Staircase Artifacts Research Articles

An adaptive image restoration algorithm based on hybrid total variation regularization

In imaging systems, the mixed Poisson-Gaussian noise (MPGN) model can accurately describe the noise present. Total variation (TV) regularization-based methods have been widely utilized for Poisson-Gaussian removal with edge-preserving. However, TV regularization sometimes causes staircase artifacts with piecewise constants. To overcome this issue, we propose a new model in which the regularization term is represented by a combination of total variation and high-order total variation. We study the existence and uniqueness of the minimizer for the considered model. Numerically, the minimization problem can be efficiently solved by the alternating minimization method. Furthermore, we give rigorous convergence analyses of our algorithm. Experiments results are provided to demonstrate the superiority of our proposed hybrid model and algorithm for deblurring and denoising images simultaneously, in comparison with several state-of-the-art numerical algorithms.

High-Resolution 3D MRI With Deep Generative Networks via Novel Slice-Profile Transformation Super-Resolution.

High-resolution magnetic resonance imaging (MRI) sequences, such as 3D turbo or fast spin-echo (TSE/FSE) imaging, are clinically desirable but suffer from long scanning time-related blurring when reformatted into preferred orientations. Instead, multi-slice two-dimensional (2D) TSE imaging is commonly used because of its high in-plane resolution but is limited clinically by poor through-plane resolution due to elongated voxels and the inability to generate multi-planar reformations due to staircase artifacts. Therefore, multiple 2D TSE scans are acquired in various orthogonal imaging planes, increasing the overall MRI scan time. In this study, we propose a novel slice-profile transformation super-resolution (SPTSR) framework with deep generative learning for through-plane super-resolution (SR) of multi-slice 2D TSE imaging. The deep generative networks were trained by synthesized low-resolution training input via slice-profile downsampling (SP-DS), and the trained networks inferred on the slice profile convolved (SP-conv) testing input for 5.5x through-plane SR. The network output was further slice-profile deconvolved (SP-deconv) to achieve an isotropic super-resolution. Compared to SMORE SR method and the networks trained by conventional downsampling, our SPTSR framework demonstrated the best overall image quality from 50 testing cases, evaluated by two abdominal radiologists. The quantitative analysis cross-validated the expert reader study results. 3D simulation experiments confirmed the quantitative improvement of the proposed SPTSR and the effectiveness of the SP-deconv step, compared to 3D ground-truths. Ablation studies were conducted on the individual contributions of SP-DS and SP-conv, networks structure, training dataset size, and different slice profiles.

Wavelet oriented SAR image despeckling using fractional-order TV and a non-convex sparse prior

Speckle is an inborn deformity caused by the interaction of backscattered waves from the target in active coherent imaging sensors such as synthetic aperture radar (SAR). Its presence severely limits the utility of SAR imagery in terms of detecting ground targets, retrieving information and analyzing scenes. The wavelet-based methods employ a threshold value on the noisy image for sparse wavelet representation. However, the noisy image coefficients exceeding the threshold are the cause of spurious noise spikes around the discontinuities. The edge preserving total variation (TV) regularizer is effective against speckle. Nevertheless, it is associated with staircase artifact. In this work, the wavelet-based forward model is integrated with a fractional order TV (FrTV) regularizer in the presence of a non-convex sparse prior to exploit the benefits of both methods. This combination aids in avoiding staircasing artifacts and preserving discontinuities while eliminating noise. Under some constraints, the optimization problem is convex, and it is solved using the alternating direction method of multipliers (ADMM). The alternating framework is iteratively solved by employing a thresholding operation, a shrinkage function, and quadratic minimization. The proposed method’s convergence is investigated both mathematically and empirically. The experimental results on both simulated and practical SAR data show that the proposed technique outperforms the previous algorithms in terms of speckle removal.

Non-Convex High-Order TV and ℓ 0-Norm Wavelet Frame-Based Speckle Noise Reduction

To obtain natural restorations from the noisy images contaminated by speckle noise, this brief presents a novel hybrid non-convex regularizers model for image denoising. The proposed new variational model closely combines the superiorities of non-convex high-order total variation function and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{0}$ </tex-math></inline-formula> -norm wavelet frame. This combination helps to avoid the staircase artifacts and maintain discontinuities while removing noise. Numerically, by integrating two popular tools: iteratively reweighted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> algorithm and variable splitting method, a modified alternating minimization method is adopted to optimize the resulting minimization problem. Finally, compared with several despeckling methods, numerical experiments indicate the competitive performance of our solver in visual improvement and objective measurement.

Viscoelastic transcranial wave propagation modeling for neuronavigated focused ultrasound procedures in humans

Transcranial focused ultrasound (FUS) has gained significant attention as a non-invasive therapeutic technique that can reach both cortical and subcortical targets in the human brain. However, the skull barrier distorts the ultrasound beam and introduces significant losses that need to be accounted for. In this talk, I will present our efforts to develop high precise transcranial ultrasound modeling based on the open-source viscoelastic wave propagation solver BabelViscoFDTD and its application in neuronavigated procedures for FUS-based neuromodulation. The viscoelastic wave equation is expressed in isotropic stress tensors and displacement vectors, and their nodes are placed in a staggered grid arrangement. The solver uses a Cartesian O(4)-space O(2)-time FDTD scheme. A narrow-band quality factor models attenuation. A reduction of staircase artifacts can be enabled using a superposition operator. BabelViscoFDTD is optimized for multiple computing GPU and CPU backends (CUDA, OpenCL, Metal, and X86-64) and includes GPU-accelerated solvers of the Rayleigh-Sommerfeld equation and Bio-Heat thermal equations. We adapted the viscoelastic and thermal solvers to neuronavigate two FUS devices: A 128-element concaved array operable at 250 kHz and 700 kHz and a 4-ring concaved array operable at 500 kHz. The high degree of optimization of the solvers allow that numerical procedures (neuronavigation and modeling) can be performed in an Apple M1 Max (64 GB RAM) laptop computer.

Feature-preserving Mumford–Shah mesh processing via nonsmooth nonconvex regularization

Motivated by the success in image processing, the Mumford–Shah functional has attracted extensive attentions in geometry processing. Existing methods, mainly focusing on discretizations on the triangulated mesh, either over-smooth sharp features or are sensitive to noises or outliers. In this paper, we first introduce a nonsmooth nonconvex Mumford–Shah model for a feature-preserving filtering of face normal field to ameliorate the staircasing artifacts that appear in the original Mumford–Shah total variation (MSTV) and develop an alternating minimization scheme based on alternating direction method of multipliers to realize the proposed model. After restoring the face normal field, vertex updating is then employed by incorporating the oriented normal constraints and discontinuities to achieve a detail-preserving reconstruction of mesh geometry. Extensive experimental results demonstrate the effectiveness of the above shape optimization routine for various geometry processing applications such as mesh denoising, mesh inpainting and mesh segmentation.

Speckle Reduction in Ultrasound Images of the Common Carotid Artery Based on Integer and Fractional-Order Total Variation.

Designing a technique with higher speckle noise suppressing capability, better edge preserving performance, and lower time complexity is a research objective for the common carotid artery (CCA) ultrasound despeckling. Total variation based techniques have been widely used in the image denoising and have good performance in preserving the edges in the images. However, the total variation based filters can produce the staircase artifacts. To address this issue, second-order total variation based techniques have been proposed for the image denoising. However, the previous study has been proved that the fractional differential model has better performance in reducing the speckles in ultrasound despeckling compared with the second-order model. Thus, to improve the performance of ultrasound despeckling and edge preserving, a novel despeckling model based on integer and fractional-order total variation (IFOTV) is proposed for CCA ultrasound images. Moreover, the minimization problems in our despeckling model are solved by the alternating direction method of multiplier (ADMM). In results with synthetic images, the edge preservation index (EPI) values of proposed method are 0.9524, 0.8797, and 0.7351 as well as 0.9137, 0.8253, and 0.6847 under three different levels of noise, which are the highest among four advanced methods. In results with simulated CCA ultrasound images, the speckle suppression and mean preservation indices of proposed method are 0.5596, 0.6571, and 0.8106 under three different levels of noise, which are the best among four advanced methods. In results with clinical images, the average absolute error of intima-media thickness measurements of proposed method is 0.0660 ± 0.0679 (mean ± std in mm), which is the lowest among four advanced methods. In conclusion, the IFOTV method has improved performance in suppressing the speckle noise and preserving the edge, and is thus a potential alternative to the current filters for the CCA ultrasound despeckling.

Total variation combining nonlocal means filtration for image reconstruction in X-ray computed tomography.

Image reconstruction for realistic medical images under incomplete observation is still one of the core tasks for computed tomography (CT). However, the stair-case artifacts of Total variation (TV) based ones have restricted the usage of the reconstructed images. This work aims to propose and test an accurate and efficient algorithm to improve reconstruction quality under the idea of synergy between local and nonlocal regularizations. The total variation combining the nonlocal means filtration is proposed and the alternating direction method of multipliers is utilized to develop an efficient algorithm. The first order approximation of linear expansion at intermediate point is applied to overcome the computation of the huge CT system matrix. The proposed method improves root mean squared error by 25.6% compared to the recent block-matching sparsity regularization (BMSR) on simulation dataset of 19 views. The structure similarities of image of the new method is higher than 0.95, while that of BMSR is about 0.92. Moreover, on real rabbit dataset of 20 views, the peak signal-to-noise ratio (PSNR) of the new method is 36.84, while using other methods PSNR are lower than 35.81. The proposed method shows advantages on noise suppression and detail preservations over the competing algorithms used in CT image reconstruction.

A Hybrid Method for 3D Reconstruction of MR Images.

Three-dimensional surface reconstruction is a well-known task in medical imaging. In procedures for intervention or radiation treatment planning, the generated models should be accurate and reflect the natural appearance. Traditional methods for this task, such as Marching Cubes, use smoothing post processing to reduce staircase artifacts from mesh generation and exhibit the natural look. However, smoothing algorithms often reduce the quality and degrade the accuracy. Other methods, such as MPU implicits, based on adaptive implicit functions, inherently produce smooth 3D models. However, the integration in the implicit functions of both smoothness and accuracy of the shape approximation may impact the precision of the reconstruction. Having these limitations in mind, we propose a hybrid method for 3D reconstruction of MR images. This method is based on a parallel Marching Cubes algorithm called Flying Edges (FE) and Multi-level Partition of Unity (MPU) implicits. We aim to combine the robustness of the Marching Cubes algorithm with the smooth implicit curve tracking enabled by the use of implicit models in order to provide higher geometry precision. Towards this end, the regions that closely fit to the segmentation data, and thus regions that are not impacted by reconstruction issues, are first extracted from both methods. These regions are then merged and used to reconstruct the final model. Experimental studies were performed on a number of MRI datasets, providing images and error statistics generated from our results. The results obtained show that our method reduces the geometric errors of the reconstructed surfaces when compared to the MPU and FE approaches, producing a more accurate 3D reconstruction.

Multichannel impedance inversion in the frequency domain via anisotropic total variation with overlapping group sparsity regularization

Abstract Total variation regularization is widely used in geophysical inverse problems for preserving the edges of geological structures. However, it may lead to staircase artifacts and other inversion errors. To overcome this drawback, we present an impedance inversion method by using anisotropic total variation with overlapping group sparsity regularization. This method can not only preserve edges very well but also makes use of the group sparsity feature of acoustic impedance to reduce inversion error. Moreover, we make full use of the properties of the Toeplitz matrix and speed up the inversion process in the frequency domain. The synthetic data and field data inversion results show that the proposed method has the advantages of stronger anti-noise, faster inversion speed, and less error comparing with the conventional total variation regularization inversion method. In addition, our method can effectively alleviate staircase artifacts and therefore improves resolution.

Assimilation of Images via Dictionary Learning-Based Sparsity Regularization Strategy: An Application for Retrieving Fluid Flows

In this work, we propose a structure sparsity regularization strategy in the framework of 4-D variational data assimilation (4-D Var). In meteorology and oceanography, the number of unknown model variables is far fewer than that of image observations, often leading to solve an underdetermined nonlinear inverse problem. In recent years, the l¹-norm-based sparsity regularization approach has attracted great attention in the field of 4-D Var because of its data structure preservation and noise suppression. To avoid little underlying physical priors considered, we introduce a widely used dictionary learning (DL) method to adaptively derive an efficient sparse approximation via learning a basis from a given dataset. For our target application of estimating sea surface flows, we consider a DL sparsity constraint on the variable of flow vorticity due to its rich spatial variation related to flows evolution. A novel anisotropic regularization method combined with fluid dynamics characteristics could overcome magnitude underestimation and staircase artifacts appearing in the gradient regularization-based 4-D Var method. The split Bregman iteration with fast convergence property is employed to solve the l¹+l² nonsmooth minimization problem. The promising fluid flows estimation performance in real test cases (assimilation of image sequences collected from CORIOLIS experimental turntable) demonstrates the efficiency of our approach.

Smoothed-NUV Priors for Imaging.

Variations of L1 -regularization including, in particular, total variation regularization, have hugely improved computational imaging. However, sharper edges and fewer staircase artifacts can be achieved with convex-concave regularizers. We present a new class of such regularizers using normal priors with unknown variance (NUV), which include smoothed versions of the logarithm function and smoothed versions of Lp norms with p ≤ 1 . All NUV priors allow variational representations that lead to efficient algorithms for image reconstruction by iterative reweighted descent. A preferred such algorithm is iterative reweighted coordinate descent, which has no parameters (in particular, no step size to control) and is empirically robust and efficient. The proposed priors and algorithms are demonstrated with applications to tomography. We also note that the proposed priors come with built-in edge detection, which is demonstrated by an application to image segmentation.

Restoration of Poissonian Images Using Nonconvex Regularizer with Overlapping Group Sparsity

Aimed at achieving the accurate restoration of Poissonian images that exhibit neat edges and no staircase effect, this article develops a novel hybrid nonconvex double regularizer model. The proposed scheme closely takes the advantages of total variation with overlapping group sparsity and nonconvex high-order total variation priors. The overlapping group sparsity is adopted to globally suppress the staircase artifacts, while the nonconvex high-order regularization plays the role of locally preserving the significant image features and edge details. Computationally, a quite efficient alternating direction method of multipliers, associated with the iteratively reweighted ${\ell _{1}}$ algorithm and the majorization-minimization method, is employed to settle the optimization problem iteratively. Finally, exhaustive simulation experiments are executed for recovering Poissonian images, which are made comparisons with several state-of-the-art restoration strategies, indicate the brilliant performance of our model in terms of intuitive effects and accuracy evaluation.

An [formula omitted]-overlapping group sparse total variation for impulse noise image restoration

Total variation (TV) based methods are effective models in image restoration. For eliminating impulse noise, an effective way is to use the ℓ1-norm total variation model. However, the TV image restoration always yields staircase artifacts, especially in high-density noise levels. Additionally, the ℓ1-norm tends to over penalize solutions and is not robust to outlier characteristics of impulse noise. In this paper, we propose a new total variation model to effectively remove the staircase effects and eliminate impulse noise. The proposed model uses the ℓ0-norm data fidelity to effectively remove the impulse noise while the overlapping group sparse total variation (OGSTV) acts as a regularizer to eliminate the staircase artifacts. Since the proposed method requires solving an ℓ0-norm and an OGSTV optimization problem, a formulation using the mathematical program with equilibrium constraints (MPEC) and the majorization–minimization (MM) method are respectively used together with the alternating direction method of multipliers (ADMM). Experiments demonstrate that our proposed model performs better than several state-of-the-art algorithms such as the ℓ1 total generalized variation, ℓ0 total variation, and the ℓ1 overlapping group sparse total variation in terms of the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM).

Spatially adaptive TGV-regularized variational model for single image dehazing

Due to the intrinsic limitations of hyperparameters, most dehazing algorithms easily suffer from overenhancement or staircase artifacts. To suppress these problems, a spatially adaptive total generalized variational (TGV)-based single image dehazing algorithm is developed. The algorithm contain two modules, i.e., an adaptive coarse transmission map estimation module and a spatially adaptive TGV-based transmission refine module. The adaptive coarse transmission map estimation module is designed to prevent the dehazing result from being overenhanced with a dark channel-based adaptive control parameter. The TGV-based transmission refine module is designed to refine the coarse transmission with a texture prior-based spatially adaptive TGV-regularized variational model. Numerous experiments reveal that the proposed algorithm is comparable with or even outperforms the state-of-the-art techniques.

A deep-learning approach for direct whole-heart mesh reconstruction.

Automated construction of surface geometries of cardiac structures from volumetric medical images is important for a number of clinical applications. While deep-learning-based approaches have demonstrated promising reconstruction precision, these approaches have mostly focused on voxel-wise segmentation followed by surface reconstruction and post-processing techniques. However, such approaches suffer from a number of limitations including disconnected regions or incorrect surface topology due to erroneous segmentation and stair-case artifacts due to limited segmentation resolution. We propose a novel deep-learning-based approach that directly predicts whole heart surface meshes from volumetric CT and MR image data. Our approach leverages a graph convolutional neural network to predict deformation on mesh vertices from a pre-defined mesh template to reconstruct multiple anatomical structures in a 3D image volume. Our method demonstrated promising performance of generating whole heart reconstructions with as good or better accuracy than prior deep-learning-based methods on both CT and MR data. Furthermore, by deforming a template mesh, our method can generate whole heart geometries with better anatomical consistency and produce high-resolution geometries from lower resolution input image data. Our method was also able to produce temporally-consistent surface mesh predictions for heart motion from CT or MR cine sequences, and therefore can potentially be applied for efficiently constructing 4D whole heart dynamics. Our code and pre-trained networks are available at https://github.com/fkong7/MeshDeformNet.

Sparse inversion-based seismic random noise attenuation via self-paced learning

Seismic random noise reduction is an important task in seismic data processing at the Chinese loess plateau area, which benefits the geologic structure interpretation and further reservoir prediction. The sparse inversion is one of the widely used tools for seismic random noise reduction, which is often solved via the sparse approximation with a regularization term. The ℓ1 norm and total variation (TV) regularization term are two commonly used regularization terms. However, the ℓ1 norm is only a relaxation of the ℓ0 norm, which cannot always provide a sparse result. The TV regularization term may provide unexpected staircase artifacts. To avoid these disadvantages, we proposed a workflow for seismic random noise reduction by using the self-paced learning (SPL) scheme and a sparse representation (i.e. the continuous wavelet transform, CWT) with a mixed norm regularization, which includes the ℓp norm and the TV regularization. In the implementation, the SPL, which is inspired by human cognitive learning, is introduced to avoid the bad minima of the non-convex cost function. The SPL can first select the high signal-to-noise ratio (SNR) seismic data and then gradually select the low SNR seismic data into the proposed workflow. Moreover, the generalized Beta wavelet (GBW) is adopted as the basic wavelet of the CWT to better match for seismic wavelets and then obtain a more localized time-frequency (TF) representation. It should be noted that the GBW can easily constitute a tight frame, which saves the calculation time. Synthetic and field data examples are adopted to demonstrate the effectiveness of the proposed workflow for effectively suppressing seismic random noises and accurately preserving valid seismic reflections.

Multidirectional Anisotropic Total Variation and Its Application in the Tomography of the Surrounding Rock of Coal Mining Faces

The computed tomography (CT) reconstruction algorithm is one of the crucial components of the CT system. To date, total variation (TV) has been widely used in CT reconstruction algorithms. Although TV utilizes the a priori information of the longitudinal and lateral gradient sparsity of an image, it introduces some staircase artifacts. To overcome the current limitations of TV and improve imaging quality, we propose a multidirectional anisotropic total variation (MATV) that uses multidirectional gradient information. The surrounding rock of coal mining faces uses principles of tomography similar to those of medical X-rays. The velocity distribution for the surrounding rock can be obtained by the first-arrival traveltime tomography of the transmitted waves in the coal mining face. Combined with the geological data, we can interpret the geological hazards in the coal mining face. To perform traveltime tomography, we first established the objective function of the first-arrival traveltime tomography of the transmitted waves based on the MATV regularization and then used the split Bregman method to solve the objective function. The simulated data and real data show that the MATV regularization method proposed in this paper can better maintain the boundaries of geological anomalies and reduce the artifacts compared with the isotropic total variation regularization method and the anisotropic total variation regularization method. Furthermore, this approach describes the distribution of geological anomalies more accurately and effectively and improves imaging accuracy.

Reconstruction of conductivity distribution with a compound variational strategy in electrical impedance tomography

AbstractAs a potential imaging technique, electrical impedance tomography (EIT) is advantageous for reconstructing conductivity distribution. However, due to insufficient measurement, visualization is inevitably an ill‐posed inverse problem. Moreover, reconstruction quality is affected by noise. To address these challenges, a novel variational model with an Lp‐norm as fidelity and a hybrid total variation as penalty (Lp‐HTV) is proposed for conductivity distribution reconstruction. Iterative reweighted L1 algorithm transforms the Lp‐norm to an L1‐norm and alternating direction method of multipliers is then utilized to solve objective function. Meanwhile, region of interest is defined to enhance robustness to noise and reduce staircase artifact. The performance of the proposed compound method is validated by several cases. Phantom experiments are also conducted. Compared with classic regularization methods, it is found that images reconstructed by the proposed method show large improvement. The results demonstrate that the proposed strategy is more competitive in visualizing conductivity distribution.

GPR noise reduction by TVD and TVD-EMD

The existence of coherent and incoherent (random) noises in the ground penetration radar (GPR) signals using high-frequency electromagnetic waves is inevitable; therefore, the elimination of noise from GPR data before performing any additional analysis is of great importance to increase the efficiency of the interpretations. We apply the Total Variation De-noising (TVD) and Savitzky-Golay (SG) filter, on the synthetic and real GPR data. For a better perception, we compare the same trace of the data before and after the experiences. The results indicate that the TVD method is more effective than common adaptive filtering in the time domain for reducing noise such as the SG filter which acts as a low-pass filter for smoothing data based on a polynomial least-squares approximation; however, due to the visibility of staircase artifacts using the TVD method, GPR data is first transferred to the empirical mode decomposition (EMD) frame which is useful for non-linear and non-stationary signal processing, then the TVD method is applied on it; ultimately, noise reduction using TVD is compared in the time and EMD domains. The comparison of the outputs shows that the TVD algorithm in the EMD domain, based on the sequential extraction of the energy belonging to the different intrinsic time scales of the signal, provides better noise attenuation than the other algorithms. In addition, TVD-EMD preserves the event forms, signal forms and improves the continuity in sections.