Anisotropic Total Variation Research Articles

Phase asymmetry ultrasound despeckling with fractional anisotropic diffusion and total variation.

We propose an ultrasound speckle filtering method for not only preserving various edge features but also filtering tissue-dependent complex speckle noises in ultrasound images. The key idea is to detect these various edges using a phase congruence-based edge significance measure called phase asymmetry (PAS), which is invariant to the intensity amplitude of edges and takes 0 in non-edge smooth regions and 1 at the idea step edge, while also taking intermediate values at slowly varying ramp edges. By leveraging the PAS metric in designing weighting coefficients to maintain a balance between fractional-order anisotropic diffusion and total variation (TV) filters in TV cost function, we propose a new fractional TV framework to not only achieve the best despeckling performance with ramp edge preservation but also reduce the staircase effect produced by integral-order filters. Then, we exploit the PAS metric in designing a new fractional-order diffusion coefficient to properly preserve low-contrast edges in diffusion filtering. Finally, different from fixed fractional-order diffusion filters, an adaptive fractional order is introduced based on the PAS metric to enhance various weak edges in the spatially transitional areas between objects. The proposed fractional TV model is minimized using the gradient descent method to obtain the final denoised image. The experimental results and real application of ultrasound breast image segmentation show that the proposed method outperforms other state-of-the-art ultrasound despeckling filters for both speckle reduction and feature preservation in terms of visual evaluation and quantitative indices. The best scores on feature similarity indices have achieved 0.867, 0.844 and 0.834 under three different levels of noise, while the best breast ultrasound segmentation accuracy in terms of the mean and median dice similarity coefficient are 96.25% and 96.15%, respectively.

A nonconvex and nonsmooth anisotropic total variation model for image noise and blur removal

In this paper, a nonconvex and nonsmooth anisotropic total variation model is proposed, which can provide a very sparser representation of the derivatives of the function in horizontal and vertical directions. The new model can preserve sharp edges and alleviate the staircase effect often arising in total variation (TV) based models. We use graduated nonconvexity (GNC) algorithm to solve the proposed nonconvex and nonsmooth minimization problem. Starting with a convex initialization, it uses a family of nonconvex functional to gradually approach the original nonconvex functional. For each subproblem, we use function splitting technique to separately address the nonconvex and nonsmooth properties, and use augmented Lagrangian method (ALM) to solve it. Experiments are conducted for both synthetic and real images to demonstrate the effectiveness of the proposed model. In addition, we compare it with several state-of-the-art models in denoising and deblurring applications. The numerical results show that our model has the best performance in terms of PSNR and MSSIM indexes.

An iterative reconstruction algorithm for pole figure inversion using total variation regularization

This paper describes a new discrete method for inverting X-ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal-volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward-projection model is combined with an anisotropic total variation term to iteratively determine the ODF. The efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.

Morphological Component Image Restoration by Employing Bregmanized Sparse Regularization and Anisotropic Total Variation

Image deblurring is a fundamental problem in imaging field which often needs to recover the important structure of images. This paper addresses the image deblurring problem by considering an image as a combination of its cartoon (the piecewise smooth part of the image) and texture (the oscillation part of the image) components. To recover both of these parts, we propose the use of coupled analysis-based sparse representations to regularize the cartoon structure and the texture part of the image. We apply anisotropic total variation with a quadratic term to enhance the edges existing in the cartoon part. Furthermore, we develop a multivariable Bregman optimization method to solve the proposed image restoration model by combining the alternating minimization method and the split Bregman iteration. The experiments show that the proposed algorithm not only performs well for image decomposition, but also outperforms the previously established methods in terms of the visual residual error, the structure similarity index and the peak signal-to-noise ratio for image deblurring.

Step phase reconstruction using an anisotropic total variation regularization method in a diffraction phase microscopy.

This paper presents an approach to estimate the phase distribution with step features or edge characteristics from an interferogram obtained in diffraction phase microscopy. The proposed approach relies on formulation of a cost function for the interferogram and subsequent application of anisotropic total variation regularization based optimization. In our approach, the cost function is minimized by using a proximal gradient method based iterative approach with alternative updates of the amplitude and the phase. The performance of the proposed approach for retrieving phase maps with rapid edge variations is shown via numerical simulations. Further, the experimental validity of the proposed method is demonstrated for surface topography in diffraction phase microscopy.

Expectation propagation for Poisson data

The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation propagation for approximating the posterior distribution formed from the Poisson likelihood function and a Laplace type prior distribution, e.g. the anisotropic total variation prior. The approach iteratively yields a Gaussian approximation, and at each iteration, it updates the Gaussian approximation to one factor of the posterior distribution by moment matching. We derive explicit update formulas in terms of one-dimensional integrals, and also discuss stable and efficient quadrature rules for evaluating these integrals. The method is showcased on two-dimensional PET images.

Single-arc VMAT optimization for dual-layer MLC

Dual-layer multi-leaf collimator (DLMLC) has recently attracted renewed interest due to its good balance among resolution, low leakage, and high fabricability. However, existing progressive sampling based volumetric modulated arc therapy (VMAT) algorithm is ineffective for DLMLC, requiring more arcs to achieve dosimetry comparable to VMAT plans with higher resolution single-layer MLC (SLMLC). In this study, we develop a novel single-arc VMAT optimization framework to take advantage of the unique DLMLC characteristics fully. Direct aperture optimization (DAO) for single-arc DLMLC VMAT was formulated as a least square dose fidelity objective, along with an anisotropic total variation term to regulate the fluence smoothness and a single segment term for forming simple apertures. The DAO was solved through alternating optimization approach. The DLMLC deliverability constraint and the MLC leaf speed constraint were formulated as the optimization constraints and solved using a graph optimization algorithm. Feasibility of the proposed framework was tested on a brain, a lung, and a prostate cancer patient. The framework was further adapted for a simultaneous integrated boost (SIB) case. The single-arc DLMLC-10 mm (leaf width) plan was compared against single-arc SLMLC VMAT plans including SLMLC-5mm, SLMLC-10mm, and SLMLC with 10 mm leaf width and 5 mm leaf step size (SLMLC-10mm-5mm). Compared with the SLMLC-10mm plan and the SLMLC-10mm-5mm plan, with the same target coverage, the DLMLC-10 mm plan reduced R50 by 30.7% and 10.0%, the average max OAR dose by 5.79% and 3.7% of the prescription dose, and the average mean OAR dose by 4.18% and 2.1% of the prescription dose, respectively. The plan quality is comparable to that of the SLMLC-5mm plan. The novel single-arc VMAT optimization framework for DLMLC utilizes two MLC layers to improve the effective modulation resolution and afford more sophisticated modulation. Consequently, DLMLC VMAT achieves superior dosimetry to SLMLC VMAT with the same leaf width.

Local Frequency Interpretation and Non-Local Self-Similarity on Graph for Point Cloud Inpainting.

As 3D scanning devices and depth sensors mature, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation and heritage reconstruction. However, point clouds usually exhibit holes of missing data, mainly due to the limitation of acquisition techniques and complicated structure. Further, point clouds are defined on irregular non- Euclidean domains, which is challenging to address especially with conventional signal processing tools. Hence, leveraging on recent advances in graph signal processing, we propose an efficient point cloud inpainting method, exploiting both the local smoothness and the non-local self-similarity in point clouds. Specifically, we first propose a frequency interpretation in graph nodal domain, based on which we derive the smoothing and denoising properties of a graph-signal smoothness prior in order to describe the local smoothness of point clouds. Secondly, we explore the characteristics of non-local self-similarity, by globally searching for the most similar area to the missing region. The similarity metric between two areas is defined based on the direct component and the anisotropic graph total variation of normals in each area. Finally, we formulate the hole-filling step as an optimization problem based on the selected most similar area and regularized by the graph-signal smoothness prior. Besides, we propose voxelization and automatic hole detection methods for the point cloud prior to inpainting. Experimental results show that the proposed approach outperforms four competing methods significantly, both in objective and subjective quality.

Image denoising via a new anisotropic total-variation-based model

To keep local structures when denoising the degraded image, we propose a new anisotropic total variation (TV)-based restored model based on the combination of the gradient operator ∇ and the adaptive weighted matrix ,T into the ℓ1-norm regularized term. The weighted matrix ,T depends on the edge indicator function along the x and y-axis directions, so this matrix can rotate the direction of the gradient operator tending to bigger weight and the proposed model can thus describe the local features in image. In order to cope with this nonsmooth model, we employ the alternating direction method of multipliers (ADMM) to solve it. Relying on the convexity, the convergence of the proposed numerical algorithm is provided as well. Denoising experiments on the artificial images and benchmark images show the effectiveness of the proposed model by comparing it to other well-known total-variation-based models in terms of the restored quality.

A Krasnoselskii-Mann Algorithm With an Improved EM Preconditioner for PET Image Reconstruction.

This paper presents a preconditioned Krasnoselskii-Mann (KM) algorithm with an improved EM preconditioner (IEM-PKMA) for higher-order total variation (HOTV) regularized positron emission tomography (PET) image reconstruction. The PET reconstruction problem can be formulated as a three-term convex optimization model consisting of the Kullback-Leibler (KL) fidelity term, a nonsmooth penalty term, and a nonnegative constraint term which is also nonsmooth. We develop an efficient KM algorithm for solving this optimization problem based on a fixed-point characterization of its solution, with a preconditioner and a momentum technique for accelerating convergence. By combining the EM precondtioner, a thresholding, and a good inexpensive estimate of the solution, we propose an improved EM preconditioner that can not only accelerate convergence but also avoid the reconstructed image being "stuck at zero." Numerical results in this paper show that the proposed IEM-PKMA outperforms existing state-of-the-art algorithms including, the optimization transfer descent algorithm and the preconditioned L-BFGS-B algorithm for the differentiable smoothed anisotropic total variation regularized model, the preconditioned alternating projection algorithm, and the alternating direction method of multipliers for the nondifferentiable HOTV regularized model. Encouraging initial experiments using clinical data are presented.

Image edge detection method based on anisotropic diffusion and total variation models

In this study, a novel image edge detection technique based on the combination of total variation (TV) and anisotropic diffusion (PM) models is presented. In the proposed technique, the authors first use the gradient magnitude to eliminate the noise, then utilise the adaptive weight function to detect the edges of the image. The adaptive weight function has a high ability to adapt and change according to the areas information (edges or flats areas). More specifically, TV filter is applied on the areas which suffer from double and false edges, whereas, anisotropic diffusion filter is applied on the areas which suffer from weak and discontinuous edges. Applying TV filter on the double edges areas will allow one to remove most of the false edges, and thus to obtain much sharper edges. While, applying anisotropic diffusion filter on the discontinuous edges areas will lead to obtaining robust and continuous edges. Consequently, less false edges besides high localisation accuracy were obtained. Experimental results demonstrate the superiority of the new approach in terms of removing the false edges and improving the localisation accuracy of the edges. As objective quantitative performance measures, the peak signal-to-noise ratio (PSNR) and Pratt's figure of merit (FOM) were used.

Nonblind Image Deblurring Based on Bi-Composition Decomposition by Local Smoothness and Nonlocal Self-Similarity Priors

Image deblurring is a classical inverse problem in image processing and computer vision. The vital task is to construct the proper image prior model to obtain the high-quality restored image with salient edges and rich details. A new nonblind image deblurring method by combining local smoothness and nonlocal self-similarity of natural images in the regularization framework is proposed. First, the observed image is decomposed into two components: structure component and detail component by a global gradient extraction scheme. Second, the four-directional anisotropic total variation regularization satisfying the local smoothness property is adopted for the structure component, and a new nonlocal statistical modeling for self-similarity is used for the detail component, respectively. At last, the split Bregman-based iteration algorithm and four-directional fast gradient projection algorithm are introduced to optimize the proposed L 1 -regularized problem. The extensive experiments demonstrate the efficiency and viability of the proposed method for preserving salient edges and texture details while alleviating the artifacts.

ALIGNet

The process of aligning a pair of shapes is a fundamental operation in computer graphics. Traditional approaches rely heavily on matching corresponding points or features to guide the alignment, a paradigm that falters when significant shape portions are missing. These techniques generally do not incorporate prior knowledge about expected shape characteristics, which can help compensate for any misleading cues left by inaccuracies exhibited in the input shapes. We present an approach based on a deep neural network, leveraging shape datasets to learn a shape-aware prior for source-to-target alignment that is robust to shape incompleteness. In the absence of ground truth alignments for supervision, we train a network on the task of shape alignment using incomplete shapes generated from full shapes for self-supervision. Our network, called ALIGNet , is trained to warp complete source shapes to incomplete targets, as if the target shapes were complete, thus essentially rendering the alignment partial-shape agnostic . We aim for the network to develop specialized expertise over the common characteristics of the shapes in each dataset, thereby achieving a higher-level understanding of the expected shape space to which a local approach would be oblivious. We constrain ALIGNet through an anisotropic total variation identity regularization to promote piecewise smooth deformation fields, facilitating both partial-shape agnosticism and post-deformation applications. We demonstrate that ALIGNet learns to align geometrically distinct shapes and is able to infer plausible mappings even when the target shape is significantly incomplete. We show that our network learns the common expected characteristics of shape collections without over-fitting or memorization, enabling it to produce plausible deformations on unseen data during test time.

Destriping of Multispectral Remote Sensing Image Using Low-Rank Tensor Decomposition

Multispectral image (MSI) destriping is a challenging topic and has been attracting much research attention in remote sensing area due to its importance in improving the image qualities and subsequent applications. The existing destriping methods mainly focus on matrix-based modeling representation, which fails to fully discover the correlation of the stripe component in both spatial dimensions. In this paper, we propose a novel low-rank tensor decomposition framework based MSI destriping method by decomposing the striped image into the image component and stripe component. Specifically, for the image component, we use the anisotropic spatial unidirectional total variation (TV) and spectral TV regularization to enhance the piecewise smoothness in both spatial and spectral domains. Moreover, for the stripe component, we adopt tensor Tucker decomposition and $\ell _{2,1}$ -norm regularization to model the spatial correlation and group sparsity characteristic among all bands, respectively. An efficient algorithm using the augmented Lagrange multiplier method is designed to solve the proposed optimization model. Experiments under various cases of simulated data and real-world data demonstrate the effectiveness of the proposed model over the existing single-band and MSI destriping methods in terms of the qualitative and quantitative.

A Novel 3D Anisotropic Total Variation Regularized Low Rank Method for Hyperspectral Image Mixed Denoising

Known to be structured in several patterns at the same time, the prior image of interest is always modeled with the idea of enforcing multiple constraints on unknown signals. For instance, when dealing with a hyperspectral restoration problem, the combination of constraints with piece-wise smoothness and low rank has yielded promising reconstruction results. In this paper, we propose a novel mixed-noise removal method by employing 3D anisotropic total variation and low rank constraints simultaneously for the problem of hyperspectral image (HSI) restoration. The main idea of the proposed method is based on the assumption that the spectra in an HSI lies in the same low rank subspace and both spatial and spectral domains exhibit the property of piecewise smoothness. The low rankness of an HSI is approximately exploited by the nuclear norm, while the spectral-spatial smoothness is explored using 3D anisotropic total variation (3DATV), which is defined as a combination of 2D spatial TV and 1D spectral TV of the HSI cube. Finally, the proposed restoration model is effectively solved by the alternating direction method of multipliers (ADMM). Experimental results of both simulated and real HSI datasets validate the superior performance of the proposed method in terms of quantitative assessment and visual quality.

Planar array magnetic induction tomography further improvement

PurposeMagnetic induction tomography (MIT) is a tomographic imaging technique with a wide range of potential industrial applications. Planar array MIT is a convenient setup but unable to access freely from the entire periphery as it only collects measurements from one surface, so it remains challenging given the limited data. This study aims to assess the use of sparse regularization methods for accurate position and depth detection in planar array MIT.Design/methodology/approachThe most difficult challenges in MIT are to solve the inverse and forward problems. The inversion of planar MIT is severely ill-posed due to limited access data. Thus, this paper posed a total variation (TV) problem and solved it efficiently with the Split Bregman formulation to overcome this difficulty. Both isotropic and anisotropic TV formulations are compared to Tikhonov regularization with experimental MIT data.FindingsThe results show that Tikhonov method failed or underestimated the object position and depth. Both isotropic and anisotropic TV led to accurate recovery of depth and position.Originality/valueThere are numerous potential applications for planar array MIT where access to the materials under testing is restrict. Sparse regularization methods are a promising approach to improving depth detection for limited MIT data.

A compound method for random noise attenuation

ABSTRACTRandom noise attenuation, preserving the events and weak features by improving signal‐to‐noise ratio and resolution of seismic data are the most important issues in geophysics. To achieve this objective, we proposed a novel seismic random noise attenuation method by building a compound algorithm. The proposed method combines sparsity prior regularization based on shearlet transform and anisotropic variational regularization. The anisotropic variational regularization which is based on the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation attenuates noises while preserving the events of seismic data and it effectively avoids the fine‐scale artefacts due to shearlets from the restored seismic data. The proposed method is formulated as a convex optimization problem and the split Bregman iteration is applied to solve the optimization problem. To verify the effectiveness of the proposed method, we test it on several synthetic seismic datasets and real datasets. Compared with three methods (the linear combination of weighted anisotropic total variation and anisotropic second‐order total variation, shearlets and shearlet‐based weighted anisotropic total variation), the numerical experiments indicate that the proposed method attenuates random noises while alleviating artefact and preserving events and features of seismic data. The obtained result also confirms that the proposed method improves the signal‐to‐noise ratio.

Scale-Space Anisotropic Total Variation for Limited Angle Tomography

This paper addresses streak reduction in limited angle tomography. Although the iterative reweighted total variation (wTV) algorithm reduces small streaks well, it is rather inept at eliminating large ones since total variation (TV) regularization is scale-dependent and may regard these streaks as homogeneous areas. Hence, the main purpose of this paper is to reduce streak artifacts at various scales. We propose the scale-space anisotropic total variation (ssaTV) algorithm in two different implementations. The first implementation (ssaTV-1) utilizes an anisotropic gradient-like operator which uses 2s neighboring pixels along the streaks' normal direction at each scale s. The second implementation (ssaTV-2) makes use of anisotropic down-sampling and up-sampling operations, similarly oriented along the streaks' normal direction, to apply TV regularization at various scales. Experiments on numerical and clinical data demonstrate that both ssaTV algorithms reduce streak artifacts more effectively and efficiently than wTV, particularly when using multiple scales.

Fast multi-trace impedance inversion using anisotropic total p-variation regularization in the frequency domain

In this article, we find that the transformational matrix between the natural logarithm of the acoustic impedance and the reflection coefficient is a Toeplitz matrix. As a result, we can convert the matrix multiplication into convolution operation according to properties of the Toeplitz matrix. In this way, we calculate the convolution of matrices through a dot product operation in the frequency domain based on the convolution theorem. Thus a fast multi-trace impedance inversion method by using two dimensional fast Fourier transform in the frequency domain is proposed, which can greatly improve the inversion speed. Considering the non-convex Lp (0 ≤ p < 1) quasi-norm is more suitable for sparse optimization than the L1 norm, anisotropic total variation regularization based on the Lp quasi-norm is used to improve the inversion result. Synthetic seismic data and field data inversion results show that the proposed method improves the inversion speed more than ten times compared with the multi-trace inversion method with total variation (TV) regularization in the time domain. At the same time, the proposed method has the advantages over the inversion methods with TV regularization in the time domain of less inversion error and better depiction of thin layers.

A novel optimization framework for VMAT with dynamic gantry couch rotation

Existing volumetric modulated arc therapy (VMAT) optimization using coplanar arcs is highly efficient but usually dosimetrically inferior to intensity modulated radiation therapy (IMRT) with optimized non-coplanar beams. To achieve both dosimetric quality and delivery efficiency, we proposed in this study, a novel integrated optimization method for non-coplanar VMAT (4πVMAT). 4πVMAT with direct aperture optimization (DAO) was achieved by utilizing a least square dose fidelity objective, along with an anisotropic total variation term for regularizing the fluence smoothness, a single segment term for imposing simple apertures, and a group sparsity term for selecting beam angles. Continuous gantry/couch angle trajectories were selected using the Dijkstra’s algorithm, where the edge and node costs were determined based on the maximal gantry rotation speed and the estimated fluence map at the current iteration, respectively. The couch–gantry–patient collision space was calculated based on actual machine geometry and a human subject 3D surface. Beams leading to collision are excluded from the DAO and beam trajectory selection (BTS). An alternating optimization strategy was implemented to solve the integrated DAO and BTS problem. The feasibility of 4πVMAT using one full-arc or two full-arcs was tested on nine patients with brain, lung, or prostate cancer. The plan was compared against a coplanar VMAT (2πVMAT) plan using one additional arc and collimator rotation. Compared to 2πVMAT, 4πVMAT reduced the average maximum and mean organs-at-risk dose by 9.63% and 3.08% of the prescription dose with the same target coverage. R50 was reduced by 23.0%. Maximum doses to the dose limiting organs, such as the brainstem, the major vessels, and the proximal bronchus, were reduced by 8.1 Gy (64.8%), 16.3 Gy (41.5%), and 19.83 Gy (55.5%), respectively. The novel 4πVMAT approach affords efficient delivery of non-coplanar arc trajectories that lead to dosimetric improvements compared with coplanar VMAT using more arcs.