Total Variation Minimization Algorithm Research Articles

Three-dimensional reconstruction of Y-IrNi rhombic dodecahedron nanoframe by STEM/EDS tomography

The structural analysis of nanocrystals via transmission electron microscopy (TEM) is a valuable technique for the material science field. Recently, two-dimensional images by scanning TEM (STEM) and energy-dispersive X-ray spectroscopy (EDS) have successfully extended to three-dimensional (3D) imaging by tomography. However, despite improving TEM instruments and measurement techniques, detector shadowing, the missing-wedge problem, X-ray absorption effects, etc., significant challenges still remain; therefore, the various required corrections should be considered and applied when performing quantitative tomography. Nonetheless, this 3D reconstruction technique can facilitate active site analysis and the development of nanocatalyst systems, such as water electrolysis and fuel cell. Herein, we present a 3D reconstruction technique to obtain tomograms of IrNi rhombic dodecahedral nanoframes (IrNi-RFs) from STEM and EDS images by applying simultaneous iterative reconstruction technique and total variation minimization algorithms. From characterizing the morphology and spatial chemical composition of the Ir and Ni atoms in the nanoframes, we were able to infer the origin of the physical and catalytic durability of IrNi-RFs. Also, by calculating the surface area and volume of the 3D reconstructed model, we were able to quantify the Ir-to-Ni composition ratio and compare it to the EDS measurement result.

Constrained one-step material decomposition reconstruction of head CT data from a silicon photon-counting prototype.

Spectral CT material decomposition provides quantitative information but is challenged by the instability of the inversion into basis materials. We have previously proposed the constrained One-Step Spectral CT Image Reconstruction (cOSSCIR) algorithm to stabilize the material decomposition inversion by directly estimating basis material images from spectral CT data. cOSSCIR was previously investigated on phantomdata. This study investigates the performance of cOSSCIR using head CT datasets acquired on a clinical photon-counting CT (PCCT) prototype. This is the first investigation of cOSSCIR for large-scale, anatomically complex, clinical PCCT data. The cOSSCIR decomposition is preceded by a spectrum estimation and nonlinear counts correction calibration step to address nonideal detectoreffects. Head CT data were acquired on an early prototype clinical PCCT system using an edge-on silicon detector with eight energy bins. Calibration data of a step wedge phantom were also acquired and used to train a spectral model to account for the source spectrum and detector spectral response, and also to train a nonlinear counts correction model to account for pulse pileup effects. The cOSSCIR algorithm optimized the bone and adipose basis images directly from the photon counts data, while placing a grouped total variation (TV) constraint on the basis images. For comparison, basis images were also reconstructed by a two-step projection-domain approach of Maximum Likelihood Estimation (MLE) for decomposing basis sinograms, followed by filtered backprojection (MLE + FBP) or a TV minimization algorithm (MLE + TVmin ) to reconstruct basis images. We hypothesize that the cOSSCIR approach will provide a more stable inversion into basis images compared to two-step approaches. To investigate this hypothesis, the noise standard deviation in bone and soft-tissue regions of interest (ROIs) in the reconstructed images were compared between cOSSCIR and the two-step methods for a range of regularization constraintsettings. cOSSCIR reduced the noise standard deviation in the basis images by a factor of two to six compared to that of MLE + TVmin , when both algorithms were constrained to produce images with the same TV. The cOSSCIR images demonstrated qualitatively improved spatial resolution and depiction of fine anatomical detail. The MLE + TVmin algorithm resulted in lower noise standard deviation than cOSSCIR for the virtual monoenergetic images (VMIs) at higher energy levels and constraint settings, while the cOSSCIR VMIs resulted in lower noise standard deviation at lower energy levels and overall higher qualitative spatial resolution. There were no statistically significant differences in the mean values within the bone region of images reconstructed by the studied algorithms. There were statistically significant differences in the mean values within the soft-tissue region of the reconstructed images, with cOSSCIR producing mean values closer to the expectedvalues. The cOSSCIR algorithm, combined with our previously proposed spectral model estimation and nonlinear counts correction method, successfully estimated bone and adipose basis images from high resolution, large-scale patient data from a clinical PCCT prototype. The cOSSCIR basis images were able to depict fine anatomical details with a factor of two to six reduction in noise standard deviation compared to that of the MLE + TVmin two-stepapproach.

Image reconstruction based on a single-pixel camera and left optimization

Subject of study. A set of schemes that can make the single-pixel camera use the prior information of the image to improve the image reconstruction effect is proposed. Method. After the measurement data of the single-pixel camera is processed by standardization or left optimization, the energy and direction information of the signal can be reflected by the processed data. According to the energy and direction information characteristics of the reconstructed image by orthogonal matching pursuit, the use of total variation minimization algorithms in a specific area can improve the image reconstruction effect. Main Results. Based on the [0,1] random matrix and the [0,1] circulant matrix, the measurement data of the single-pixel camera cannot effectively reflect the energy and direction information of the signal. After the measurement data of a single-pixel camera are processed by standardization, the energy information of the signal can be more clearly reflected. Although the direction information is also reflected, it is not very obvious. After the measurement data of the single-pixel camera are processed by left optimization, both the energy and direction information of the signal can be well reflected. Therefore, the energy and direction information of the measurement data of the single-pixel camera after left optimization can be used as criteria for evaluating the quality of the signal reconstruction. Experimental results show that based on such criteria, using orthogonal matching pursuit and total variation minimization algorithms in different columns of the measurement data can greatly improve the image reconstruction. Even if the measurement data contains noise, the signal- to-noise ratio can be improved by more than 16 dB. Practical significance. In real compressed sensing engineering applications, the measurement data and measurement matrix are the only known factors. Because the real image is unknown, the quality of the reconstruction can only be evaluated based on long-term work experience or logical reasoning on the basis of the results of simulation experiments. Based on the energy and direction information of the measurement data of the single-pixel camera after left optimization, the result of image reconstruction can be evaluated objectively.

High Spatial Resolution Tomographic Gamma Scanning Reconstruction With Improved MLEM Iterative Algorithm Based on Split Bregman Total Variation Regularization

High spatial resolution tomographic gamma scanning (TGS) reconstruction is very important for the radioassay of drummed low-level radioactive waste. High spatial resolution means that the divided voxels are finer. Due to the large size of the drum, the traditional image reconstruction method based on complete samples takes a long time to scan. To limit the scanning time of the drum, sparse sampling is required. The maximum likelihood expectation maximization (MLEM) is widely used in TGS image reconstruction from projection data, but for high spatial resolution TGS imaging, its quality is insufficient to accurately describe the media boundary and determine radioactivity. The improved MLEM algorithm based on total variation (TV) regularization, such as the MLEM- TV minimization (TVM) algorithm, has been applied to reconstruct high spatial resolution TGS images. The split Bregman algorithm can quickly solve the partial differential equations of TV regularization. In this work, the split Bregman anisotropic TV (SBATV) and the split Bregman isotropic TV (SBITV) are the first time adopted to improve the iterative process of the MLEM algorithm, which are MLEM- SBATV and MLEM- SBITV. Experimental results show that both the MLEM- SBATV algorithm and the MLEM- SBITV algorithm can accurately reconstruct high spatial resolution TGS transmission images with sparse sampling. The MLEM- SBITV algorithm performs better in reconstructing the TGS emission images from sparse sampling than the traditional MLEM, MLEM- TVM, and MLEM- SBATV algorithms, increasing radionuclide positioning and radioactivity reconstruction accuracy.

A fast-iterative reconstruction algorithm for sparse angle CT based on compressed sensing

When conducting computed tomography (CT) image reconstruction, the existing algorithms do not analyze the physical and mathematical bases of CT image reconstruction, which leads to the lack of detailed information of reconstructed images and the problem of poor reconstruction effect. In this research, compressed sensing theory is applied in the process of fast-iterative CT reconstruction. The physical and mathematical basis for CT reconstruction is analyzed. A fast-iterative reconstruction algorithm for sparse angle CT images is proposed. Combined with algebraic iterative algorithm and gradient total variation minimization algorithm, CT reconstruction problem is transformed into gradient optimal solution problem, to complete the fast-iterative reconstruction of sparse angle CT images. Experimental results show that the proposed algorithm has high signal-to-noise ratio for CT image reconstruction, small reconstruction error, and good reconstruction effect for sparse angle CT images.

A two-stage variational jump point detection algorithm for real estate analysis

Real estate is one of the most important forms of portfolio, which plays an essential role in the economy of Hong Kong. Extensive investigations indicate that jump points in the private domestic price indices are subject to various factors such as international events, regional incidents, and government policies. Detecting jump points and identifying their relationships with these factors are indispensable since such findings can facilitate policymakers and investors to look forward. In this paper, we propose a novel two-stage variational methodology using the total variation minimization algorithm and derivative-based detector with the thresholding function for detecting jump points in the Hong Kong private domestic price indices. Our algorithm can weaken statistical fluctuation of the price indices via the total variation formulation and accurately detect jump points based on its rate of change. Comparative experimental results based on the monthly private domestic price indices from January 2010 to July 2020 reveal that the proposed method can detect 40 jump points corresponding to the aforementioned factors whereas the current state-of-the-art empirical mode decomposition approach can only detect 29 jump points, which indicates the superior performance of the proposed method.

Correlative STEM-HAADF and STEM-EDX tomography for the 3D morphological and chemical analysis of semiconductor devices

3D analysis of an arsenic-doped silicon fin sample is performed in a transmission electron microscope (TEM). High angle annular dark-field scanning TEM (STEM-HAADF) and energy-dispersive x-ray spectroscopy (STEM-EDX) modes are used simultaneously to extract 3D complementary multi-resolution information about the sample. The small pixel size and angular step chosen for the STEM-HAADF acquisition yield reliable information about the sidewall roughness and the arsenic clusters’ average volume. The chemical sensitivity of STEM-EDX tomography gives insights into the 3D conformality of the arsenic implantation and its depth distribution. Non-negative matrix factorization method is employed to identify the chemical phases present in the sample automatically. A total variation minimization algorithm, implemented in 3D, produces high-quality volumes from heavily undersampled datasets. The extension of this correlative approach to electron energy-loss spectroscopy STEM tomography and atom probe tomography is also discussed.

Research on the modulation factor of the constrained TV for optical deflection tomography reconstruction

Under the condition of extremely under-sampling, the iterative algorithm based on the total variation(TV) constrain is common for the reconstruction of optical deflection tomography. In the algorithm, the minimization of TV is implemented by the gradient descent approach, and the constraints are performed by projection on convex sets (POCS). In this paper, we discuss the modulation factor of the gradient descent method, and propose a new adaptive modulation factor for gradient descent. Experiments were done on a series of modulation factor functions under different projection angles and noise environment, and the experimental results were compared and analysed. And the algorithm proposed in this paper is compared with the soft threshold filter TV minimization algorithm. The results demonstrate that the adaptive modulation factor proposed in this paper can automatically and continuously update the value of the modulation factor, reduce the reconstruction error and improve the reconstruction quality.

Computational ghost imaging via adaptive deep dictionary learning.

Ghost imaging has gone through from quantum to classical pseudothermal to computational field over the last two decades. As a kernel part in computational ghost imaging (CGI), the reconstruction algorithm plays a decisive role in imaging quality and system practicality. In order to introduce more prior knowledge into the reconstruction algorithm, existing research adds image patch prior into CGI and improves the imaging efficiency. In this paper, the total variation minimization algorithm via adaptive deep dictionary learning (TVADDL) is proposed to update an adaptive deep dictionary through the CGI reconstruction process. The proposed algorithm framework is able to capture more precise texture features with a multi-layer architecture dictionary and adapt the learned dictionary by gradient descent on CGI reconstruction loss value. The results of simulation and experiment show that TVADDL can achieve higher peak signal-to-noise ratio than the algorithms without patch prior and the algorithms using the shallow dictionary or non-adaptive deep dictionary.

Sparse-view CT reconstruction based on gradient directional total variation

The sparse-view problem of image reconstruction encountered in computed tomography (CT) is an important research issue due to its considerable potential in decreasing radiation dose and improving detection efficiency. Among the current sparse-view CT reconstruction algorithms, iterative reconstruction algorithms that consider total variation (TV) regularization exhibit good performance. However, the gradient difference direction is singular or fixed in conventional TV algorithms, leading to undesired artefacts when minimizing TV in sparse-view CT. To effectively address this issue, based on TV minimization, the gradient difference directional information is introduced as additional prior information in the regularization term, and a new gradient-based directional total variation minimization algorithm is proposed, which adaptively chooses mutative gradient directions to calculate the directional difference operators, and calculates the sum of the direction difference operators. In addition, to solve the fault tolerance and computational load, considering redundant blocks of reconstructed image, we can estimate the gradient directional information of each subblock via the gradient approximation method. For simplicity, the proposed algorithm is termed the BDTV algorithm. To demonstrate the superiority of the proposed algorithm, the simulation data and actual CT data from different algorithms are compared, and the results indicate that the proposed algorithm is effective at preserving details that are lost in the TV minimization, artefact reduction and noise suppression in sparse-view CT.

基于天牛须搜索的全变分最小化算法在计算机断层成像内重建中的应用

基于天牛须搜索的全变分最小化算法在计算机断层成像内重建中的应用

Terahertz wave near-field compressive imaging with a spatial resolution of over λ/100.

We demonstrate terahertz (THz) wave near-field imaging with a spatial resolution of ∼4.5 μm using single-pixel compressive sensing enabled by femtosecond-laser (fs-laser) driven vanadium dioxide (VO2)-based spatial light modulator. By fs-laser patterning a 180nm thick VO2 nanofilm with a digital micromirror device, we spatially encode the near-field THz evanescent waves. With single-pixel Hadamard detection of the evanescent waves, we reconstructed the THz wave near-field image of an object from a serial of encoded sequential measurements, yielding improved signal-to-noise ratio by one order of magnitude over a raster-scanning technique. Further, we demonstrate that the acquisition time was compressed by a factor of over four with 90% fidelity using a total variation minimization algorithm. The proposed THz wave near-field imaging technique inspires new and challenging applications such as cellular imaging.

Reconstruction of Compressed-Sensed Multiview Video With Disparity- and Motion-Compensated Total Variation Minimization

Compressed sensing (CS) is the theory and practice of sub-Nyquist sampling of sparse signals of interest. Exact reconstruction may then be possible with much fewer than the Nyquist-required number of data. In this paper, we consider a multiview video system in which multiple cameras at different locations perform independent CS to simultaneously capture different views of a scene. At the decoder, we propose a disparity- and motion-compensated total variation minimization algorithm to jointly reconstruct the multiview video sequence. The experimental results show that the proposed joint reconstruction algorithm successfully exploits simultaneously intra-frame, inter-frame, and inter-view sparsity and significantly outperforms existing independent-view reconstruction, residue-view reconstruction, and motion-adaptive reconstruction algorithms.

Performance evaluation of image denoising developed using convolutional denoising autoencoders in chest radiography

When processing medical images, image denoising is an important pre-processing step. Various image denoising algorithms have been developed in the past few decades. Recently, image denoising using the deep learning method has shown excellent performance compared to conventional image denoising algorithms. In this study, we introduce an image denoising technique based on a convolutional denoising autoencoder (CDAE) and evaluate clinical applications by comparing existing image denoising algorithms. We train the proposed CDAE model using 3000 chest radiograms training data. To evaluate the performance of the developed CDAE model, we compare it with conventional denoising algorithms including median filter, total variation (TV) minimization, and non-local mean (NLM) algorithms. Furthermore, to verify the clinical effectiveness of the developed denoising model with CDAE, we investigate the performance of the developed denoising algorithm on chest radiograms acquired from real patients. The results demonstrate that the proposed denoising algorithm developed using CDAE achieves a superior noise-reduction effect in chest radiograms compared to TV minimization and NLM algorithms, which are state-of-the-art algorithms for image noise reduction. For example, the peak signal-to-noise ratio and structure similarity index measure of CDAE were at least 10% higher compared to conventional denoising algorithms. In conclusion, the image denoising algorithm developed using CDAE effectively eliminated noise without loss of information on anatomical structures in chest radiograms. It is expected that the proposed denoising algorithm developed using CDAE will be effective for medical images with microscopic anatomical structures, such as terminal bronchioles.

A separable quadratic surrogate total variation minimization algorithm for accelerating accurate CT reconstruction from few-views and limited-angle data.

Total variation minimization (TVM) is a popular and useful method for accurate CT reconstruction from few-views and limited-angle data. However, the optimization procedure of previous TVM-based algorithms is very time-consuming. The purpose of this paper was to accelerate the high image quality CT reconstruction from few-views and limited-angle data. A new optimization algorithm based on the optimization transfer principle is proposed. The proposed algorithm uses TVM as the regularization term of the cost function that ensures the quality of the CT image reconstructed from few-views and limited-angle data. Additionally, half of the square of the difference between the original projection and the forward projection is used as the fidelity term. We then proved that the regularization term, i.e., 2-norm TV, is a convex function. Based on the convexity of the regularization and fidelity terms, a separable quadratic surrogate (SQS) function was proposed to substitute the regularization and fidelity terms. The solution of the cost function can be obtained by minimizing the SQS function and building the next SQS function at the minimum point. Both numerical simulations and simulations using real experimental data showed that the proposed algorithm reconstruct high-quality CT image from few-views and limited-angle data. The differences between the image reconstructed by the proposed algorithm and the images reconstructed by the previous algorithms are very small. However, the proposed algorithm required less than 1/10 time of the computational time of the previous algorithms. The image quality is not assessed in a rigorous way. The proposed algorithm can greatly accelerate the accurate CT reconstruction from few-views and limited-angle data relative to previous algorithms.

CT reconstruction from few-views with anisotropic edge-guided total variance

To overcome the oversmoothing drawback in the edge areas when reconstructing few-view CT with total variation (TV) minimization, in this paper, we propose an anisotropic edge-guided TV minimization framework for few-view CT reconstruction. In the framework, anisotropic TV is summed with pre-weighted image gradient and then used as the object function for minimizing. It includes edge-guided TV minimization (EGTV) and edge-guided adaptive-weighted TV minimization (EGAwTV) algorithms. For EGTV algorithm, the weights of the TV discretization term are updated by anisotropic edge information detected from the image, whereas the weights for EGAwTV are determined based on edge information and local image-intensity gradients. To solve the minimization problem of the proposed algorithm, a similar TV-based minimization implementation is developed to address the raw data fidelity and other constraints. The evaluation results using both computer simulations with the Shepp-Logan phantom and experimental data from a physical phantom demonstrate that the proposed algorithms exhibit noticeable gains in the merits of spatial resolution compared with the conventional TV and other modified TV algorithms.

X-ray CT image reconstruction from few-views via total generalized p-variation minimization.

Total variation (TV)-based CT image reconstruction, employing the image gradient sparsity, has shown to be experimentally capable of reducing the X-ray sampling rate and removing the unwanted artifacts, yet may cause unfavorable over-smoothing and staircase effects by the piecewise constant assumption. In this paper, we present a total generalized p-variation (TGpV) regularization model to adaptively preserve the edge information while avoiding the staircase effect. The new model is solved by splitting variables with an efficient alternating minimization scheme. With the utilization of generalized p-shrinkage mappings and partial Fourier transform, all the subproblems have closed solutions. The proposed method shows excellent properties of edge preserving as well as the smoothness features by the consideration of high order derivatives. Experimental results indicate that the proposed method could avoid the mentioned effects and reconstruct more accurately than both the TV and TGV minimization algorithms when applied to a few-view problem.

Holographic display based on compressive sensing (Invited Paper)

We propose a method to improve the quality of the reconstructed images based on compressive sensing principles. The pseudo-inverse matrix and the total variation minimization algorithms are combined to reduce the sampling number of the computer generated hologram. Numerical simulations are performed and the results indicate that the peak signal to noise ratio is increased and the sampling ratio is decreased at the same time for holographic display.

Accelerated 4D flow imaging using randomly undersampled echo planer imaging with compressed-sensing reconstruction

Background 4D flow imaging using phase contrast CMR (PC CMR) allows visualization and quantification of blood flow. One of the major limitations of 4D flow imaging is its long scan time (in the order of 10-20 min). In this study, we sought to investigate an accelerate 4D flow imaging sequence that combines an efficient data sampling strategy using echo planar imaging (EPI) with randomly undersampled 3D k-space sampling pattern. The randomly undersampled k-space data are then reconstructed using compressed sensing (CS). Methods Figure 1 shows the k-space acquisition strategy. Similar to regular EPI acquisition, the k-space data are divided into multiple segments. For each segment, the profiles are undersampled with the CS rate such that all EPI segments have the same undersampling pattern. The proposed EPI random sampling strategy was implemented. Seven subjects were recruited (26 ± 12 years; 3 males) for 4D flow CMR on a 1.5T Philips Achieva magnet. Images were acquired axially using a GRE sequence (FOV =3 40 ×2 80 ×6 0 mm 3 ,r esolution =2× 2×3m m 3 ,T R/TE/a = 7.4/3.8 ms/20°, EPI factor = 3, Turbo Factor =2 , CS rate =3 ) in av olume covering the ascending and descending aorta, and the aortic bifurcation. Only foot-head flow encoding was used to provide an adequate temporal resolution of 30 ms for the measurements. A single beam navigator placed on the right hemi-diaphragm was used to gate the acquisition with the respiratory cycle. The nominal scan time for this scan was 3:30 minutes at 70 bpm assuming 100% gating efficiency (vs. 8:40 minutes if standard parallel imaging with rate 4 was used). For each subject, the 4D-PC scan was followed by a standard breath-hold 2D-PC scan with the same flow encoding direction (FOV = 340 × 280 mm2, resolution = 2 × 2 mm 2 , slice thickness = 5 mm 3 , SENSE rate = 2.5). The acquired 2D slice is selected from the previously obtained 4D scan and approximately at the aortic bifurcation. Data are then transferred to a separate station where the CS reconstruction was performed using a total variation minimization algorithm. Next, flow quantifications were performed on both the ascending and the descending aorta for all acquisitions and then compared between the 2D scans and the corresponding slices in the 4D scans.

Sequentially reweighted TV minimization for CT metal artifact reduction

Metal artifact reduction has long been an important topic in x-ray CT image reconstruction. In this work, the authors propose an iterative method that sequentially minimizes a reweighted total variation (TV) of the image and produces substantially artifact-reduced reconstructions. A sequentially reweighted TV minimization algorithm is proposed to fully exploit the sparseness of image gradients (IG). The authors first formulate a constrained optimization model that minimizes a weighted TV of the image, subject to the constraint that the estimated projection data are within a specified tolerance of the available projection measurements, with image non-negativity enforced. The authors then solve a sequence of weighted TV minimization problems where weights used for the next iteration are computed from the current solution. Using the complete projection data, the algorithm first reconstructs an image from which a binary metal image can be extracted. Forward projection of the binary image identifies metal traces in the projection space. The metal-free background image is then reconstructed from the metal-trace-excluded projection data by employing a different set of weights. Each minimization problem is solved using a gradient method that alternates projection-onto-convex-sets and steepest descent. A series of simulation and experimental studies are performed to evaluate the proposed approach. Our study shows that the sequentially reweighted scheme, by altering a single parameter in the weighting function, flexibly controls the sparsity of the IG and reconstructs artifacts-free images in a two-stage process. It successfully produces images with significantly reduced streak artifacts, suppressed noise and well-preserved contrast and edge properties. The sequentially reweighed TV minimization provides a systematic approach for suppressing CT metal artifacts. The technique can also be generalized to other "missing data" problems in CT image reconstruction.