionally. Moreover, the total variation (TV) regularization reconstruction method is optimized based on the Adam algorithm. With low compression ratios and computationally constrained environments, the proposed optimization method can reconstruct images with high quality. Numerous experiments were simulated and analyzed to validate that the proposed 2DCS-based cryptosystems possess well performance, such as image reconstruction effect, security against various attacks, and good robustness.

Optimized Reconstruction Procedure of Photoacoustic Imaging for Reflection Artifacts Reduction.

Photoacoustic (PA) imaging technology is of some value in medical diagnoses such as breast cancer detection, vasculature imaging, and surgery navigating. While as most imaging objects are bounded, the received RF signals consist of the direct-arrived signals (DAS) from the PA sources and the boundary-reflected signals (BRS). The undesired BRS will severely impair the quality during the image reconstruction. They will bring in many artifacts and confuse the actual shape and location of the PA sources. We improved the reconstruction procedure by removing the BRS before the regular reconstruction process to suppress those artifacts. To verify our proposed method, we compared the results of the conventional and optimized procedures experimentally. In terms of qualitative observation, the reconstructed images by the optimized procedure illustrate fewer artifacts and more accurate shapes of the PA sources. To quantitatively evaluate the traditional and the optimized imaging procedure, we calculated the Distribution Relative Error (DRE) between each experiment result and its standard drawing of the phantoms. For both phantoms and the ex-vivo sample, the DREs of reconstruction result by the optimized reconstruction procedure decrease significantly. The results suggest that the optimized reconstruction process can effectively suppress the reflection artifacts and improve the shape accuracy of the PA sources.

ComplexGen

We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. , vertices, edges and surface patches, and the correspondence of primitives, which are holistically modeled as a chain complex, and show that by modeling such comprehensive structures more complete and regularized reconstructions can be achieved. We solve the complex generation problem in two steps. First, we propose a novel neural framework that consists of a sparse CNN encoder for input point cloud processing and a tri-path transformer decoder for generating geometric primitives and their mutual relationships with estimated probabilities. Second, given the probabilistic structure predicted by the neural network, we recover a definite B-Rep chain complex by solving a global optimization maximizing the likelihood under structural validness constraints and applying geometric refinements. Extensive tests on large scale CAD datasets demonstrate that the modeling of B-Rep chain complex structure enables more accurate detection for learning and more constrained reconstruction for optimization, leading to structurally more faithful and complete CAD B-Rep models than previous results.

A Regularization-Guided Deep Imaging Method for Electrical Impedance Tomography

Electrical Impedance Tomography (EIT) is a promising technique for the process monitoring. However, due to the inherent nonlinearity and ill- posedness of the image reconstruction in EIT, it remains a great challenge for EIT application. A regularization-guided deep imaging (RGDI) method which combines the mathematical structure of the regularization reconstruction method with deep learning is proposed. As a &#x2018;gray-box&#x2019;, RGDI can not only solve the problem of parameter selection in regularization algorithms, but also depend less on the complete database. The structure of RGDI is composed of three sequentially connected modules, i.e. data pre-processing, feature extraction and image reconstruction. The feature extraction module contains five blocks, and each block consists of a regularization network and a convolutional neural network (CNN) with the function of an &#x2018;encoding-decoding&#x2019;. To obtain more accurate reconstruction images, a two-layer fully connected neural network (FCNN) is applied. During the training of RGDI network, prior information of structural features is added to avoid the overfitting problem and accelerate its convergence. The experimental results illustrate that the image quality of RGDI is better than that of numerical imaging methods and several reported deep learning methods.

Postural control during single leg stance in individuals with clinical indication for combined reconstruction of the anterior cruciate and the anterolateral ligaments of the knee: a cross-sectional study

BackgroundSeveral studies have shown persistent postural control deficits and rotatory instability in patients after isolated Anterior Cruciate Ligament (ACL) reconstruction. There is evidence to support that the Anterolateral Ligament (ALL) plays an important role in the remaining anterolateral rotatory laxity of the knee. There are no further evidences in order to understand how patients with a combined ACL + ALL reconstruction surgery indication behave regarding postural control. The aim of this cross-sectional study was to assess if patients with a clinical indication for the combined ACL + ALL surgery showed a deficient postural control in single leg stance compared to subjects with a regular ACL reconstruction indication and to a control group.MethodsAn assessment of static postural control on single leg stance was performed on a force plate, with eyes open and closed, and the center of pressure (COP) displacement variables were analyzed: maximum and mean amplitude in anteroposterior (AP) and in mediolateral (ML) direction; mean velocity of displacement and area of displacement. Eighty-nine male individuals participated and were divided into 3 groups: ACL Group, ACL + ALL Group and Control Group.ResultsThe ACL+ ALL Group showed significantly greater COP displacement in most variables in the injured leg for the eyes closed test, compared to the ACL Group, as detailed: Total ML displacement (9.8 ± 6.77 vs. 13.98 ± 6.64, p < 0.001); Mean ML displacement (2.58 ± 2.02 vs. 3.72 ± 1.99, p < 0.001); Total AP displacement (9.5 ± 3.97 vs. 11.7 ± 3.66, p = 0.001); Mean AP displacement (1.77 ± 0.87 vs. 2.27 ± 0.86, p = 0.001); Area of displacement (111.44 ± 127.3 vs. 183.69 ± 131.48, p < 0.001).ConclusionSubjects with a clinical indication for ACL + ALL combined reconstruction surgery showed increased COP displacement compared to patients with indication for an ACL isolated reconstruction surgery.

A fast Tikhonov regularization method based on homotopic mapping for electrical resistance tomography.

Electrical resistance tomography (ERT) is considered a novel sensing technique for monitoring conductivity distribution. Image reconstruction of ERT is an ill-posed inverse problem. In this paper, an improved regularization reconstruction method is presented to solve this issue. We adopted homotopic mapping to choose the regularization parameter of the iterative Tikhonov algorithm. The standard normal distribution function was used to continuously adjust the regularization parameter. Subsequently, the resultant image vector was deployed as the initial value of the iterative Tikhonov algorithm to improve the image quality. Finally, the improved method was combined with a projection algorithm based on the Krylov subspace, which was also effective in reducing the computational time. Both simulation and experimental results indicated that the new algorithm could improve the real-time performance and imaging quality.

Model of catalyst layers for proton exchange membrane fuel cells: Progress and perspective

<p indent="0mm">The proton exchange membrane fuel cell (PEMFC) is one of the most high-efficient energy conversion devices with zero carbon emission, which is of great significance to achieve the strategic goal of “carbon emission peak and carbon neutrality”. The catalyst directly determines the cell performance and is the core in the large-scale commercial application of PEMFCs. Due to the complex multi-physics and multi-scale process in catalyst layers, it is necessary to establish an accurate numerical model to reveal the internal mechanisms of transport and reactions. The present work reviews the progress of modeling catalyst layers, and the models can be divided into five types: Interface model, homogeneous model, agglomerate model, pore-scale model and particle model. The modeling ideas are introduced, and their typical applications are discussed. The interface model assumes that the catalyst layer is infinitely thin, so it is simple to set up and fast to calculate. It can be used to study the reaction process in fuel cells except the catalyst layer. However, due to the excessively simple assumption, the simulation under high current densities disagrees with the experiment result, which limits the application of the model. The homogeneous model assumes uniform distribution of substances in the catalyst layer. This model completely simulates the reaction and mass transfer process in the cell and has the ability to guide the cell optimization. However, the homogeneity hypothesis does not conform to the image of the catalyst layer observed in the experiment, so the model is not suitable for the study of the catalyst layer with high precision. The agglomerate model assumes that the substances in the catalyst layer agglomerate into a specific geometric shape. There are more parameters about catalyst layers in the agglomerate model, so it can be used to optimize the structure of the catalyst layer. However, some parameters are difficult to be measured experimentally and can only be assumed, which makes the model less scientific. In addition, it also takes the homogeneity hypothesis. The pore-scale model reconstructs the complex structure of the catalyst layer. It has the highest accuracy in theory but lacks perfect reconstruction methods. Regular reconstruction, stochastic reconstruction and process-based reconstruction cannot reflect the real structure characteristics of catalyst layers. Image-based reconstructions and statistical function-based reconstructions are limited by the image resolution and experimental error. Therefore, the pore-scale model is not a perfect model for catalyst layers. The particle model can accurately simulate microcosmic processes, but lacks the ability to combine with macroscopic simulations. So, the catalyst layer model still needs to be further developed. It is suggested to develop advanced experiment methods to ensure the accuracy of catalyst layer model parameters and verify the prediction result of the model. In addition, more complete catalyst layer model with multi-scale and multi-physics should be further developed, incorporating microscopic model results into macroscopic models, thus to fully understand the influence of the microscopic process of catalyst layers on the cell performance. It is also suggested that more research on low platinum, non-platinum catalysts as well as cell performance degradation should be carried out and new models considering their different reaction process and degradation mechanisms should be developed in the future. Moreover, similarity analysis approach is suggested to be adopted for cell models, which can reveal output characteristics and save cell optimization time.

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.