Edge-preserving Total Variation Research Articles

An edge-preserving total nuclear variation minimization algorithm in EPR image reconstruction

ObjectiveCurrently, slow scanning speed has become a technical bottleneck limiting the development of electron paramagnetic resonance imaging (EPRI), a novel oxygen imaging modality. Image reconstruction from sparse-view projections is an important imaging configuration to achieve fast scanning in EPRI. However, EPR images reconstructed from sparse-view projections using traditional analytic algorithms suffer from sparse artifacts, causing severe image degradation. In this work, we aim to use an optimization-based approach to achieve high-precision sparse reconstruction for EPRI. Methods. Inspired by the success of total nuclear variation (TVN) for denoising multi-channel spectral CT images and adaptive-weighted total variation (awTV) for improving the edge-preserving performance of TV, we proposed an edge-preserving total nuclear variation (EPTVN) minimization algorithm for sparse reconstruction in EPRI. The EPTVN combines the advantage of TVN in modelling structural similarity and low-rank prior between multi-channel images for denoising with the advantage of awTV for edge-preserving, which can better protect the edge structure of images while suppressing sparse artifacts. Results. We designed two numerical phantoms with different properties, a piecewise-constant phantom and a gradient phantom, and a physical phantom, and then performed inverse crime, simulation study and real-data study. Experimental results show that the EPTVN minimization algorithm can reconstruct more accurate EPR images from sparse-view projections for both the numerical and physical phantoms. Significance. The proposed method can effectively suppress sparse artifacts and protect edge structures of reconstructed images, thus achieving high-precision sparse-view reconstruction for EPRI. The insights of this work can also be applied to multi-channel image denoising tasks.

Scaled, Inexact, and Adaptive Generalized FISTA for Strongly Convex Optimization

We consider a variable metric and inexact version of the FISTA-type algorithm considered in (Chambolle, Pock, 2016, Calatroni, Chambolle, 2019) for the minimization of the sum of two (possibly strongly) convex functions. The proposed algorithm is combined with an adaptive (non-monotone) backtracking strategy, which allows for the adjustment of the algorithmic step-size along the iterations in order to improve the convergence speed. We prove a linear convergence result for the function values, which depends on both the strong convexity moduli of the two functions and the upper and lower bounds on the spectrum of the variable metric operators. We validate the proposed algorithm, named Scaled Adaptive GEneralized FISTA (SAGE-FISTA), on exemplar image denoising and deblurring problems where edge-preserving Total Variation (TV) regularization is combined with Kullback-Leibler-type fidelity terms, as it is common in applications where signal-dependent Poisson noise is assumed in the data.

Projected Newton method for noise constrained ℓ p regularization

Choosing an appropriate regularization term is necessary to obtain a meaningful solution to an ill-posed linear inverse problem contaminated with measurement errors or noise. The ℓ p norm covers a wide range of choices for the regularization term since its behavior critically depends on the choice of p and since it can easily be combined with a suitable regularization matrix. We develop an efficient algorithm that simultaneously determines the regularization parameter and corresponding ℓ p regularized solution such that the discrepancy principle is satisfied. We project the problem on a low-dimensional generalized Krylov subspace and compute the Newton direction for this much smaller problem. We illustrate some interesting properties of the algorithm and compare its performance with other state-of-the-art approaches using a number of numerical experiments, with a special focus of the sparsity inducing ℓ 1 norm and edge-preserving total variation regularization.

Material Identification in Presence of Metal for Baggage Screening

Dual-energy imaging has emerged as a superior way to recognize materials in X-ray computed tomography. To estimate material properties such as effective atomic number and density, one often generates images in terms of basis functions. This requires decomposition of the dual-energy sinograms into basis sinograms, and subsequently reconstructing the basis images. However, the presence of metal can distort the reconstructed images. In this paper we investigate how photoelectric and Compton basis functions, and synthesized monochromatic basis (SMB) functions behave in the presence of metal and its effect on estimation of effective atomic number and density. Our results indicate that SMB functions, along with edge-preserving total variation regularization, show promise for improved material estimation in the presence of metal. The results are demonstrated using both simulated data as well as data collected from a dualenergy medical CT scanner.

Edge-preserving total variation regularization for dual-energy CT images

Edge-preserving total variation regularization for dual-energy CT images

Multisensor inverse synthetic aperture radar imaging and phase adjustment based on combination of sparsity and total variation

Compared with conventional single-sensor inverse synthetic aperture radar (ISAR), multisensor ISAR technique can reduce the integration time and improve the resolution of the image effectively. One solution is investigated for multisensor ISAR imaging and phase adjustment with sparse measurements via the compressed sensing (CS) framework. In most previous research of CS-based radar imaging, the target is modeled as a few strong scatterers that randomly distributed in the imaging plane and only the image domain sparsity assumption is used in image reconstruction, which will result in the degradation of image quality, especially when the measurements are limited. In practical ISAR imaging, some strong scatterers facing the radar always form flat regions in high-resolution radar imaging. Therefore, the dependence and redundancy of these scatterers can also be exploited in target reconstruction. We utilize this information and propose a multiplatform ISAR imaging method that combines the image domain sparsity and edge-preserving total variation to improve the image quality with sparse measurements. Meanwhile, an iterative minimization approach is also used to process the phase adjustment with the discontinuous echo data. Experimental results show the effectiveness of the proposed method.

Low dose CBCT reconstruction via prior contour based total variation (PCTV) regularization: a feasibility study

Purpose: compressed sensing reconstruction using total variation (TV) tends to over-smooth the edge information by uniformly penalizing the image gradient. The goal of this study is to develop a novel prior contour based TV (PCTV) method to enhance the edge information in compressed sensing reconstruction for CBCT.Methods: the edge information is extracted from prior planning-CT via edge detection. Prior CT is first registered with on-board CBCT reconstructed with TV method through rigid or deformable registration. The edge contours in prior-CT is then mapped to CBCT and used as the weight map for TV regularization to enhance edge information in CBCT reconstruction. The PCTV method was evaluated using extended-cardiac-torso (XCAT) phantom, physical CatPhan phantom and brain patient data. Results were compared with both TV and edge preserving TV (EPTV) methods which are commonly used for limited projection CBCT reconstruction. Relative error was used to calculate pixel value difference and edge cross correlation was defined as the similarity of edge information between reconstructed images and ground truth in the quantitative evaluation.Results: compared to TV and EPTV, PCTV enhanced the edge information of bone, lung vessels and tumor in XCAT reconstruction and complex bony structures in brain patient CBCT. In XCAT study using 45 half-fan CBCT projections, compared with ground truth, relative errors were 1.5%, 0.7% and 0.3% and edge cross correlations were 0.66, 0.72 and 0.78 for TV, EPTV and PCTV, respectively. PCTV is more robust to the projection number reduction. Edge enhancement was reduced slightly with noisy projections but PCTV was still superior to other methods. PCTV can maintain resolution while reducing the noise in the low mAs CatPhan reconstruction. Low contrast edges were preserved better with PCTV compared with TV and EPTV.Conclusion: PCTV preserved edge information as well as reduced streak artifacts and noise in low dose CBCT reconstruction. PCTV is superior to TV and EPTV methods in edge enhancement, which can potentially improve the localization accuracy in radiation therapy.

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.

An adaptive random compressive partial sampling method with TV recovery

Different from standard sampling strategy in compressive sensing (CS), we present a compressive partial sampling framework called adaptive-random sampling and recovery (ASR) for image. It could faithfully recover images by hybridizing random samples with edge-extracted pixels with much lower sampling rate. The new framework preserves edge pixels containing essential information of images, and meanwhile employs the edge-preserving total variation (TV) regularizer. Assisted with the edges, three steps are adopted to recover the high-quality image. First, we extract the edges of a coarse image recovered with completely random measurements in our sampling framework. Then, the TV algorithm in the CS theory is employed for solving the Lagrangian regularization problem. Finally, we refine the coarse image to obtain a high-quality one with both the extracted edges and previous random measurements. Experimental results show that the novel ASR strategy achieves significant performance improvements over the current state-of-the-art schemes.

A Recursive Born Approach to Nonlinear Inverse Scattering

The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.

PET Reconstruction With an Anatomical MRI Prior Using Parallel Level Sets.

The combination of positron emission tomography (PET) and magnetic resonance imaging (MRI) offers unique possibilities. In this paper we aim to exploit the high spatial resolution of MRI to enhance the reconstruction of simultaneously acquired PET data. We propose a new prior to incorporate structural side information into a maximum a posteriori reconstruction. The new prior combines the strengths of previously proposed priors for the same problem: it is very efficient in guiding the reconstruction at edges available from the side information and it reduces locally to edge-preserving total variation in the degenerate case when no structural information is available. In addition, this prior is segmentation-free, convex and no a priori assumptions are made on the correlation of edge directions of the PET and MRI images. We present results for a simulated brain phantom and for real data acquired by the Siemens Biograph mMR for a hardware phantom and a clinical scan. The results from simulations show that the new prior has a better trade-off between enhancing common anatomical boundaries and preserving unique features than several other priors. Moreover, it has a better mean absolute bias-to-mean standard deviation trade-off and yields reconstructions with superior relative l2-error and structural similarity index. These findings are underpinned by the real data results from a hardware phantom and a clinical patient confirming that the new prior is capable of promoting well-defined anatomical boundaries.

An ordered‐subsets proximal preconditioned gradient algorithm for edge‐preserving PET image reconstruction

In iterative positron emission tomography (PET) image reconstruction, the statistical variability of the PET data precorrected for random coincidences or acquired in sufficiently high count rates can be properly approximated by a Gaussian distribution, which can lead to a penalized weighted least-squares (PWLS) cost function. In this study, the authors propose a proximal preconditioned gradient algorithm accelerated with ordered subsets (PPG-OS) for the optimization of the PWLS cost function and develop a framework to incorporate boundary side information into edge-preserving total variation (TV) and Huber regularizations. The PPG-OS algorithm is proposed to address two issues encountered in the optimization of PWLS function with edge-preserving regularizers. First, the second derivative of this function (Hessian matrix) is shift-variant and ill-conditioned due to the weighting matrix (which includes emission data, attenuation, and normalization correction factors) and the regularizer. As a result, the paraboloidal surrogate functions (used in the optimization transfer techniques) end up with high curvatures and gradient-based algorithms take smaller step-sizes toward the solution, leading to a slow convergence. In addition, preconditioners used to improve the condition number of the problem, and thus to speed up the convergence, would poorly act on the resulting ill-conditioned Hessian matrix. Second, the PWLS function with a nondifferentiable penalty such as TV is not amenable to optimization using gradient-based algorithms. To deal with these issues and also to enhance edge-preservation of the TV and Huber regularizers by incorporating adaptively or anatomically derived boundary side information, the authors followed a proximal splitting method. Thereby, the optimization of the PWLS function is split into a gradient descent step (upgraded by preconditioning, step size optimization, and ordered subsets) and a proximal mapping associated with boundary weighted TV and Huber regularizers. The proximal mapping is then iteratively solved by dual formulation of the regularizers. The convergence performance of the proposed algorithm was studied with three different diagonal preconditioners and compared with the state-of-the-art separable paraboloidal surrogates accelerated with ordered-subsets (SPS-OS) algorithm. In simulation studies using a realistic numerical phantom, it was shown that the proposed algorithm depicts a considerably improved convergence rate over the SPS-OS algorithm. Furthermore, the results of bias-variance and signal-to-noise evaluations showed that the proposed algorithm with anatomical edge information depicts an improved performance over conventional regularization. Finally, the proposed PPG-OS algorithm is used for image reconstruction of a clinical study with adaptively derived boundary edge information, demonstrating the potential of the algorithm for fast and edge-preserving PET image reconstruction. The proposed PPG-OS algorithm shows an improved convergence rate with the ability of incorporating additional boundary information in regularized PET image reconstruction.

An efficient decision-based and edge-preserving method for salt-and-pepper noise removal

In this paper, we propose an improved two-stage scheme for the removal of salt-and-pepper noise based on an efficient impulse detector and the edge-preserving total variation inpainting model. We test the proposed algorithm on the four images corrupted by salt-and-pepper noise with a wide range of noise levels varied from 10% to 95%, and compare it with the six other well known filters. Further, we evaluate quantitatively the performance of these filters with the peak signal-to-noise ratio (PSNR), the measure of structural similarity (SSIM) and the image enhancement factor (IEF). The experimental results have demonstrated that the proposed filter performs impressively in noise suppression and edge preservation.

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.

GPU-based Iterative CT Reconstruction via Edge-preserving Total Variation Regula

High radiation dose in CT scans increases a lifetime risk of cancer and is always a major concern. Two possible ways to decrease the dose are using fewer projections for reconstruction or lower the X-ray tube current. The former may require new hardware while the latter can be readily implemented. However, conventional filtered backprojection (FBP) reconstruction algorithms failed in both ways. Recently, iterative reconstruction algorithm with Total Variation (TV) regularization has been developed to reduce the imaging dose.

TU‐D‐204B‐04: 4DCT Reconstruction from Undersampled Projections Using Edge‐Preserving Total Variation and Non Local Means

Purpose: Four‐dimensional computed tomography (4DCT) is widely used in radiotherapy planning for thorax and upper abdomen to take respiratory motion into consideration. However, its high radiation dose becomes a major concern and impedes its wide application. In this work, we proposed an iterative 4DCT reconstruction algorithm with both an Edge‐Preserving Total Variation (EPTV) regularization and a Non‐Local Means (NLM) regularization to accurately reconstruct 4DCT images from highly undersampled projections to reduce imaging dose. Methods and Materials: In 4DCT, images of neighboring phases usually share similar structures, though these structures are apart from each other spatially in neighboring phases due to breathing motion. To take this temporal correlation into the reconstruction process, we propose to use NLM as a temporal regularization in 4DCT reconstruction. For this purpose, each phase of the 4DCT is iteratively reconstructed by a modified total variation method, namely EPTV method. NLM regularization is imposed in each iteration step to enhance image quality. Specifically, we consider every possible small patch in all phases. Patches spatially close to each other in successive phases are weighted averaged, with high weights assigned to similar patches. We tested our reconstruction algorithm on a NCAT phantom at thorax region and a real patient 4DCT thorax data. 4DCT images obtained from our EPTV+NLM approach are compared with those obtained from the EPTV method. Relative errors are computed and are used to evaluate the reconstruction quality. Results: About 40 x‐ray projections for each breathing phase are enough to accurately reconstruct the 4DCT image in both test cases. The images reconstructed with NLM regularization are found to have lower relative error and hence better image quality than those reconstructed otherwise. Conclusions: Our proposed EPTV+NLM method is a robust approach for the 4DCT reconstruction, where NLM as a temporal regularization can considerably enhance the reconstructed image quality.

TU-B-201B-03: CT Reconstruction from Undersampled Projection Data Via Edge-Preserving Total Variation Regularization

Purpose: High radiation dose in CT scans increases a lifetime risk of cancer and is always a major concern. Recently, iterative reconstruction algorithm with Total Variation (TV) regularization has been developed to reconstructCTimages from highly undersampled data in order to reduce the imaging dose. Nonetheless, CTimagesreconstructed in this approach are sometimes over‐smoothed and edge information is lost. In this work, we developed an iterative CTreconstruction algorithm with edge preserving TV regularization to accurately reconstructCTimages from highly undersampled data. Methods and Material: The CTimage is reconstructed by minimizing TV norm under a constraint posed by few X‐ray projections. To avoid over‐smoothed edge, an edge‐preserving penalty was proposed and added to the TV norm. We tested our reconstruction algorithm on 4 cases, namely, Shepp‐Logan head phantom, NCAT phantom at thorax region, a real patient head case and a real patient lung case. The reconstruction accuracy was evaluated using relative error and edge correlation coefficient. Conventional FDK filtered backprojection algorithm and conventional TV regularization method without edge preserving term were also studied for comparison purpose. Results: It is found that 30 equi‐angle projections are enough for reconstructing the CTimages in phantom experiments and 40 projections for real patient experiments. Our approach outperforms the FDK algorithm and the conventional TV algorithm in terms of the relative error and the edge correlation coefficient in all the four test cases. In particular, the reconstructed images using our approach contain less noise and sharp edges. Conclusion: The edge‐preserving TV performs better in CTimages reconstruction. About 30∼40 X‐ray projections are enough to accurately reconstruct the CTimages, which implies a potential radiation dose reduction by about 20 times.