Total Variation Method Research Articles

An Improved Mapping with Super-Resolved Multispectral Images for Geostationary Satellites

Super-resolution (SR) technology has shown great potential for improving the performance of the mapping and classification of multispectral satellite images. However, it is very challenging to solve ill-conditioned problems such as mapping for remote sensing images due to the presence of complicated ground features. In this paper, we address this problem by proposing a super-resolution reconstruction (SRR) mapping method called the mixed sparse representation non-convex high-order total variation (MSR-NCHOTV) method in order to accurately classify multispectral images and refine object classes. Firstly, MSR-NCHOTV is employed to reconstruct high-resolution images from low-resolution time-series images obtained from the Gaofen-4 (GF-4) geostationary orbit satellite. Secondly, a support vector machine (SVM) method was used to classify the results of SRR using the GF-4 geostationary orbit satellite images. Two sets of GF-4 satellite image data were used for experiments, and the MSR-NCHOTV SRR result obtained using these data was compared with the SRR results obtained using the bilinear interpolation (BI), projection onto convex sets (POCS), and iterative back projection (IBP) methods. The sharpness of the SRR results was evaluated using the gray-level variation between adjacent pixels, and the signal-to-noise ratio (SNR) of the SRR results was evaluated by using the measurement of high spatial resolution remote sensing images. For example, compared with the values obtained using the BI method, the average sharpness and SNR of the five bands obtained using the MSR-NCHOTV method were higher by 39.54% and 51.52%, respectively, and the overall accuracy (OA) and Kappa coefficient of the classification results obtained using the MSR-NCHOTV method were higher by 32.20% and 46.14%, respectively. These results showed that the MSR-NCHOTV method can effectively improve image clarity, enrich image texture details, enhance image quality, and improve image classification accuracy. Thus, the effectiveness and feasibility of using the proposed SRR method to improve the classification accuracy of remote sensing images was verified.

Improving grazing-incidence small-angle X-ray scattering-computed tomography images by total variation minimization.

Grazing-incidence small-angle X-ray scattering (GISAXS) coupled with computed tomography (CT) has enabled the visualization of the spatial distribution of nanostructures in thin films. 2D GISAXS images are obtained by scanning along the direction perpendicular to the X-ray beam at each rotation angle. Because the intensities at the q positions contain nanostructural information, the reconstructed CT images individually represent the spatial distributions of this information (e.g. size, shape, surface, characteristic length). These images are reconstructed from the intensities acquired at angular intervals over 180°, but the total measurement time is prolonged. This increase in the radiation dosage can cause damage to the sample. One way to reduce the overall measurement time is to perform a scanning GISAXS measurement along the direction perpendicular to the X-ray beam with a limited interval angle. Using filtered back-projection (FBP), CT images are reconstructed from sinograms with limited interval angles from 3 to 48° (FBP-CT images). However, these images are blurred and have a low image quality. In this study, to optimize the CT image quality, total variation (TV) regularization is introduced to minimize sinogram image noise and artifacts. It is proposed that the TV method can be applied to downsampling of sinograms in order to improve the CT images in comparison with the FBP-CT images.

Sparse View CT Image Reconstruction Based on Total Variation and Wavelet Frame Regularization

The sparse view problem of image reconstruction encountered in computed tomography (CT) is an important research issue due to its considerable potential in lowering radiation dose. Among the researches, the total variation (TV) method is especially effective in sparse view CT reconstruction for its good ability to preserve sharp edges and suppress noise. However, TV-based methods often produce undesired staircase artifacts in smooth regions of the reconstructed images since the reconstructed problem is usually ill-posed and TV regularization favors piecewise constant functions. Moreover, the image can be accurately approximated by sparse coefficients under a proper wavelet tight frame, which has good capability of sparsely estimating the piecewise smooth functions and the quality of reconstructed image can be improved by the sparse prior information. To deal with sparse view CT reconstruction problem, a minimization hybrid reconstruction model that incorporates TV with the wavelet frame has been proposed, which is to use the TV-norm of the low-frequency wavelet frame coefficients and the $\ell _{0} $ -norm of the high-frequency wavelet frame coefficients to eliminate staircase effect while maintaining sharp edges, simultaneously provide enough regularization in smooth regions. In addition, considering that the two regularization terms produce more parameters, an alternating direction method of multipliers (ADMM) algorithm has been applied to solve the minimization problem by iteratively minimization separately. Finally, compared with several iterative reconstruction methods, the experimental results demonstrate the competitiveness of the proposed method in terms of preserving edges, suppressing staircase artifacts and denoising.

Image-Domain Based Material Decomposition by Multi-Constraint Optimization for Spectral CT

As a new generation computed tomography (CT) technology, spectral CT has great potential in many aspects, especially in the identification and decomposition of materials. To achieve higher accuracy of materials decomposition, we propose a multi-constraint based nonlocal total variation (NLTV) method, named as MCNLTV. Because image-domain based material decomposition belongs to the two-step material decomposition method, the Filter Back-Projection (FBP) algorithm or SART algorithm is used to reconstruct spectral CT images in the first step. Then the material attenuation coefficient matrix is obtained from the reconstruction results. In the second step, MCNLTV regularization is utilized to obtain the material decomposition image. Both simulation experiments and real data experiments are carried out. Experiment results show that the proposed method can obtain higher accuracy of material decomposition than traditional total variation based material decomposition (TVMD), ROF-LLT regularization and direct inverse transformation (DI) for spectral CT.

Image denoising via a non-local patch graph total variation.

Total variation (TV) based models are very popular in image denoising but suffer from some drawbacks. For example, local TV methods often cannot preserve edges and textures well when they face excessive smoothing. Non-local TV methods constitute an alternative, but their computational cost is huge. To overcome these issues, we propose an image denoising method named non-local patch graph total variation (NPGTV). Its main originality stands for the graph total variation method, which combines the total variation with graph signal processing. Schematically, we first construct a K-nearest graph from the original image using a non-local patch-based method. Then the model is solved with the Douglas-Rachford Splitting algorithm. By doing so, the image details can be well preserved while being denoised. Experiments conducted on several standard natural images illustrate the effectiveness of our method when compared to some other state-of-the-art denoising methods like classical total variation, non-local means filter (NLM), non-local graph based transform (NLGBT), adaptive graph-based total variation (AGTV).

Infrared Image Super-Resolution Reconstruction Based on Quaternion and High-Order Overlapping Group Sparse Total Variation.

Owing to the limitations of imaging principles and system imaging characteristics, infrared images generally have some shortcomings, such as low resolution, insufficient details, and blurred edges. Therefore, it is of practical significance to improve the quality of infrared images. To make full use of the information on adjacent points, preserve the image structure, and avoid staircase artifacts, this paper proposes a super-resolution reconstruction method for infrared images based on quaternion total variation and high-order overlapping group sparse. The method uses a quaternion total variation method to utilize the correlation between adjacent points to improve image anti-noise ability and reconstruction effect. It uses the sparsity of a higher-order gradient to reconstruct a clear image structure and restore smooth changes. In addition, we performed regularization by using the denoising method, alternating direction method of multipliers, and fast Fourier transform theory to improve the efficiency and robustness of our method. Our experimental results show that this method has excellent performance in objective evaluation and subjective visual effects.

A Finite Element Nonoverlapping Domain Decomposition Method with Lagrange Multipliers for the Dual Total Variation Minimizations

In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem by tearing-and-interconnecting domain decomposition. Then, the continuity constraints on the subdomain interfaces are treated by introducing Lagrange multipliers. The resulting saddle point problem is solved by the first order primal-dual algorithm. We apply the proposed method to image denoising, inpainting, and segmentation problems with either $L^2$-fidelity or $L^1$-fidelity. Numerical results show that the proposed method outperforms the existing state-of-the-art methods.

Compressed sensing for high-noise astronomical image recovery

In deep exploration, we often use high-noise and high-resolution astronomical images because of long distance transmission, cosmic noise interference, or other disturbances. Designing an effective method for high-noise astronomical image denoising plays a crucial role in this field. The famous compressed sensing (CS) has shown to be a successful technique for high-resolution image reconstruction. CS is employed to solve the denoising problem in high-noise astronomical images, and a CS reconstruction model and a CS curvelet soft thresholding (NCCST) reconstruction algorithm are proposed simultaneously. In image denoising, the <italic>l</italic>₁-norm reconstruction model based on CS cannot fully consider the internal structure of the image, thus affecting the reconstruction quality. Combined with the <italic>l</italic>₁-norm reconstruction model and group sparse total variation method, the CS reconstruction model is first established. In this framework, the NCCST algorithm uses an adaptive curvelet adjustment operator proposed to select the sparse coefficients in the stage of image sparsity transform, and then a descending VisuShrink threshold is adopted to pick out these reconstructed astronomical image coefficients in each iteration. The experimental results demonstrate that the algorithm proposed can reconstruct clear images from high-noise and high-resolution astronomical images. Meanwhile, it can preserve more astronomical image details, edges, and textures. Even at a low-compression sampling ratio, this algorithm can achieve superior reconstruction performance. The proposed algorithm can be applied in the satellite receiving station to quickly and accurately reconstruct high-resolution astronomical images with high quality.

Sparsity promoting regularization for effective noise suppression in SPECT image reconstruction

The purpose of this research is to develop an advanced reconstruction method for low-count, hence high-noise, single-photon emission computed tomography (SPECT) image reconstruction. It consists of a novel reconstruction model to suppress noise while conducting reconstruction and an efficient algorithm to solve the model. A novel regularizer is introduced as the nonconvex denoising term based on the approximate sparsity of the image under a geometric tight frame transform domain. The deblurring term is based on the negative log-likelihood of the SPECT data model. To solve the resulting nonconvex optimization problem a preconditioned fixed-point proximity algorithm (PFPA) is introduced. We prove that under appropriate assumptions, PFPA converges to a local solution of the optimization problem at a global convergence rate. Substantial numerical results for simulation data are presented to demonstrate the superiority of the proposed method in denoising, suppressing artifacts and reconstruction accuracy. We simulate noisy 2D SPECT data from two phantoms: hot Gaussian spheres on random lumpy warm background, and the anthropomorphic brain phantom, at high- and low-noise levels (64k and 90k counts, respectively), and reconstruct them using PFPA. We also perform limited comparative studies with selected competing state-of-the-art total variation (TV) and higher-order TV (HOTV) transform-based methods, and widely used post-filtered maximum-likelihood expectation-maximization. We investigate imaging performance of these methods using: contrast-to-noise ratio (CNR), ensemble variance images (EVI), background ensemble noise (BEN), normalized mean-square error (NMSE), and channelized hotelling observer (CHO) detectability. Each of the competing methods is independently optimized for each metric. We establish that the proposed method outperforms the other approaches in all image quality metrics except NMSE where it is matched by HOTV. The superiority of the proposed method is especially evident in the CHO detectability tests results. We also perform qualitative image evaluation for presence and severity of image artifacts where it also performs better in terms of suppressing ‘staircase’ artifacts, as compared to TV methods. However, edge artifacts on high-contrast regions persist. We conclude that the proposed method may offer a powerful tool for detection tasks in high-noise SPECT imaging.

Single-image super-resolution via patch-based and group-based local smoothness modeling

Local smoothness and nonlocal self-similarity of natural images are two main priors in the image restoration (IR) problem. Many IR methods have widely used patch-based modeling. Recently, the concept of grouping-based technique, the nonlocal patches with similar structures, has been introduced as the basic unit of sparse representation. In the group-based methods, the nonlocal self-similarity and the local sparsity properties are combined in a unified framework using the sparsity-based techniques. In this paper, a new model is proposed which utilizes both the patch and the group as the basic units of image modeling, called patch-based and group-based local smoothness modeling (PGLSM). More, precisely, in the proposed PGLSM scheme, the local smoothness in the patch-based unit is exploited by an isotropic total variation method and the local smoothness in the group-based unit is exploited by group-based sparse representation method. In this way, a novel technique for high-fidelity single-image super-resolution (SISR) via PGLSM is proposed, called SR-PGLSM. By adding nonlocal means (NLM) as the complementary regularization term to PGLSM, another technique for SISR is modeled, called SR_PGLSM_NLM. In order to efficiently solve the above variational problems, the split Bergman iterative technique has been leveraged. Extensive experimental results validate the effectiveness and robustness of the proposed methods. Our proposed schemes can recover more fine structures and achieve better results than the competing methods with the scaling factor of 2 and 3 and for noisy images both subjectively and objectively in most cases.

Hyperspectral Image Recovery Using Nonconvex Sparsity and Low-Rank Regularizations

Hyperspectral image (HSI) restoration is an important preprocessing step in HSI data analysis to improve the image quality for subsequent applications of HSI. In this article, we introduce a spatial–spectral patch-based nonconvex sparsity and low-rank regularization method for HSI restoration. In contrast to traditional approaches based on convex penalties or nonconvex spectral penalty alone, we consider the sparsity of HSI in the spatial–spectral domain and combine the nonconvex low-rank penalty and the nonconvex 3-D total variation (TV)-like sparsity regularization to fully exploit the correlations in both spatial–spectral dimensions of the HSI data set. In addition, we propose a fast iterative variable splitting-based algorithm to effectively solve the corresponding optimization problem. Numerical experiments on both simulated and real HSI data sets demonstrate that the proposed nonconvex low-rank and TV (NonLRTV) method significantly improves the recovered image quality compared with the state-of-the-art algorithms.

Total Variation Regularization Based on Iteratively Reweighted Least-Squares Method for Electrical Resistance Tomography

The regularization method has been utilized to address the ill-posed inverse problem of electrical resistance tomography (ERT). As one of the regularization methods, the total variation (TV) regularization method has the advantage of edge-preserving. A majority of research has been focused on the study of the penalty term in the TV method. In this article, a novel TV regularization based on iteratively reweighted least squares (TV-IRLS) method is proposed, in which, $L_{1}$ -norm is applied to the fidelity term, and a weighting matrix is applied to convert the $L_{1}$ -norm to $L_{2}$ -norm when calculating the objective function, which reduces the difficulty of solving the $L_{1}$ -norm. An improved generalized cross-validation method is adopted to determine the optimal regularization parameter (RP) automatically, and an automatic method is presented for the selection of the threshold value in the weighting matrix to guarantee the accuracy and speed of the solution. Meanwhile, a scaling factor is introduced to constrain the solution and ensure the stability of the solution. For verifying the performance of the proposed TV-IRLS regularization method, both numerical simulation and static experiments are carried out in the image reconstruction of ERT through qualitative and quantitative analysis. The results demonstrate that the proposed TV-IRLS regularization method performs well in improving the quality and resolution of the reconstructed images in ERT. Besides, it is more robust to data noises compared with the Tikhonov regularization method and TV regularization method.

A Method for the Destriping of an Orbita Hyperspectral Image with Adaptive Moment Matching and Unidirectional Total Variation

The Orbita hyperspectral satellite (OHS) is the first hyperspectral satellite with surface coating technology for sensors in the world. It includes 32 bands from visible to near-infrared wavelengths. However, technology such as the fabricating process of complementary metal–oxide–semiconductor (CMOS) sensors makes the image contain a lot of random and unsystematic stripe noise, which is so bad that it seriously affects visual interpretation, object recognition and the application of the OHS data. Although a large number of stripe removal algorithms have been proposed, very few of them take into account the characteristics of OHS sensors and analyze the causes of OHS data noise. In this paper, we propose a destriping algorithm for OHS data. Firstly, we use both the adaptive moment matching method and multi-level unidirectional total variation method to remove stripes. Then a model based on piecewise linear least squares fitting is proposed to restore the vertical details lost in the first step. Moreover, we further utilize the spectral information of the OHS image, and extend our 2-D destriping method to the 3-D case. Results demonstrate that the proposed method provides the optimal destriping result on both qualitative and quantitative assessments. Moreover, the experimental results show that our method is superior to the existing single-band and multispectral destriping methods. Also, we further use the algorithm to the stripe noise removal of other real remote sensing images, and excellent image quality is obtained, which proves the universality of the algorithm.

Total variation with overlapping group sparsity and Lp quasinorm for infrared image deblurring under salt-and-pepper noise

Because of the limitations of the infrared imaging principle and the properties of infrared imaging systems, infrared images have some drawbacks, including a lack of details, indistinct edges, and a large amount of salt-andpepper noise. To improve the sparse characteristics of the image while maintaining the image edges and weakening staircase artifacts, this paper proposes a method that uses the Lp quasinorm instead of the L1 norm and for infrared image deblurring with an overlapping group sparse total variation method. The Lp quasinorm introduces another degree of freedom, better describes image sparsity characteristics, and improves image restoration. Furthermore, we adopt the accelerated alternating direction method of multipliers and fast Fourier transform theory in the proposed method to improve the efficiency and robustness of our algorithm. Experiments show that under different conditions for blur and salt-and-pepper noise, the proposed method leads to excellent performance in terms of objective evaluation and subjective visual results.

A new total variational regularization method for nonlinear inverse problems in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an imaging way of in vivo optical imaging, which is widely used in biomedical photon imaging for its higher sensitivity. For years, the propagation process of photons in tissue is simulated based on the equation of radiative transfer. In this work, we analyze an inverse problem in FMT, which uses the reading of body surface detector to reconstruct the optical parameter distribution. We propose a novel total variational regularization method to solve the absorption parameter inversion problem in FMT. The proof of the proposed method is also provided. Finally, numerical experiments demonstrate the feasibility of the proposed method.

BM3D-based total variation algorithm for speckle removal with structure-preserving in OCT images.

In this paper, we propose a total variation based on block matching 3D (BM3D-TV method), which includes the total variation regular term, the data fidelity term, and the block matching term. In addition, we also propose a fast numerical algorithm based on the split Bregman iteration for the proposed method. By assigning suitable weights to the data fidelity term and block matching term, the image noise reduction and the image structural characteristics can be matched optimally. We test the proposed method on six human retinal and one mouse skin optical coherence tomography (OCT) images respectively, and also compare it with total variation (TV) and BM3D, which were proved to be effective in denoising. The performances of these methods are quantitatively evaluated in terms of the signal-to-noise ratio, the contrast-to-noise ratio, and the averaged equivalent number of homogeneous areas at the aspects of speckle reduction and structure protection. Vast experiments show that the BM3D-TV method can effectively reduce speckle noise in OCT images, protect important structural information and improve image quality, compared with the BM3D and TV methods.

A total variation-undecimated wavelet approach to chest radiograph image enhancement

Most often medical images such as X-Rays have a low dynamic range and many of their targeted features are difficult to identify. Intensity transformations that improve image quality usually rely onwavelet denoising and enhancement typically use the technique of thresholding to obtain better quality medical images. A disadvantage of wavelet thresholding is that even though it adequately removes noise in an image, it introduces unwanted artifacts into the image near discontinuities. We utilize a total variation method and an undecimated wavelet image enhancing algorithm for improving the image quality of chest radiographs. Our approach achieves a high level chest radiograph image deniosing in lung nodules detection while preserving the important features. Moreover, our method results in a high image sensitivity that reduces the average number of false positives on a test set of medical data.

Sparse-view statistical image reconstruction with improved total variation regularization for X-ray micro-CT imaging

Sparse-view x-ray micro computed tomography (micro-CT) reconstruction algorithms via total variation (TV) optimize the data without introducing notable noise and artifacts, resulting in significant scanning time reduction while maintaining image quality. However, due to the piecewise constant assumption for the image, a conventional TV minimization often suffers from patchy artifacts in reconstructed images. Moreover, for lack of directional gradient in TV some directional information are lost. To obviate these drawbacks, in this study we develop a penalized weighted least-square (PWLS) strategy for micro-CT sparse-view image reconstruction by incorporating an adaptive weighted total variation in combination with an adaptive weighted diagonal total variation (AwTV+AwDTV) penalty term. The AwTV considers the vertical and horizontal gradients while the AwDTV uses the diagonal gradients. The associated weights which are defined based on the anisotropic edge properties of an image, are expressed as an exponential function and can be adaptively adjusted by the amount of the difference between voxel intensities to preserve the edge details. To evaluate the presented (AwTV+AwDTV)-PWLS algorithm, both qualitative and quantitative studies were performed by computer simulations and micro-CT data experiments. The Shepp-Logan phantom for computer simulation and the micro-CT water phantom and a rat skull for micro-CT experiments are employed to perform image reconstruction. To evaluate the performance of AwTV+AwDTV algorithm, we compared it with TV and AwTV reconstruction algorithms. The simulation results show that the presented (AwTV+AwDTV)-PWLS algorithm can achieve the lowest RMSE and highest PSNR, SSIM and MTF for different number of projections as compared to the AwTV and conventional TV algorithms. The micro-CT data results confirmed the superiority of the proposed (AwTV+AwDTV) method to the AwTV and TV methods for different number of projections.

Monopulse SAR angle measurement based on total variation and monotonic iterative algorithm

Synthetic aperture radar (SAR) monopulse angle measurement is an adequate method of target angle measurement in low signal-to-clutter and noise ratio. However, there is a contradiction between the instantaneous angle measurement and the SAR coherent accumulation. In this study, the authors use the total variation method to solve the above problem, and propose the monotone iterative method to enhance the efficiency of the total variation method, which is verified in the simulation.

Low dose cone-beam computed tomography reconstruction via hybrid prior contour based total variation regularization (hybrid-PCTV).

Previously, we developed a prior contour based total variation (PCTV) method to use edge information derived from prior images for edge enhancement in low-dose cone-beam computed tomography (CBCT) reconstruction. However, the accuracy of edge enhancement in PCTV is affected by the deformable registration errors and anatomical changes from prior to on-board images. In this study, we develop a hybrid-PCTV method to address this limitation to enhance the robustness and accuracy of the PCTV method. Planning-CT is used as prior images and deformably registered with on-board CBCT reconstructed by the edge preserving TV (EPTV) method. Edges derived from planning CT are deformed based on the registered deformation vector fields to generate on-board edges for edge enhancement in PCTV reconstruction. Reference CBCT is reconstructed from the simulated projections of the deformed planning-CT. Image similarity map is then calculated between reference and on-board CBCT using structural similarity index (SSIM) method to estimate local registration accuracy. The hybrid-PCTV method enhances the edge information based on a weighted edge map that combines edges from both PCTV and EPTV methods. Higher weighting is given to PCTV edges at regions with high registration accuracy and to EPTV edges at regions with low registration accuracy. The hybrid-PCTV method was evaluated using both digital extended-cardiac-torso (XCAT) phantom and lung patient data. In XCAT study, breathing amplitude change, tumor shrinkage and new tumor were simulated from CT to CBCT. In the patient study, both simulated and real projections of lung patients were used for reconstruction. Results were compared with both EPTV and PCTV methods. EPTV led to blurring bony structures due to missing edge information, and PCTV led to blurring tumor edges due to inaccurate edge information caused by errors in the deformable registration. In contrast, hybrid-PCTV enhanced edges of both bone and tumor. In XCAT study using 30 half-fan CBCT projections, compared with ground truth, relative errors (REs) were 1.3%, 1.1% and 0.9% and edge cross-correlation were 0.66, 0.68 and 0.71 for EPTV, PCTV and hybrid-PCTV, respectively. Moreover, in the lung patient data, hybrid-PCTV avoided the wrong edge enhancement in the PCTV method while maintaining enhancements of the correct edges. Hybrid-PCTV further improved the robustness and accuracy of PCTV by accounting for uncertainties in deformable registration and anatomical changes between prior and onboard images. The accurate edge enhancement in hybrid-PCTV will be valuable for target localization in radiation therapy.