TV-based Algorithm Research Articles

TV-based phase retrieval for speckle coded diffraction imaging

Speckle coded diffraction imaging (SCDI) has emerged as a new and developing lensless imaging method, which provides an effective imaging method for dense and connected objects. The conventional alternating-projection-based phase retrieval algorithm for SCDI relies on phase constraints between multiple diffraction images, and its disadvantage is that it often necessitates a large number of measurements to ensure high-quality reconstruction. In order to reduce the measurements, we propose to regularize the non-convex phase retrieval with total variation (TV)–based prior, and thus construct the TV-based cost function for SCDI. The alternating direction method is used to solve the nonlinear cost function, and recover the object and unknown speckle illumination. As both simulations and experiments demonstrate, the proposed TV-based reconstruction algorithm can recover the complex object and the unknown speckle pattern with high fidelity using 16 measurements, compared with hundreds of measurements used for AP-based algorithm.

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.

Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm.

Low dose computed tomography (CT) has drawn much attention in the medical imaging field because of its ability to reduce the radiation dose. Recently, statistical iterative reconstruction (SIR) with total variation (TV) penalty has been developed to low dose CT image reconstruction. Nevertheless, the TV penalty has the drawback of creating blocky effects in the reconstructed images. To overcome the limitations of TV, in this paper we firstly introduce the structure tensor total variation (STV1) penalty into SIR framework for low dose CT image reconstruction. Then, an accelerated fast iterative shrinkage thresholding algorithm (AFISTA) is developed to minimize the objective function. The proposed AFISTA reconstruction algorithm was evaluated using numerical simulated low dose projection based on two CT images and realistic low dose projection data of a sheep lung CT perfusion. The experimental results demonstrated that our proposed STV1-based algorithm outperform FBP and TV-based algorithm in terms of removing noise and restraining blocky effects.

An Accelerated Convergence Algorithm for Sparse-View CT Image Reconstruction

In order to reduce radiation dose during CT scanning, sparse sampling is an effective way. Although the TV-based iterative reconstruction algorithm is a breakthrough to solve the problem of sparse-view CT image reconstruction, its applicability is still limited by huge computational burden. It is necessary to study the acceleration method of TV-based iterative algorithm. This paper show that the FISTA acceleration method is not suitable for POCS-TV algorithm, meanwhile, an improved acceleration method, IFISTA, is proposed to accelerate the convergence rate of POCS-TV. Numerical experiments show that the convergence rate of POCS-TV-IFISTA is about 35% faster than POCS-TV.

An improved median filtering anti-forensics with better image quality and forensic undetectability

Median filtering has received considerable attention and popularity for image enhancement and anti-forensics. It can be utilized as an image denoising and smoothing tool to disguise the footprints of image processing operations such as image resampling and JPEG compression. A two-step median filtering anti-forensic framework is proposed in this paper to fool the existing median filtering forensic detectors by hiding the median filtering artifacts. In the proposed framework, a variational deconvolution approach is initially employed to generate a median filtered forgery. Now, this forgery is further processed in the second step by considering Total Variation (TV) based minimization optimization problem to eradicate the median filtering artifacts left during deconvolution operation. Moreover, the proposed TV-based minimization algorithms significantly reduce the unnatural (grainy) noise left during the variational deconvolution. Two types of TV-based minimization problems are suggested, first relies on the TV of energy by considering the image gradient and second on the structure of a given image. The performance of the proposed scheme is evaluated by considering the worst-case and optimal scenarios. The experimental results based on UCID and BOSSBase dataset images demonstrate that the proposed anti-forensic methods provide superior results in terms of image visual quality and forensic undetectability as compared to the existing approaches, with slight increase in computational time.

Feasibility Study for Application of Total-Variation-Based Noise-Removal Algorithm with 450-kVp High-Energy Industrial Computed-Tomography Imaging System for Non-destructive Testing

Several important technological trends for the detection of faults in the internal structure of a material utilize industrial computed-tomography (CT) X-ray imaging systems in non-destructive testing (NDT). In this system, the total-variation-(TV)-based noise-removal algorithm is a powerful method for denoising with a high edge-information preservation. In this study, we confirm the application feasibility of the TV-based noise-removal algorithm with an established 450-kVp high-energy industrial CT imaging system for NDT. The results obtained using two phantoms (SEDENTEX cone-beam CT image-quality phantom and pressure-head phantom) with our established imaging system reveal excellent normalized noise power spectrum, contrast–to–noise ratio, and coefficient of variation of the images obtained using the TV-based noise-removal algorithm. Therefore, this study reveals that the TV-based noise-removal algorithm can improve the noise characteristics in an industrial CT imaging system for NDT.

Photoacoustic imaging reconstruction using combined nonlocal patch and total-variation regularization for straight-line scanning

BackgroundFor practical straight-line scanning in photoacoustic imaging (PAI), serious artifacts caused by missing data will occur. Traditional total variation (TV)-based algorithms fail to obtain satisfactory results, with an over-smoothed and blurred geometric structure. Therefore, it is important to develop a new algorithm to improve the quality of practical straight-line reconstructed images.MethodsIn this paper, a combined nonlocal patch and TV-based regularization model for PAI reconstruction is proposed to solve these problems. A modified adaptive nonlocal weight function is adopted to provide more reliable estimations for the similarities between patches. Similar patches are searched for throughout the entire image; thus, this model realizes adaptive search for the neighborhood of the patch. The optimization problem is simplified to a common iterative PAI reconstruction problem.Results and conclusionThe proposed algorithm is validated by a series of numerical simulations and an in vitro experiment for straight-line scanning. The results of patch-TV are compared to those of two mainstream TV-based algorithms as well as the iterative algorithm only with patch-based regularization. Moreover, the peak signal-to-noise ratio, the noise robustness, and the convergence and calculation speeds are compared and discussed. The results show that the proposed patch-TV yields significant improvement over the other three algorithms qualitatively and quantitatively. These simulations and experiment indicate that the patch-TV algorithm successfully solves the problems of PAI reconstruction and is highly effective in practical PAI applications.

A sparse representation and dictionary learning based algorithm for image restoration in the presence of Rician noise.

Rician noise removal for Magnetic Resonance Imaging (MRI) is very important because the MRI has been widely used in various clinical applications and the associated Rician noise deteriorates the image quality and causes errors in interpreting the images. Great efforts have recently been devoted to develop the corresponding noise-removal algorithms, particularly the development based on the newly-established Total Variation (TV) theorem. However, all the TV-based algorithms depend mainly on the gradient information and have been shown to produce the so called "blocky" artifact, which also deteriorates the image quality and causes image interpretation errors. In order to avoid producing the artifact, this paper presents a new de-noising model based on sparse representation and dictionary learning. The Split Bregman Iteration strategy is employed to implement the model. Furthermore, an appropriate dictionary is designed by the use of the Kernel Singular Value Decomposition method, resulting in a new Rician noise removal algorithm. Compared with other de-noising algorithms, the presented new algorithm can achieve superior performance, in terms of quantitative measures of the Structural Similarity Index and Peak Signal to Noise Ratio, by a series of experiments using different images in the presence of Rician noise.

Parameter selection in limited data cone-beam CT reconstruction using edge-preserving total variation algorithms

There are a number of powerful total variation (TV) regularization methods that have great promise in limited data cone-beam CT reconstruction with an enhancement of image quality. These promising TV methods require careful selection of the image reconstruction parameters, for which there are no well-established criteria. This paper presents a comprehensive evaluation of parameter selection in a number of major TV-based reconstruction algorithms. An appropriate way of selecting the values for each individual parameter has been suggested. Finally, a new adaptive-weighted projection-controlled steepest descent (AwPCSD) algorithm is presented, which implements the edge-preserving function for CBCT reconstruction with limited data. The proposed algorithm shows significant robustness compared to three other existing algorithms: ASD-POCS, AwASD-POCS and PCSD. The proposed AwPCSD algorithm is able to preserve the edges of the reconstructed images better with fewer sensitive parameters to tune.

Optimization-based image reconstruction incomputed tomography by alternating direction method with ordered subsets.

Nowadays, diversities of task-specific applications for computed tomography (CT) have already proposed multiple challenges for algorithm design of image reconstructions. Consequently, efficient algorithm design tool is necessary to be established. A fast and efficient algorithm design framework for CT image reconstruction, which is based on alternating direction method (ADM) with ordered subsets (OS), is proposed, termed as OS-ADM. The general ideas of ADM and OS have been abstractly introduced and then they are combined for solving convex optimizations in CT image reconstruction. Standard procedures are concluded for algorithm design which contain 1) model mapping, 2) sub-problem dividing and 3) solving, 4) OS level setting and 5) algorithm evaluation. Typical reconstruction problems are modeled as convex optimizations, including (non-negative) least-square, constrained L1 minimization, constrained total variation (TV) minimization and TV minimizations with different data fidelity terms. Efficient working algorithms for these problems are derived with detailed derivations by the proposed framework. In addition, both simulations and real CT projections are tested to verify the performances of two TV-based algorithms. Experimental investigations indicate that these algorithms are of the state-of-the-art performances. The algorithm instances show that the proposed OS-ADM framework is promising for practical applications.

Total variation-based method for generation of intravoxel incoherent motion parametric images in MRI.

Total variation (TV) method has been used widely for image restoration and reconstruction. In this work, we propose a TV-based algorithm for parametric image generation in intravoxel incoherent motion (IVIM) diffusion-weighted magnetic resonance imaging (DW-MRI). We used simulated and real data to investigate whether the proposed TV-based method can provide reliable parametric images. Parametric images of IVIM parameters including perfusion fraction (PF), diffusion coefficient (D), and pseudo-diffusion coefficient (D*) were estimated using DW-MRI data and TV through fitting the IVIM model. The Levenberg-Marquardt (LM) method, which has often been used in the context of IVIM analysis, was employed as the standard method for comparison of the resulting parametric images. The simulation results show that the proposed method outperforms the LM algorithm in terms of precision, providing a 40-81%, 90-93%, and 68-84% improvement for PF, D and D*, respectively, at signal-to-noise ratio (SNR) of 30. For real data, the proposed method showed an average five-fold, three-fold, and four-fold improvement in the SNR for PF, D and D*, respectively. We introduced the use of TV to produce parametric images, and demonstrated that the proposed TV-based method is effective in improving the parametric image quality. Magn Reson Med 78:1383-1391, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Penalized weighted least-squares approach for multienergy computed tomography image reconstruction via structure tensor total variation regularization

Multienergy computed tomography (MECT) allows identifying and differentiating different materials through simultaneous capture of multiple sets of energy-selective data belonging to specific energy windows. However, because sufficient photon counts are not available in each energy window compared with that in the whole energy window, the MECT images reconstructed by the analytical approach often suffer from poor signal-to-noise and strong streak artifacts. To address the particular challenge, this work presents a penalized weighted least-squares (PWLS) scheme by incorporating the new concept of structure tensor total variation (STV) regularization, which is henceforth referred to as ‘PWLS-STV’ for simplicity. Specifically, the STV regularization is derived by penalizing higher-order derivatives of the desired MECT images. Thus it could provide more robust measures of image variation, which can eliminate the patchy artifacts often observed in total variation (TV) regularization. Subsequently, an alternating optimization algorithm was adopted to minimize the objective function. Extensive experiments with a digital XCAT phantom and meat specimen clearly demonstrate that the present PWLS-STV algorithm can achieve more gains than the existing TV-based algorithms and the conventional filtered backpeojection (FBP) algorithm in terms of both quantitative and visual quality evaluations.

Investigation of cone-beam CT image quality trade-off for image-guided radiation therapy

It is well-known that projections acquired over an angular range slightly over 180° (so-called short scan) are sufficient for fan-beam reconstruction. However, due to practical imaging conditions (projection data and reconstruction image discretization, physical factors, and data noise), the short-scan reconstructions may have different appearances and properties from the full-scan (scans over 360°) reconstructions. Nevertheless, short-scan configurations have been used in applications such as cone-beam CT (CBCT) for head-neck-cancer image-guided radiation therapy (IGRT) that only requires a small field of view due to the potential reduced imaging time and dose. In this work, we studied the image quality trade-off for full, short, and full/short scan configurations with both conventional filtered-backprojection (FBP) reconstruction and iterative reconstruction algorithms based on total-variation (TV) minimization for head-neck-cancer IGRT. Anthropomorphic and Catphan phantoms were scanned at different exposure levels with a clinical scanner used in IGRT. Both visualization- and numerical-metric-based evaluation studies were performed. The results indicate that the optimal exposure level and number of views are in the middle range for both FBP and TV-based iterative algorithms and the optimization is object-dependent and task-dependent. The optimal view numbers decrease with the total exposure levels for both FBP and TV-based algorithms. The results also indicate there are slight differences between FBP and TV-based iterative algorithms for the image quality trade-off: FBP seems to be more in favor of larger number of views while the TV-based algorithm is more robust to different data conditions (number of views and exposure levels) than the FBP algorithm. The studies can provide a general guideline for image-quality optimization for CBCT used in IGRT and other applications.

Speckle reduction via higher order total variation approach.

Multiplicative noise (also known as speckle) reduction is a prerequisite for many image-processing tasks in coherent imaging systems, such as the synthetic aperture radar. One approach extensively used in this area is based on total variation (TV) regularization, which can recover significantly sharp edges of an image, but suffers from the staircase-like artifacts. In order to overcome the undesirable deficiency, we propose two novel models for removing multiplicative noise based on total generalized variation (TGV) penalty. The TGV regularization has been mathematically proven to be able to eliminate the staircasing artifacts by being aware of higher order smoothness. Furthermore, an efficient algorithm is developed for solving the TGV-based optimization problems. Numerical experiments demonstrate that our proposed methods achieve state-of-the-art results, both visually and quantitatively. In particular, when the image has some higher order smoothness, our methods outperform the TV-based algorithms.

Total Variation-Stokes Strategy for Sparse-View X-ray CT Image Reconstruction

Previous studies have shown that by minimizing the total variation (TV) of the to-be-estimated image with some data and/or other constraints, a piecewise-smooth X-ray computed tomography image can be reconstructed from sparse-view projection data. However, due to the piecewise constant assumption for the TV model, the reconstructed images are frequently reported to suffer from the blocky or patchy artifacts. To eliminate this drawback, we present a total variation-stokes-projection onto convex sets (TVS-POCS) reconstruction method in this paper. The TVS model is derived by introducing isophote directions for the purpose of recovering possible missing information in the sparse-view data situation. Thus the desired consistencies along both the normal and the tangent directions are preserved in the resulting images. Compared to the previous TV-based image reconstruction algorithms, the preserved consistencies by the TVS-POCS method are expected to generate noticeable gains in terms of eliminating the patchy artifacts and preserving subtle structures. To evaluate the presented TVS-POCS method, both qualitative and quantitative studies were performed using digital phantom, physical phantom and clinical data experiments. The results reveal that the presented method can yield images with several noticeable gains, measured by the universal quality index and the full-width-at-half-maximum merit, as compared to its corresponding TV-based algorithms. In addition, the results further indicate that the TVS-POCS method approaches to the gold standard result of the filtered back-projection reconstruction in the full-view data case as theoretically expected, while most previous iterative methods may fail in the full-view case because of their artificial textures in the results.

Reconstruction of multi-view compressed imaging using weighted total variation

This paper concentrates on the problem of image reconstruction from compressed sensing (CS) measurements in multi-view compressed imaging systems, where each view is acquired independently by CS technique. In order to take advantage of both the inter-view correlation and the spatial prior information in multi-view image sets, a weighted total variation (TV) regularized model, which combines the TV norm of a target view and the TV norm of the corresponding residual, is proposed. To efficiently solve the weighted TV regularization constrained problem, novel algorithms are presented for both the anisotropy TV and the isotropy TV cases. Given the multi-view CS measurements, a sliding window-based recovery framework is also developed to work with the weighted TV-based reconstruction algorithms and produce high-quality results. We show by experiments that the proposed methods greatly outperform the straight forward reconstruction which applies view by view image reconstruction independently, and also have significant advantages over other benchmark methods.

Digital tomosynthesis (DTS) with a Circular X-ray tube: Its image reconstruction based on total-variation minimization and the image characteristics

In this paper, we introduce an effective imaging system for digital tomosynthesis (DTS) with a circular X-ray tube, the so-called circular-DTS (CDTS) system, and its image reconstruction algorithm based on the total-variation (TV) minimization method for low-dose, high-accuracy X-ray imaging. Here, the X-ray tube is equipped with a series of cathodes distributed around a rotating anode, and the detector remains stationary throughout the image acquisition. We considered a TV-based reconstruction algorithm that exploited the sparsity of the image with substantially high image accuracy. We implemented the algorithm for the CDTS geometry and successfully reconstructed images of high accuracy. The image characteristics were investigated quantitatively by using some figures of merit, including the universal-quality index (UQI) and the depth resolution. For selected tomographic angles of 20, 40, and 60°, the corresponding UQI values in the tomographic view were estimated to be about 0.94, 0.97, and 0.98, and the depth resolutions were about 4.6, 3.1, and 1.2 voxels in full width at half maximum (FWHM), respectively. We expect the proposed method to be applicable to developing a next-generation dental or breast X-ray imaging system.

Image reconstruction algorithm based on inexact alternating direction total-variation minimization

Image reconstruction algorithms implemented in existing computed tomography (CT) scanners require that the projection data should be available in proportional-space. The image reconstruction from the projections viewed from few angles has already been one of the hot problems in the research of iterative reconstruction algorithms. Total variation (TV)-based CT image reconstruction has shown to be experimentally capable of producing accurate reconstructions from sparse-view data. Reconstruction algorithms based on alternating direction method (ADM) show higher performance among these TV-based algorithms. However, computing the pseudoinverse at each iteration is too costly to implement numerically in the exact ADM algorithm. For this problem, then inexact ADM is adopted, which uses linearization and proximal points techniques such that computing the pseudoinverse can be accomplished by fast Fourier transforms. Experimental results demonstrate that the proposed method can accelerate the exact ADM algorithm, with little accuracy loss, and the computing time is approximatively reduced by 30%.

Total variation based gradient descent algorithm for sparse-view photoacoustic image reconstruction

In photoacoustic imaging (PAI), reconstruction from sparse-view sampling data is a remaining challenge in the cases of fast or real-time imaging. In this paper, we present our study on a total variation based gradient descent (TV-GD) algorithm for sparse-view PAI reconstruction. This algorithm involves the total variation (TV) method in compressed sensing (CS) theory. The objective function of the algorithm is modified by adding the TV value of the reconstructed image. With this modification, the reconstructed image could be closer to the real optical energy distribution map. Additionally in the proposed algorithm, the photoacoustic data is processed and the image is updated individually at each detection point. In this way, the calculation with large matrix can be avoided and a more frequent image update can be obtained. Through the numerical simulations, the proposed algorithm is verified and compared with other reconstruction algorithms which have been widely used in PAI. The peak signal-to-noise ratio (PSNR) of the image reconstructed by this algorithm is higher than those by the other algorithms. Additionally, the convergence of the algorithm, the robustness to noise and the tunable parameter are further discussed. The TV-based algorithm is also implemented in the in vitro experiment. The better performance of the proposed method is revealed in the experiments results. From the results, it is seen that the TV-GD algorithm may be a practical and efficient algorithm for sparse-view PAI reconstruction.

Low-dose CT reconstruction via edge-preserving total variation regularization

High radiation dose in computed tomography (CT) scans increases the lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with total variation (TV) regularization have been developed to reconstruct CT images from highly undersampled data acquired at low mAs levels in order to reduce the imaging dose. Nonetheless, the low-contrast structures tend to be smoothed out by the TV regularization, posing a great challenge for the TV method. To solve this problem, in this work we develop an iterative CT reconstruction algorithm with edge-preserving TV (EPTV) regularization to reconstruct CT images from highly undersampled data obtained at low mAs levels. The CT image is reconstructed by minimizing energy consisting of an EPTV norm and a data fidelity term posed by the x-ray projections. The EPTV term is proposed to preferentially perform smoothing only on the non-edge part of the image in order to better preserve the edges, which is realized by introducing a penalty weight to the original TV norm. During the reconstruction process, the pixels at the edges would be gradually identified and given low penalty weight. Our iterative algorithm is implemented on graphics processing unit to improve its speed. We test our reconstruction algorithm on a digital NURBS-based cardiac-troso phantom, a physical chest phantom and a Catphan phantom. Reconstruction results from a conventional filtered backprojection (FBP) algorithm and a TV regularization method without edge-preserving penalty are also presented for comparison purposes. The experimental results illustrate that both the TV-based algorithm and our EPTV algorithm outperform the conventional FBP algorithm in suppressing the streaking artifacts and image noise under a low-dose context. Our edge-preserving algorithm is superior to the TV-based algorithm in that it can preserve more information of low-contrast structures and therefore maintain acceptable spatial resolution.