Iterative Total Variation Research Articles

Electrode Placement Optimization for Electrical Impedance Tomography Using Active Learning

Electrical impedance tomography (EIT) offers a versatile imaging modality with a multitude of applications, although it encounters accuracy limitations. Herein, a novel systematic framework is presented that integrates a neural network (NN), active learning, and transfer learning to optimize electrode placement, improving image reconstruction performance based on user‐defined metrics. Given the many‐to‐one mapping between electrode configuration and the performance metric, the approach utilizes a NN that predicts performance metrics from electrode placement input. To maintain NN's prediction accuracy for unseen electrode configurations, performance metrics are maximized while iteratively updating the NN via active learning during the optimization process. Transfer learning is employed to expedite optimization of electrode placements for time‐consuming iterative reconstruction techniques by fine‐tuning a NN initially trained on one‐step reconstruction data. The method is validated using two representative reconstruction methods: one‐step reconstruction with Newton's one‐step error reconstructor prior and the iterative total variation method. This research underscores the potential of the proposed framework in addressing EIT's inherent limitations and augmenting its performance across diverse applications and reconstruction methods. The framework could potentially contribute to the advancement of noninvasive medical imaging, structural health monitoring, strain sensing, robotics, and other fields that depend on EIT.

A method of reconstructing compressive spectral imaging with a complementary prior constraint

Compressed spectral imaging (CSI) is a technique for acquiring a cube of spectral image data in a single snapshot. In this paper, we propose a reconstruction method for the CSI system that integrates complementary prior constraints on spectral data to significantly enhance the accuracy of reconstructed data. The fundamental concepts are as follows: (1) Firstly, by conducting a thorough analysis of the corresponding feature maps of spectral data on the convolution dictionaries, we confirm the feasibility of utilizing the stationary response characteristics of spectral data on the convolution dictionaries as a reconstruction constraint to enhance spectral accuracy. (2) To compensate for the limitations of Convolutional Sparse Coding in reconstructing low-frequency signals, this paper proposes utilizing iterative Total Variation operators to estimate the low-frequency portion of spectral data. This approach results in improved performance in reconstructing low-frequency data and noise suppression. (3) Convolutional Sparse Coding and Total Variation are utilized as constraints for high and low-frequency complementary reconstruction, resulting in a multi-constraint solution problem within the Plug-and-Play framework that simplifies the overall reconstruction process. The proposed method surpasses the state-of-the-art reconstruction methods in both spatial reconstruction quality and spectral accuracy, while also significantly enhancing the level of detail in reconstructed spectral images.

Privacy-preserving image compressed sensing by embedding a controllable noise-injected transformation for IoT devices

Recently, compressed sensing (CS) based cryptosystem has received extensive attention in information security field. However, this cryptosystem cannot resist known-plaintext attack (KPA) under the secret key multi-time-using (MTU) scenario because of its linear sampling process. To address this concern, a privacy-preserving image CS scheme is proposed, which embeds a controllable noise-injected transformation (CNT) into the linear sampling process of CS to resist KPA. First, a CNT operation is applied to pre-encrypt the image. Second, the pre-encrypted image is re-encrypted and compressed by using CS at the same time. Third, the final CS measurements are quantized into bits. Since the embedding of CNT operation destroys the linearity of CS, the proposed cryptosystem can resist the existing KPA method under the secret key MTU scenario. Lastly, an iterative total variation (TV) algorithm based on ADMM framework, called TV-ADMM, is proposed for image recovery. Simulation results demonstrate that the proposed cryptosystem significantly enhances the security of the CS-based cryptosystem with slightly sacrificing the compression performance in high compression rate cases.

Dose reduction and image enhancement in micro-CT using deep learning.

In preclinical settings, micro-computed tomography (CT) provides a powerful tool to acquire high resolution anatomical images of rodents and offers the advantage to in vivo non-invasively assess disease progression and therapy efficacy. Much higher resolutions are needed to achieve scale-equivalent discriminatory capabilities in rodents as those in humans. High resolution imaging however comes at the expense of increased scan times and higher doses. Specifically, with preclinical longitudinal imaging, there are concerns that dose accumulation may affect experimental outcomes of animal models. Dose reduction efforts under the ALARA (as low as reasonably achievable) principles are thus a key point of attention. However, low dose CT acquisitions inherently induce higher noise levels which deteriorate image quality and negatively impact diagnostic performance. Many denoising techniques already exist, and deep learning (DL) has become increasingly popular for image denoising, but research has mostly focused on clinical CT with limited studies conducted on preclinical CT imaging. We investigate the potential of convolutional neural networks (CNN) for restoring high quality micro-CT images from low dose (noisy) images. The novelty of the CNN denoising frameworks presented in this work consists of utilizingimage pairs with realistic CT noise present in the input as well as thetarget image used for the model training; a noisier image acquired with a low dose protocol is matched to a less noisy image acquired with a higher dose scan of the same mouse. Low and high dose ex vivo micro-CT scans of 38 mice were acquired. Two CNN models, based on a 2D and 3D four-layer U-Net, were trained with mean absolute error (30 training, 4 validation and 4 test sets). To assess denoising performance, ex vivo mice and phantom data were used. Both CNN approaches were compared to existing methods, like spatial filtering (Gaussian, Median, Wiener) and iterative total variation image reconstruction algorithm. Image quality metrics were derived from the phantom images. A first observer study (n=23) was set-up to rank overall quality of differently denoised images. A second observer study (n=18) estimated the dose reduction factor of the investigated 2D CNN method. Visual and quantitative results show that both CNN algorithms exhibit superior performance in terms of noise suppression, structural preservation and contrast enhancement over comparator methods. The quality scoring by 23 medical imaging experts also indicates that the investigated 2D CNN approach is consistently evaluated as the best performing denoising method. Results from the second observer study and quantitative measurements suggest that CNN-based denoising could offer a 2-4× dose reduction, with an estimated dose reduction factor of about 3.2 for the considered 2D network. Our results demonstrate the potential of DL in micro-CT for higher quality imaging at low dose acquisition settings. In the context of preclinical research, this offers promising future prospects for managing the cumulative severity effects of radiation in longitudinal studies.

Addressing CT metal artifacts using photon-counting detectors and one-step spectral CT image reconstruction.

The constrained one-step spectral CT image reconstruction (cOSSCIR) algorithm with a nonconvex alternating direction method of multipliers optimizer is proposed for addressing computed tomography (CT) metal artifacts caused by beam hardening, noise, and photon starvation. The quantitative performance of cOSSCIR is investigated through a series of photon-counting CT simulations. cOSSCIR directly estimates basis material maps from photon-counting data using a physics-based forward model that accounts for beam hardening. The cOSSCIR optimization framework places constraints on the basis maps, which we hypothesize will stabilize the decomposition and reduce streaks caused by noise and photon starvation. Another advantage of cOSSCIR is that the spectral data need not be registered, so that a ray can be used even if some energy window measurements are unavailable. Photon-counting CT acquisitions of a virtual pelvic phantom with low-contrast soft tissue texture and bilateral hip prostheses were simulated. Bone and water basis maps were estimated using the cOSSCIR algorithm and combined to form a virtual monoenergetic image for the evaluation of metal artifacts. The cOSSCIR images were compared to a "two-step" decomposition approach that first estimated basis sinograms using a maximum likelihood algorithm and then reconstructed basis maps using an iterative total variation constrained least-squares optimization (MLE+TV ). Images were also compared to a nonspectral TV reconstruction of the total number of counts detected for each ray with and without normalized metal artifact reduction (NMAR) applied. The simulated metal density was increased to investigate the effects of increasing photon starvation. The quantitative error and standard deviation in regions of the phantom were compared across the investigated algorithms. The ability of cOSSCIR to reproduce the soft-tissue texture, while reducing metal artifacts, was quantitativelyevaluated. Noiseless simulations demonstrated the convergence of the cOSSCIR and MLE+TV algorithms to the correct basis maps in the presence of beam-hardening effects. When noise was simulated, cOSSCIR demonstrated a quantitative error of -1 HU, compared to 2 HU error for the MLE+TV algorithm and -154 HU error for the nonspectral TV +NMAR algorithm. For the cOSSCIR algorithm, the standard deviation in the central iodine region of interest was 20 HU, compared to 299 HU for the MLE+TV algorithm, 41 HU for the MLE+TV +Mask algorithm that excluded rays through metal, and 55 HU for the nonspectral TV +NMAR algorithm. Increasing levels of photon starvation did not impact the bias or standard deviation of the cOSSCIR images. cOSSCIR was able to reproduce the soft-tissue texture when an appropriate regularization constraint value wasselected. By directly inverting photon-counting CT data into basis maps using an accurate physics-based forward model and a constrained optimization algorithm, cOSSCIR avoids metal artifacts due to beam hardening, noise, and photon starvation. The cOSSCIR algorithm demonstrated improved stability and accuracy compared to a two-step method of decomposition followed byreconstruction.

Image quality of dual-energy cone-beam CT with total nuclear variation regularization

Despite the improvements in image quality of cone beam computed tomography (CBCT) scans, application remains limited to patient positioning. In this study, we propose to improve image quality by dual energy (DE) imaging and iterative reconstruction using least squares fitting with total variation (TV) regularization. The generalization of TV called total nuclear variation (TNV) was used to generate DE images. We acquired single energy (SE) and DE scans of an image quality phantom (IQP) and of an anthropomorphic human male phantom (HMP). The DE scans were dual arc acquisitions of 70 kV and 130 kV with a variable dose partitioning between low energy (LE) and high energy (HE) arcs. To investigate potential benefits from a larger spectral separation between LE and HE, DE scans with an additional 2 mm copper beam filtration in the HE arc were acquired for the IQP. The DE TNV scans were compared to SE scans reconstructed with FDK and iterative TV with varying parameters. The contrast-to-noise ratio (CNR), spatial frequency, and structural similarity (SSIM) were used as image quality metrics. Results showed largely improved image quality for DE TNV over FDK for both phantoms. DE TNV with the highest dose allocation in the LE arm yielded the highest CNR. Compared to SE TV, these DE TNV results had a slightly lower CNR with similar spatial resolution for the IQP. A decrease in the dose allocated to the LE arm improved the spatial resolution with a trade-off against CNR. For the HMP, DE TNV displayed a lower CNR and/or lower spatial resolution depending on the reconstruction parameters. Regarding the SSIM, DE TNV was superior to FDK and SE TV for both phantoms. The additional beam filtration for the IQP led to improved image quality in all metrics, surpassing the SE TV results in CNR and spatial resolution.

An Efficient Point-Matching Method-of-Moments for 2D and 3D Electrical Impedance Tomography Using Radial Basis Functions.

The inverse problem of computing conductivity distributions in 2D and 3D objects interrogated by low-frequency electrical signals, which is called Electrical Impedance Tomography (EIT), is treated using a Method-of-Moment technique. A Point-Matching-Method-of-Moment technique is used to formulate a global integral equation solver. Radial Basis Functions are adopted to express the conductivity distribution. Single-step quadratic-norm ( L2) and iterative total variation ( L1) regularization techniques are exploited to solve the inverse problem. Simulation and experimental tests on a circular reconstruction domain show satisfactory performance in deriving conductivity distribution, achieving a Correlation Coefficient ( CC) up to 0.863 for 70 dB voltage SNR and 0.842 for 40 dB voltage SNR. The proposed methodology with L2-norm regularization provided better results than traditional iterative Gauss-Newton's approach, whereas with L1-norm regularization it showed promising performance. Moreover, 3D reconstructions on a cylindrical cavity demonstrated superior results near the electrodes' planes compared to those of the conventional linearized approach. Finally, application to EIT medical data for dynamic lung imaging successfully revealed the breath-cycle conductivity changes. The results show that the proposed method can be effective for both 2D and 3D EIT and applicable to many applications. Strong conductivity variations are successfully tackled with a very good Correlation Coefficient. In contrast to conventional EIT solutions based on weak-form and linearization on small conductivity changes, the proposed method requires only one step to converge with L2-norm regularization. The proposed method with L1-norm regularization also achieves good reconstruction quality with a low number of iterations.

Optical satellite image MTF compensation for remote-sensing data production

Modulation Transfer Function (MTF) compensation had been widely used in Remote-Sensing (RS) imagery processing for texture feature enhancement and high-frequency details restoration. In this paper, we propose an optical satellite MTF Compensation (MTFC) method for engineering applications and RS data production. The framework mainly includes Point Spread Function (PSF) model estimation and non-blind image deconvolution. In PSF estimation, we used the iterative total variation algorithm and 2D Gaussian model fitting to reduce the dependence on slant-edge quality and improve the efficiency of PSF measurement. The PSF model estimation error is less than 3% using the results from standard commercial software as an evaluation benchmark. In image deconvolution, we adopted a regularisation-based non-blind deconvolution method using hyper-Laplacian prior. Compared with the widely used methods, the MTF has been improved more than double in high-frequency part. Its processing efficiency and image quality can meet the requirements of RS image products. These results can effectively prove the engineering application value of our proposed method.

DeepRegularizer: Rapid Resolution Enhancement of Tomographic Imaging Using Deep Learning.

Optical diffraction tomography measures the three-dimensional refractive index map of a specimen and visualizes biochemical phenomena at the nanoscale in a non-destructive manner. One major drawback of optical diffraction tomography is poor axial resolution due to limited access to the three-dimensional optical transfer function. This missing cone problem has been addressed through regularization algorithms that use a priori information, such as non-negativity and sample smoothness. However, the iterative nature of these algorithms and their parameter dependency make real-time visualization impossible. In this article, we propose and experimentally demonstrate a deep neural network, which we term DeepRegularizer, that rapidly improves the resolution of a three-dimensional refractive index map. Trained with pairs of datasets (a raw refractive index tomogram and a resolution-enhanced refractive index tomogram via the iterative total variation algorithm), the three-dimensional U-net-based convolutional neural network learns a transformation between the two tomogram domains. The feasibility and generalizability of our network are demonstrated using bacterial cells and a human leukaemic cell line, and by validating the model across different samples. DeepRegularizer offers more than an order of magnitude faster regularization performance compared to the conventional iterative method. We envision that the proposed data-driven approach can bypass the high time complexity of various image reconstructions in other imaging modalities.

Application of Deep Neural Network to the Reconstruction of Two-Phase Material Imaging by Capacitively Coupled Electrical Resistance Tomography

A convolutional neural network (CNN)-based image reconstruction algorithm for two-phase material imaging is presented and verified with experimental data from a capacitively coupled electrical resistance tomography (CCERT) sensor. As a contactless version of electrical resistance tomography (ERT), CCERT has advantages such as no invasion, low cost, no radiation, and rapid response for two-phase material imaging. Besides that, CCERT avoids contact error of ERT by imaging from outside of the pipe. Forward modeling was implemented based on the practical circular array sensor, and the inverse image reconstruction was realized by a CNN-based supervised learning algorithm, as well as the well-known total variation (TV) regularization algorithm for comparison. The 2D, monochrome, 2500-pixel image was divided into 625 clusters, and each cluster was used individually to train its own CNN to solve the 16 classes classification problem. Inherent regularization for the assumption of binary materials enabled us to use a classification algorithm with CNN. The iterative TV regularization algorithm achieved a close state of the two-phase material reconstruction by its sparsity-based assumption. The supervised learning algorithm established the mathematical model that mapped the simulated resistance measurement to the pixel patterns of the clusters. The training process was carried out only using simulated measurement data, but simulated and experimental tests were both conducted to investigate the feasibility of applying a multi-layer CNN for CCERT imaging. The performance of the CNN algorithm on the simulated data is demonstrated, and the comparison between the results created by the TV-based algorithm and the proposed CNN algorithm with the real-world data is also provided.

Quantitative Evaluations with 2d Electrical Resistance Tomography in the Low-Conductivity Solutions Using 3d-Printed Phantoms and Sucrose Crystal Agglomerate Assessments.

Crystallization is a significant procedure in the manufacturing of many pharmaceutical and solid food products. In-situ electrical resistance tomography (ERT) is a novel process analytical tool (PAT) to provide a cheap and quick way to test, visualize, and evaluate the progress of crystallization processes. In this work, the spatial accuracy of the nonconductive phantoms in low-conductivity solutions was evaluated. Gauss–Newton, linear back projection, and iterative total variation reconstruction algorithms were used to compare the phantom reconstructions for tap water, industrial-grade saturated sucrose solution, and demineralized water. A cylindrical phantom measuring 10 mm in diameter and a cross-section area of 1.5% of the total beaker area was detected at the center of the beaker. Two phantoms with a 10-mm diameter were visualized separately in noncentral locations. The quantitative evaluations were done for the phantoms with radii ranging from 10 mm to 50 mm in demineralized water. Multiple factors, such as ERT device and sensor development, Finite Element Model (FEM) mesh density and simulations, image reconstruction algorithms, number of iterations, segmentation methods, and morphological image processing methods, were discussed and analyzed to achieve spatial accuracy. The development of ERT imaging modality for the purpose of monitoring crystallization in low-conductivity solutions was performed satisfactorily.

Sparse-view CT reconstruction based on multi-level wavelet convolution neural network.

Sparse-view computed tomography (CT) is a recent approach to reducing the radiation dose in patients and speeding up the data acquisition. Consequently, sparse-view CT has been of particular interest among researchers within the CT community. Advanced reconstruction algorithms for sparse-view CT, such as iterative algorithms with total-variation (TV), have been studied along with the problem of increasing computational burden and the blurring of artifacts in the reconstructed images. Studies on deep-learning-based approaches applying U-NET have recently achieved remarkable outcomes in various domains including low-dose CT. In this study, we propose a new method for sparse-view CT reconstruction based on a multi-level wavelet convolutional neural network (MWCNN). First, a filtered backprojection (FBP) was used to reconstruct a sparsely sampled sinogram from 60, 120, and 180 projections. Subsequently, the sparse-view data obtained from FBP were fed to a deep-learning network, i.e., the MWCNN. Our network architecture combines a wavelet transform and modified U-NET without pooling. By replacing the pooling function with the wavelet transform, the receptive field is enlarged to improve the performance. We qualitatively and quantitatively evaluated the interpolation, iterative TV method, and standard U-NET in terms of a reduction in the streaking artifacts and a preservation of the anatomical structures. When compared with other methods, the proposed method showed the highest performance based on various evaluation parameters such as the structural similarity, root mean square error, and resolution. These results indicate that the MWCNN possesses a powerful potential for achieving a sparse-view CT reconstruction.

Artifact removal using a hybrid-domain convolutional neural network for limited-angle computed tomography imaging

The suppression of streak artifacts in computed tomography with a limited-angle configuration is challenging. Conventional analytical algorithms, such as filtered backprojection (FBP), are not successful due to incomplete projection data. Moreover, model-based iterative total variation algorithms effectively reduce small streaks but do not work well at eliminating large streaks. In contrast, FBP mapping networks and deep-learning-based postprocessing networks are outstanding at removing large streak artifacts; however, these methods perform processing in separate domains, and the advantages of multiple deep learning algorithms operating in different domains have not been simultaneously explored. In this paper, we present a hybrid-domain convolutional neural network (hdNet) for the reduction of streak artifacts in limited-angle computed tomography. The network consists of three components: the first component is a convolutional neural network operating in the sinogram domain, the second is a domain transformation operation, and the last is a convolutional neural network operating in the CT image domain. After training the network, we can obtain artifact-suppressed CT images directly from the sinogram domain. Verification results based on numerical, experimental and clinical data confirm that the proposed method can significantly reduce serious artifacts.

Interior photon counting computed tomography for quantification of coronary artery calcium: pre-clinical phantom study

Computed tomography (CT) is the reference method for cardiac imaging, but concerns have been raised regarding the radiation dose of CT examinations. Recently, photon counting detectors (PCDs) and interior tomography, in which the radiation beam is limited to the organ-of-interest, have been suggested for patient dose reduction. In this study, we investigated interior PCD-CT (iPCD-CT) for non-enhanced quantification of coronary artery calcium (CAC) using an anthropomorphic torso phantom and ex vivo coronary artery samples. We reconstructed the iPCD-CT measurements with filtered back projection (FBP), iterative total variation (TV) regularization, padded FBP, and adaptively detruncated FBP and adaptively detruncated TV. We compared the organ doses between conventional CT and iPCD-CT geometries, assessed the truncation and cupping artifacts with iPCD-CT, and evaluated the CAC quantification performance of iPCD-CT. With approximately the same effective dose between conventional CT geometry (0.30 mSv) and interior PCD-CT with 10.2 cm field-of-view (0.27 mSv), the organ dose of the heart was increased by 52.3% with interior PCD-CT when compared to CT. Conversely, the organ doses to peripheral and radiosensitive organs, such as the stomach (55.0% reduction), were often reduced with interior PCD-CT. FBP and TV did not sufficiently reduce the truncation artifact, whereas padded FBP and adaptively detruncated FBP and TV yielded satisfactory truncation artifact reduction. Notably, the adaptive detruncation algorithm reduced truncation artifacts effectively when it was combined with reconstruction detrending. With this approach, the CAC quantification accuracy was good, and the coronary artery disease grade reclassification rate was particularly low (5.6%). Thus, our results confirm that CAC quantification can be performed with the interior CT geometry, that the artifacts are effectively reduced with suitable interior reconstruction methods, and that interior tomography provides efficient patient dose reduction.

Simulation of a Gamma-Ray Computed Tomography System Using Two Radioisotopes for Structural Inspections: A Preliminary Study

Gamma-ray computed tomography (CT) has widely been used to inspect cracks, obstructions, and fluid flow in pipes. Previous studies have shown that the inspection accuracy is limited when materials in the pipe have a similar density. To overcome this drawback, we investigated a method to discriminate small density differences using a dual-energy gamma-ray CT. In this paper, the performance of a gamma-ray CT system was simulated using Geant4 Application for Tomographic Emission with three types of sources (Am-241, Co-57, and Cs-137). A polyvinyl chloride (PVC) pipe containing oil and sludge was modeled as a phantom. Sparsely acquired data were reconstructed using filtered back-projection and iterative total variation (TV) denoising algorithms. Each material discrimination procedure was performed with a postreconstruction technique. Our results clearly showed that the gamma-ray CT imaging with Am-241 and Co-57 sources and the TV denoising reconstruction algorithm can be used to inspect the internal structures based on discriminated images. The calculated areas of discriminated oil and sludge were within an error margin of 2% (oil: 78.4% and sludge: 21.6%) compared with the simulated phantom (oil: 80% and sludge: 20%). For both gamma sources, the calculated contrast-to-noise ratio (CNR) values with the TV denoising algorithm were the highest values for all structures (Am-241/Co-57: 18.03/28.95 for oil versus sludge, 41.67/31.53 for oil versus PVC pipe, and 23.64/31.53 for sludge versus PVC pipe). The feasibility of our approach and results indicates it usefulness for industrial fields that require structural inspections.

Imaging metallic samples using electrical capacitance tomography: forward modelling and reconstruction algorithms

Electrical capacitance tomography (ECT) is an imaging technology used to reconstruct the permittivity distribution within the sensing region. So far, ECT has been primarily used to image non-conductive media only, since if the conductivity of the imaged object is high, the capacitance measuring circuit will be almost shortened by the conductivity path and a clear image cannot be produced using the standard image reconstruction approaches. This paper tackles the problem of imaging metallic samples using conventional ECT systems by investigating the two main aspects of image reconstruction algorithms, namely the forward problem and the inverse problem. For the forward problem, two different methods to model the region of high conductivity in ECT is presented. On the other hand, for the inverse problem, three different algorithms to reconstruct the high contrast images are examined. The first two methods are the linear single step Tikhonov method and the iterative total variation regularization method, and use two sets of ECT data to reconstruct the image in time difference mode. The third method, namely the level set method, uses absolute ECT measurements and was developed using a metallic forward model. The results indicate that the applications of conventional ECT systems can be extended to metal samples using the suggested algorithms and forward model, especially using a level set algorithm to find the boundary of the metal.

EIT Image Reconstruction Using Iterative TV Regularized PD-IPM Algorithm

Biological tissues have electrical conductivity and permittivity properties which depend on tissue composition, structure and health status. Bioelectrical properties can be utilized for non invasive diagnosis. Electrical Impedance Tomography (EIT) is a method for reconstructing the image of distribution of electrical conductivity and permittivity inside a volume from measurements made at the surface of the volume. EIT image reconstruction is an ill-posed problem that requires a priori information called regularization. The Total Variation (TV) regularization is often used in solving EIT inverse problem. In this paper, simulation has been carried out in noise free and noisy cases and TV regularized iterative Primal Dual Interior Point Method (PD-IPM) has been used to reconstruct the difference conductivity image.

4D cone-beam CT reconstruction using multi-organ meshes for sliding motion modeling

A simultaneous motion estimation and image reconstruction (SMEIR) strategy was proposed for 4D cone-beam CT (4D-CBCT) reconstruction and showed excellent results in both phantom and lung cancer patient studies. In the original SMEIR algorithm, the deformation vector field (DVF) was defined on voxel grid and estimated by enforcing a global smoothness regularization term on the motion fields. The objective of this work is to improve the computation efficiency and motion estimation accuracy of SMEIR for 4D-CBCT through developing a multi-organ meshing model. Feature-based adaptive meshes were generated to reduce the number of unknowns in the DVF estimation and accurately capture the organ shapes and motion. Additionally, the discontinuity in the motion fields between different organs during respiration was explicitly considered in the multi-organ mesh model. This will help with the accurate visualization and motion estimation of the tumor on the organ boundaries in 4D-CBCT. To further improve the computational efficiency, a GPU-based parallel implementation was designed. The performance of the proposed algorithm was evaluated on a synthetic sliding motion phantom, a 4D NCAT phantom, and four lung cancer patients. The proposed multi-organ mesh based strategy outperformed the conventional Feldkamp–Davis–Kress, iterative total variation minimization, original SMEIR and single meshing method based on both qualitative and quantitative evaluations.

Iterative total-variation reconstruction versus weighted filtered-backprojection reconstruction with edge-preserving filtering

Iterative image reconstruction with the total-variation (TV) constraint has become an active research area in recent years, especially in x-ray CT and MRI. Based on Green's one-step-late algorithm, this paper develops a transmission noise weighted iterative algorithm with a TV prior. This paper compares the reconstructions from this iterative TV algorithm with reconstructions from our previously developed non-iterative reconstruction method that consists of a noise-weighted filtered backprojection (FBP) reconstruction algorithm and a nonlinear edge-preserving post filtering algorithm. This paper gives a mathematical proof that the noise-weighted FBP provides an optimal solution. The results from both methods are compared using clinical data and computer simulation data. The two methods give comparable image quality, while the non-iterative method has the advantage of requiring much shorter computation times.

Iterative global and local methods of image restoration

Most of the reconstruction algorithms smooth out the edges of the reconstructed images but iterative total variation regularization and local adaptive methods preserve the edge information without any prior knowledge about the image geometric details. The restoration performance of the proposed algorithms for image deblurring is compared in terms of the mean squared error. Computer simulation results are provided and discussed.