Staircase Artifacts Research Articles

Transcranial ultrasound modeling using the spectral-element method.

This work explores techniques for accurately modeling the propagation of ultrasound waves in lossy fluid-solid media, such as within transcranial ultrasound, using the spectral-element method. The objectives of this work are twofold, namely, (1) to present a formulation of the coupled viscoacoustic-viscoelastic wave equation for the spectral-element method in order to incorporate attenuation in both fluid and solid regions and (2) to provide an end-to-end workflow for performing spectral-element simulations in transcranial ultrasound. The matrix-free implementation of this high-order finite-element method is very well-suited for performing waveform-based ultrasound simulations for both transcranial imaging and focused ultrasound treatment thanks to its excellent accuracy, flexibility for dealing with complex geometries, and computational efficiency. The ability to explicitly mesh distinct interfaces between regions with high impedance contrasts eliminates staircasing artifacts, which are otherwise non-trivial to mitigate within discretization approaches based on regular grids. This work demonstrates the efficacy of this modeling technique for transcranial ultrasound through a number of numerical examples. While the examples in this work primarily focus on transcranial applications, this type of modeling is equally relevant within other soft tissue-bone systems such as in limb or spine imaging.

MISNeR: Medical Implicit Shape Neural Representation for Image Volume Visualisation

AbstractThree‐dimensional visualisation of mesh reconstruction of the medical images is commonly used for various clinical applications including pre / post‐surgical planning. Such meshes are conventionally generated by extracting the surface from volumetric segmentation masks. Therefore, they have inherent limitations of staircase artefacts due to their anisotropic voxel dimensions. The time‐consuming process for manual refinement to remove artefacts and/or the isolated regions further adds to these limitations. Methods for directly generating meshes from volumetric data by template deformation are often limited to simple topological structures, and methods that use implicit functions for continuous surfaces, do not achieve the level of mesh reconstruction accuracy when compared to segmentation‐based methods. In this study, we address these limitations by combining the implicit function representation with a multi‐level deep learning architecture. We introduce a novel multi‐level local feature sampling component which leverages the spatial features for the implicit function regression to enhance the segmentation result. We further introduce a shape boundary estimator that accelerates the explicit mesh reconstruction by minimising the number of the signed distance queries during model inference. The result is a multi‐level deep learning network that directly regresses the implicit function from medical image volumes to a continuous surface model, which can be used for mesh reconstruction from arbitrary high volume resolution to minimise staircase artefacts. We evaluated our method using pelvic computed tomography (CT) dataset from two public sources with varying z‐axis resolutions. We show that our method minimised the staircase artefacts while achieving comparable results in surface accuracy when compared to the state‐of‐the‐art segmentation algorithms. Furthermore, our method was 9 times faster in volume reconstruction than comparable implicit shape representation networks.

Cauchy noise removal using high-order total variation and overlapping group sparsity

Image denoising presents a significant challenge in computer vision, aiming to eliminate unwanted noise from images and restore their original quality. Cauchy noise, characterized by its heavy-tailed distribution, poses a unique hurdle among various types of noise. While several denoising models have been proposed, Total Variation (TV)-based methods, such as the Remove Cauchy Noise model, are widely used for their effectiveness. However, these approaches often suffer from issues such as oversmoothing, staircase artifacts, and the introduction of false details. To address these limitations, recent research has explored the combination of high-order TV with Overlapping Group Sparsity (OGS), showing promising results in noise removal. Inspired by this, our article introduces a novel Cauchy denoising model. Our approach leverages OGS and directional higher-order TV to effectively remove Cauchy noise while preserving image details and minimizing aliasing and smoothing artifacts. The Chambolle-Pock algorithm efficiently solves the underlying optimization problem. Through qualitative and quantitative evaluations, including visualization and parameter measurements, we demonstrate the competitiveness of our model compared to existing methods.

Edge-preserving image restoration based on a weighted anisotropic diffusion model

Partial differential equation-based methods have been widely applied in image restoration. The anisotropic diffusion model has a good noise removal capability without affecting significant edges. However, existing anisotropic diffusion-based models closely depend on the diffusion coefficient function and threshold parameter. This paper proposes a new weighted anisotropic diffusion coefficient model with multiple scales, and it has a higher speed of closing to X-axis and exploits adaptive threshold parameters. Meanwhile, the proposed algorithm is verified to be suitable for multiple types of noise. Numerical metrics and visual comparison of simulation experiments show the proposed model has significant superiority in edge-preserving and staircase artifacts reducing over the existing anisotropic diffusion-based techniques.

Generalized nonconvex nonsmooth four-directional total variation with overlapping group sparsity for image restoration

In this paper, we address the challenge of image deblurring in the presence of Gaussian noise. To achieve high-quality image restoration, we introduce an optimization framework that integrates four-directional total variation regularization, overlapping group sparsity, and a range of nonconvex penalties. This novel model effectively mitigates the staircase artifacts associated with total variation regularization and enhances restoration quality by leveraging domain-specific information about image pixels. Compared to the ℓ1 norm, the nonconvex penalty applied to overlapping groups promotes sparsity in image gradients at the group level. To solve this nonconvex optimization problem, we propose a proximal alternating reweighted minimization algorithm, which has a proximal alternating scheme with a reweighted approximation of its subproblem. Theoretically, we establish that the sequences generated by the proposed algorithm converge to a critical point using the Kurdyka–Łojasiewicz property. Experimental results validate the superiority of our approach over competing methods.

Impulse Noise Image Restoration Using Nonconvex Variational Model and Difference of Convex Functions Algorithm.

In this article, the problem of impulse noise image restoration is investigated. A typical way to eliminate impulse noise is to use an L1 norm data fitting term and a total variation (TV) regularization. However, a convex optimization method designed in this way always yields staircase artifacts. In addition, the L1 norm fitting term tends to penalize corrupted and noise-free data equally, and is not robust to impulse noise. In order to seek a solution of high recovery quality, we propose a new variational model that integrates the nonconvex data fitting term and the nonconvex TV regularization. The usage of the nonconvex TV regularizer helps to eliminate the staircase artifacts. Moreover, the nonconvex fidelity term can detect impulse noise effectively in the way that it is enforced when the observed data is slightly corrupted, while is less enforced for the severely corrupted pixels. A novel difference of convex functions algorithm is also developed to solve the variational model. Using the variational method, we prove that the sequence generated by the proposed algorithm converges to a stationary point of the nonconvex objective function. Experimental results show that our proposed algorithm is efficient and compares favorably with state-of-the-art methods.

Boosting MR Image Impulse Noise Removal With Overlapping Group Sparse Fractional-Order Total Variation and Minimax Concave Penalty

The acquisition and transmission of magnetic resonance images are susceptible to noise, particularly impulse noise. Although the method based on the ℓ0-norm and overlapping group sparse total variation (ℓ0-OGSTV) is effective for impulse noise image restoration, it can only mitigate the staircase artifacts to a certain extent. To boost the impulse noise removal performance of ℓ0-OGSTV, we propose a new restoration model that consists of two terms. Specifically, in the first term, we keep using the ℓ0-norm as the data fidelity term to eliminate impulse noise. In the second term, we first introduce an overlapping group sparsity fractional-order total variation regularizer to eliminate staircase artifacts while preserving structural information. Then, we adopt the minimax-concave penalty to further accurately estimate the image edges. Finally, we employ an alternate direction method of multipliers to solve the proposed optimization model. Clinical experiments demonstrate its effectiveness in denoising medical images.

Joint first and second order total variation decomposition for remote sensing images destriping

ABSTRACT Stripe noise remains a significant source of errors and image quality degradation in remote sensing systems. A prominent approach for tackling this problem is the first-order Total Variation (TV) regularization, which has a proven efficiency in dealing with stripe noise. Unfortunately, denoised images, in this case, may suffer from texture loss and staircase artefacts around smooth areas. In this paper, a novel image decomposition scheme is proposed to tackle these drawbacks. This decomposition is based on the use of directional first- and second-order TV regularizers that are employed to separate the clear image from the stripe component while considering the directionality and smoothness of the latter. The proposed model is solved using a Chambolle-based algorithm and its performance is compared to traditional destriping methods using different noise structures and intensities. The results have shown comparable performance to the existing state-of-the-art methods with some improvements in structure preservation and noise cancellation.

Mixed Gaussian-impulse noise removal using non-convex high-order TV penalty

To restore images with clear edge details and no staircase artifacts from degraded versions, this paper incorporates the ℓ2 plus ℓ0 data fidelity and non-convex high-order total variation regularizer to establish an optimization model for eliminating mixed Gaussian-impulse noise. Among them, the ℓ2 fidelity is adopted to suppress Gaussian noise, while the ℓ0-norm is more suitable for detecting and removing impulse noise. In addition, the non-convex regularization displays excellent performance in overcoming the staircase effect and preserving edge details. Computationally, by using the iteratively reweighted ℓ1 algorithm and variable splitting method, this work designs a modified alternating minimization method to solve the optimization problem we construct. In theory, the convergence proof of our resulting algorithm is also presented. Finally, in the experimental section, we conduct extensive numerical experiments on degraded images and compare with other existing techniques. From the intuitive effects and restoration accuracy, it follows that our newly proposed method is effective and competitive for image deblurring and mixed noise removal.

Edge-aware nonlinear diffusion-driven regularization model for despeckling synthetic aperture radar images

Speckle noise corrupts synthetic aperture radar (SAR) images and limits their applications in sensitive scientific and engineering fields. This challenge has attracted several scholars because of the wide demand of SAR images in forestry, oceanography, geology, glaciology, and topography. Despite some significant efforts to address the challenge, an open-ended research question remains to simultaneously suppress speckle noise and to restore semantic features in SAR images. Therefore, this work establishes a diffusion-driven nonlinear method with edge-awareness capabilities to restore corrupted SAR images while protecting critical image features, such as contours and textures. The proposed method incorporates two terms that promote effective noise removal: (1) high-order diffusion kernel; and (2) fractional regularization term that is sensitive to speckle noise. These terms have been carefully designed to ensure that the restored SAR images contain stronger edges and well-preserved textures. Empirical results show that the proposed model produces content-rich images with higher subjective and objective values. Furthermore, our model generates images with unnoticeable staircase and block artifacts, which are commonly found in the classical Perona–Malik and Total variation models.

Nonconvex fractional order total variation based image denoising model under mixed stripe and Gaussian noise

In this paper, we propose a minimization-based image denoising model for the removal of mixed stripe and Gaussian noise. The objective function includes the prior information from both the stripe noise and image. Specifically, we adopted a unidirectional regularization term and a nonconvex group sparsity term for the stripe noise component, while we utilized a nonconvex fractional order total variation (FTV) regularization for the image component. The priors for stripes enable adequate extraction of periodic or non-periodic stripes from an image in the presence of high levels of Gaussian noise. Moreover, the nonconvex FTV facilitates image restoration with less staircase artifacts and well-preserved edges and textures. To solve the nonconvex problem, we employed an iteratively reweighted $ \ell_1 $ algorithm, and then the alternating direction method of multipliers was adopted for solving subproblems. This led to an efficient iterative algorithm, and its global convergence was proven. Numerical results show that the proposed model provides better denoising performance than existing models with respect to visual features and image quality evaluations.

Group sparse representation and saturation-value total variation based color image denoising under multiplicative noise

<abstract><p>In this article, we propose a novel group-based sparse representation (GSR) model for restoring color images in the presence of multiplicative noise. This model consists of a convex data-fidelity term, and two regularizations including GSR and saturation-value-based total variation (SVTV). The data-fidelity term is suitable for handling heavy multiplicative noise. GSR enables the retention of textures and details while sufficiently removing noise in smooth regions without producing the staircase artifacts engendered by total variation-based models. Furthermore, we introduce a multi-color channel-based GSR that involves coupling between three color channels. This avoids the generation of color artifacts caused by decoupled color channel-based methods. SVTV further improves the visual quality of restored images by diminishing certain artifacts induced by patch-based methods. To solve the proposed nonconvex model and its subproblem, we exploit the alternating direction method of multipliers, which contributes to an efficient iterative algorithm. Numerical results demonstrate the outstanding performance of the proposed model compared to other existing models regarding visual aspect and image quality evaluation values.</p></abstract>

Cuttlefish: Pushing the Limits of Graphical 3-D Printing.

This article presents Cuttlefish, a 3-D printer driver developed at the Fraunhofer Institute for Computer Graphics Research IGD. Cuttlefish maximizes the reproduction quality of shape and appearance in multimaterial 3-D printing systems. It controls various printing systems and material sets, including color, transparent, and flexible materials. The article provides an overview of Cuttlefish's graphical 3-D printing pipeline and focuses on its unique features: Displaced signed distance fields for robust voxelization of objects not designed for 3-D printing, joint color and translucency reproduction, accurate color and translucency characterization, shape dithering to eliminate quantization-based staircase artifacts, and support for displacement maps and constructive solid geometry operations. The article concludes by showcasing applications of Cuttlefish in printing replacement faces for stop-motion animation, large-scale figurine production, and prosthetic eye printing.

An Image-Denoising Framework Using ℓq Norm-Based Higher Order Variation and Fractional Variation with Overlapping Group Sparsity

As one of the most significant issues in imaging science, image denoising plays a major role in plenty of image processing applications. Due to the ill-posed nature of image denoising, total variation regularization is widely used in image denoising problems for its capability to suppress noise and preserve image edges. Nevertheless, traditional total variation will inevitably yield undesirable staircase artifacts when applied to recorded images. Inspired by the success of ℓq norm minimization and overlapping group sparsity in image denoising, and the effective staircase artifacts removal by fractional total variation, the hybrid model which combines the fractional order total variation with overlapping group sparsity and higher order total variation with ℓq norm is developed in this paper to restore images corrupted by Gaussian noise. An efficient algorithm based on the parallel linear alternating direction method of multipliers is developed for solving the corresponding model and the numerical experiments demonstrate the effectiveness of the proposed approach against several state-of-the-art methods, in terms of peak signal-to-noise ratio and structure similarity index measure values.

Magnetic Resonance Image Denoising Based on Laplacian Prior Sparsity Constraint and Nonconvex Second-Order TV Penalty

Magnetic resonance (MR) imaging is considered as a very powerful imaging modality in clinical examination, but the process of image acquisition and transmission will be affected by noise, resulting in the degradation of imaging quality. In this paper, based on the Laplacian prior sparsity constraint and the nonconvex second order total variation (TV) penalty, we propose a MR images denoising model which consists of three terms. Specifically, in the first term, we use the L2-norm as the fidelity term to control the proximity between the observed image and the recovered MR image. Then, we introduce the Laplacian sparse prior constraint as the second term to mitigate the staircase artifacts in the recovered image. In the third term, we adopt the nonconvex second-order TV penalty to preserve important textures and edges. Finally, we use the alternating direction method of multipliers to solve the corresponding minimization problem. Comparative experiments on clinical data demonstrate the effectiveness of our approach in terms of PSNR and SSIM values.

Sparse representation learning for fault feature extraction and diagnosis of rotating machinery

Early fault feature extraction and fault diagnosis are of great importance for predictive maintenance of rotating machinery. To accurately extract early fault features from original noisy signals, a novel joint sparse representation learning method is developed in this paper, this method is based on the proposed nonlocal generalized minimax-concave (GMC) penalty and generalized fraction-order total variation (FTV) regularization. The motivation for this research is to leverage the benefits of joint regularizations. The proposed nonlocal GMC penalty regularization tends to preserve weak fault features, promote sparsity and avoid underestimating the amplitude of periodic fault impulses. Simultaneously, the proposed generalized FTV regularization tends to remove fault irrelevant noise and reduce staircase artifacts. Therefore, the proposed model can effectively extract early fault features from original noisy signals. The performance of the proposed model is verified by a series of experiments. In two fault diagnosis tasks, the peak signal-to-noise ratio (PSNR) of the proposed method reaches − 5 dB and − 8 dB, respectively. Compared with state-of-the-art methods, the PSNR has been improved by at least 2 dB, comparison results show that the proposed model has superior performance for early fault feature extraction.

Non-convex TGV regularized [formula omitted]-norm fidelity model for impulse noise removal

Aiming at preserving the structural features of images from degradations contaminated by impulse noise, this article proposes a novel strategy that inherits the characteristics of ℓ0-norm data fidelity and non-convex total generalized variation regularizer. The ℓ0-norm fidelity is more conducive to removing impulse noise, while the non-convex total generalized variation penalty term is both good at eliminating the staircase artifacts and maintaining neat contours. In addition, a modified alternating minimization algorithm is constructed to optimize the solution of the developed model, which merges the popular iteratively reweighted ℓ1 algorithm and primal-dual approach. Meanwhile, the convergence property of the designed algorithm is briefly presented. Finally, in the experimental part, exhaustive simulation experiments are carried out to demonstrate the effectiveness of the introduced scheme for removing impulse noise. As observed in the numerical results, our scheme possesses obvious superiorities in both visual effects and quantitative comparisons, in contrast to some existing popular image restoration methods.

Impulse noise removal by using a nonconvex TGV regularizer and nonconvex fidelity

With the aim of acquiring high-quality restored images, this paper derives a novel nonconvex variational model for the removal of impulse noise. The investigated solver integrates the superiorities of nonconvex second-order total generalized variation (TGV) regularization and nonconvex data fidelity. More precisely, the usage of a nonconvex TGV regularizer helps to eliminate the staircase artifacts and simultaneously preserve edge details. Nonconvex fidelity, which enhances sparsity, is adopted to effectively detect impulse noise. Computationally, incorporating the popular iteratively reweighted ℓ1 algorithm and variable splitting method, we propose to adopt an efficient alternating direction method of multipliers for the purpose of rapidly resolving the designed optimization problem. Additionally, simulation examples have been executed to compare our method with several state-of-the-art techniques. Experimental results and quantitative comparisons confirm that the developed strategy outperforms other competitors for suppressing impulse noise (even high density) in both visual outcomes and recovery accuracy.

NON-CONVEX HYBRID TOTAL VARIATION FOR RESTORING MEDICAL IMAGE CORRUPTED BY POISSON NOISE

Abstract. In this work, we proposed the hybrid non-convex regularizers for Poisson noise removal on medical images. The model is built by a combination of non-convex total variation and non-convex fractional total variation. The proposed model allows for avoiding the annoying staircase artifacts and obtaining the reconstruction results with sharp and neat edges during the noise removal process. For handling the minimization problem, we employ the alternating minimization method associated with the iteratively reweighted l1 algorithm. Numerical experiments illustrate the efficiency of the proposed model and corresponding algorithm.

EPLL image denoising with multi-feature dictionaries

The expected patch log likelihood (EPLL) is a patch-prior based denoising model that has become a popular tool in image restoration for its outstanding edge preservation and noise reduction abilities. However, without considering the geometrical feature of patches, the EPLL removes numerous important details and frequently suffers from the staircase effect, residual noise and artifacts. To preserve more detailed information and suppress the generation of artifacts, we propose a novel EPLL denoising model with multi-feature dictionaries (MFDs) and adaptive regularization parameters in this paper. In the proposed method, to exploit the statistical and geometrical characteristics of patches, two feature layers are designed before training the Gaussian mixture model (GMM). In the first layer, the within-class variance minimum (WCVM) method is used to learn the statistical features of patches. In the second layer, two geometrical characteristic dictionaries (GCDs) are trained. In the denoising phase, we select the corresponding dictionary for each patch. Then, each patch is denoised independently. Moreover, the mean localized spectral response (MLSR) based regularization parameters are employed in the proposed method, which is spatial self-adaptive and robust to noise. Extensive experiments demonstrate that our approach achieves desired performance in both detail preservation and artifact suppression compared to many existing denoising methods.