Bilateral Total Variation Research Articles

Enhanced osmosis model with bilateral total variation for effective shadow removal

This research paper presents an innovative technique for shadow images removal. The method involves redefining a contemporary osmosis model by incorporating bilateral total variation (TV) operators. This integration allows to take advantage of robust anisotropic diffusion, resulting in improved image restoration. The paper also outlines new mathematical derivation of the bilateral TV and a combination with nonlinear anisotropic transport term. The experimental results substantiate the effectiveness of the anisotropic osmosis model, showcasing its superior qualitative and quantitative performance when compared to current state-of-the-art techniques.

Time-fractionated anisotropic osmosis with bilateral total variation for effective shadow mitigation in image processing

This work introduces an innovative strategy for mitigating shadow effects in images through the utilization of a time-fractionated anisotropic osmosis equation. The method goes beyond conventional approaches by incorporating a newly derived bilateral total variation (BTV) term, coupled with a nonlinear anisotropic transport component. Theoretical insights are rigorously presented, accompanied by a meticulous exposition of the discretization scheme based on finite differences. In addition to the theoretical foundation, the paper conducts comprehensive numerical experiments to validate the proposed model's efficacy. These experiments not only affirm the qualitative advantages of the anisotropic osmosis model but also provide quantitative evidence of its superiority over existing state-of-the-art techniques.

Total fractional-order variation and bilateral filter for image denoising

Image denoising stands out as a primary goal in image processing. However, many existing methods encounter challenges in preserving features such as corners and edges of an image while deleting the noise. This study investigates and evaluates a fractional-order derivative based on the total α-order variation (TV) model and the bilateral total variation (BTV) model. This choice is motivated by the proven effectiveness of the TV model in noise removal and edge preservation, with the BTV model further utilized to enhance the restoration of fine and intricate details. The experimental results affirm the efficacy of the proposed model, supported by objective quantitative metrics and subjective assessments of visual appearance.

Enhancing Low‐Light Images: A Variation‐based Retinex with Modified Bilateral Total Variation and Tensor Sparse Coding

AbstractLow‐light conditions often result in the presence of significant noise and artifacts in captured images, which can be further exacerbated during the image enhancement process, leading to a decrease in visual quality. This paper aims to present an effective low‐light image enhancement model based on the variation Retinex model that successfully suppresses noise and artifacts while preserving image details. To achieve this, we propose a modified Bilateral Total Variation to better smooth out fine textures in the illuminance component while maintaining weak structures. Additionally, tensor sparse coding is employed as a regularization term to remove noise and artifacts from the reflectance component. Experimental results on extensive and challenging datasets demonstrate the effectiveness of the proposed method, exhibiting superior or comparable performance compared to state‐of‐the‐art approaches. Code, dataset and experimental results are available at https://github.com/YangWeipengscut/BTRetinex.

Lucy Richardson and Mean Modified Wiener Filter for Construction of Super-Resolution Image

The ultimate goal of the Super-Resolution (SR) technique is to generate the High-Resolution (HR) image by combining the corresponding images with Low-Resolution (LR), which is utilized for different applications such as surveillance, remote sensing, medical diagnosis, etc. The original HR image may be corrupted due to various causes such as warping, blurring, and noise addition. SR image reconstruction methods are frequently plagued by obtrusive restorative artifacts such as noise, stair casing effect, and blurring. Thus, striking a balance between smoothness and edge retention is never easy. By enhancing the visual information and autonomous machine perception, this work presented research to improve the effectiveness of SR image reconstruction The reference image is obtained from DIV2K and BSD 100 dataset, these reference LR image is converted as composed LR image using the proposed Lucy Richardson and Modified Mean Wiener (LR-MMWF) Filters. The possessed LR image is provided as input for the stage of bicubic interpolation. Afterward, the initial HR image is obtained as output from the interpolation stage which is given as input for the SR model consisting of fidelity term to decrease residual between the projected HR image and detected LR image. At last, a model based on Bilateral Total Variation (BTV) prior is utilized to improve the stability of the HR image by refining the quality of the image. The results obtained from the performance analysis show that the proposed LR-MMW filter attained better PSNR and Structural Similarity (SSIM) than the existing filters. The results obtained from the experiments show that the proposed LR-MMW filter achieved better performance and provides a higher PSNR value of 31.65dB whereas the Filter-Net and 1D,2D CNN filter achieved PSNR values of 28.95dB and 31.63dB respectively.

Structure-Preserving Texture Smoothing via Scale-Aware Bilateral Total Variation

The purpose of texture smoothing is to preserve the prominent structure in the image while smoothing the salient texture. However, the existing methods are difficult to achieve a satisfactory balance between filtering out salient textures and preserving weak edge structures and small structures. To this end, we propose a structure-preserving texture smoothing method via scale-aware bilateral total variation. First, the joint bilateral filter is introduced to construct the window bilateral variation, and combined with the window total variation, a regularizer called the bilateral total variation is formed, which accurately quantifies the characteristics of texture and structure, to finely smooth salient textures while preserving weak edge structures and small structures. Subsequently, we proposed a scale-aware scheme to make the proposed regularizer more powerful in preserving small structures and adopted an optimization scheme to convert the original non-convex optimization problem into a least squares regression problem. The effectiveness of the proposed regularizer is verified in the dataset. The experimental results demonstrate the superiority of the proposed method in texture smoothing and other applications compared to other state-of-the-art approaches.

A four-aperture super-resolution camera based on adaptive regularization parameter tuning

Multi-aperture imaging can improve spatial resolution by fusing complementary information from multiple low-resolution (LR) frames using super-resolution (SR) algorithms. The existing SR algorithms are offline used due to the lack of fast regularization parameter update solution. The classical general cross validation (GCV) and the L-curve algorithms search for a suitable solution on each updated logarithmic parameter set for a long time. In this work, we proposed an adaptive regularization parameter tuning (ARPT) method. The regularization parameter is updated by a function of the fidelity term, the standard deviation of the noise, the weighted bilateral total variation and its standard deviation. Simulations demonstrate that the PSNR and SSIM of the ARPT algorithm, are 0.27 dB and 0.002 larger than the GCV algorithm on average, and the computation time is reduced by more than four times. A four-aperture SR camera is built by randomly shifting the sensors on a sub-pixel scale. An SR image was obtained by the ARPT method using 20 LR images. The average consuming time is reduced by 6.17 times compared with the GCV algorithm. Experiments indicate that the proposed four-aperture SR camera can improve the spatial resolution, suppress the noise, and realize a high-quality and more efficient reconstruction.

On the well-posedness of a tensor-based second order PDE with bilateral term for image super-resolution

<p style='text-indent:20px;'>In this paper, we introduce a second-order equation based on a diffusion tensor combined with a bilateral total variation (BTV) term that takes the benefit from the diffusion model of Perona-Malik in the homogeneous regions, the Weickert model near sharp edge and the BTV term in reducing blur. Compared to the other partial differential equations (PDE) used in the SR context, the proposed super-resolution (SR) PDE can efficiently preserve image components such as corners and flat regions with less apparition of blur in homogeneous regions. Moreover, since the SR approaches are always ill-posed, a mathematical study of the existence and uniqueness of the solution is also checked in a Sobolev space. From the numerical experiments we can observe that the proposed PDE can efficiently improve the quality of the high-resolution (HR) image. Surprisingly, the apparition of blur in the restored image is less compared to the other methods. In addition to visual evaluation, two-based metrics are computed to confirm the improvements offered by the proposed PDE.</p>

A Hybrid Regularization-Based Multi-Frame Super-Resolution Using Bayesian Framework

The prime purpose for the image reconstruction of a multi-frame super-resolution is to reconstruct a higher-resolution image through incorporating the knowledge obtained from a series of relevant low-resolution images, which is useful in numerous fields. Nevertheless, super-resolution image reconstruction methods are usually damaged by undesirable restorative artifacts, which include blurring distortion, noises, and stair-casing effects. Consequently, it is always challenging to achieve balancing between image smoothness and preservation of the edges inside the image. In this research work, we seek to increase the effectiveness of multi-frame super-resolution image reconstruction by increasing the visual information and improving the automated machine perception, which improves human analysis and interpretation processes. Accordingly, we propose a new approach to the image reconstruction of multi-frame super-resolution, so that it is created through the use of the regularization framework. In the proposed approach, the bilateral edge preserving and bilateral total variation regularizations are employed to approximate a high-resolution image generated from a sequence of corresponding images with low-resolution to protect significant features of an image, including sharp image edges and texture details while preventing artifacts. The experimental results of the synthesized image demonstrate that the new proposed approach has improved efficacy both visually and numerically more than other approaches.

Robust approach for blind separation of noisy mixtures of independent and dependent sources

The framework of this article is to introduce a new efficient Blind Source Separation (BSS) method that handles mixtures of noise-contaminated independent / dependent sources. In order to achieve that, one can minimize a criterion that fuses a separating part, based on Kullback–Leibler divergence to set apart the observed mixtures of either dependent or independent sources, with a regularization part that employs the bilateral total variation (BTV) for the purpose of denoising the observations. The proposed algorithm utilizes a primal-dual algorithm to remove the noise, while a gradient descent method is implemented to retrieve the source signals. Our algorithm has shown its effectiveness and efficiency toward the noisy dependent / independent sources and also surpassed the standard BSS algorithms through different experimental results.

Full-Waveform Inversion for Subsurface Penetrating Radar based on Adaptive Bilateral Total Variation Regularization

Full-waveform inversion (FWI) of subsurface penetrating radar (SPR) is one of the most promising techniques for quantitative reconstruction of high-resolution dielectric properties distribution. However, due to the incomplete observation data of surface detection, there is significant ill-posedness in inversion and the inversion accuracy is lower than expected. In this paper, an FWI method for SPR data with adaptive bilateral total variation (ABTV) regularization is proposed. The method utilizes ABTV regularization to supplement the data constraints and retains the anomaly body boundary information. In addition, the regularization function of adaptive weight factor matrix is designed for the limitation of the standard bilateral total variation (BTV) regularization, which considers both the smoothing effect and the edge preservation effect. Synthetic experiment shows that the proposed method can reconstruct the permittivity distribution more accurately from 2-D SPR data.

Regularized Multiframe Super-Resolution Image Reconstruction Using Linear and Nonlinear Filters

The primary goal of the multiframe super-resolution image reconstruction is to produce an image with a higher resolution by integrating information extracted from a set of corresponding images with low resolution, which is used in various fields. However, super-resolution image reconstruction approaches are typically affected by annoying restorative artifacts, including blurring, noise, and staircasing effect. Accordingly, it is always difficult to balance between smoothness and edge preservation. In this paper, we intend to enhance the efficiency of multiframe super-resolution image reconstruction in order to optimize both analysis and human interpretation processes by improving the pictorial information and enhancing the automatic machine perception. As a result, we propose new approaches that firstly rely on estimating the initial high-resolution image through preprocessing of the reference low-resolution image based on median, mean, Lucy-Richardson, and Wiener filters. This preprocessing stage is used to overcome the degradation present in the reference low-resolution image, which is a suitable kernel for producing the initial high-resolution image to be used in the reconstruction phase of the final image. Then, L2 norm is employed for the data-fidelity term to minimize the residual among the predicted high-resolution image and the observed low-resolution images. Finally, bilateral total variation prior model is utilized to restrict the minimization function to a stable state of the generated HR image. The experimental results of the synthetic data indicate that the proposed approaches have enhanced efficiency visually and quantitatively compared to other existing approaches.

Robust Multi-Frame Super-Resolution Based on Adaptive Half-Quadratic Function and Local Structure Tensor Weighted BTV.

It is difficult to improve image resolution in hardware due to the limitations of technology and too high costs, but most application fields need high resolution images, so super-resolution technology has been produced. This paper mainly uses information redundancy to realize multi-frame super-resolution. In recent years, many researchers have proposed a variety of multi-frame super-resolution methods, but it is very difficult to preserve the image edge and texture details and remove the influence of noise effectively in practical applications. In this paper, a minimum variance method is proposed to select the low resolution images with appropriate quality quickly for super-resolution. The half-quadratic function is used as the loss function to minimize the observation error between the estimated high resolution image and low-resolution images. The function parameter is determined adaptively according to observation errors of each low-resolution image. The combination of a local structure tensor and Bilateral Total Variation (BTV) as image prior knowledge preserves the details of the image and suppresses the noise simultaneously. The experimental results on synthetic data and real data show that our proposed method can better preserve the details of the image than the existing methods.

Blind deconvolution using bilateral total variation regularization: a theoretical study and application

ABSTRACT Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations.

Nonlocal Low-Rank Regularization Combined with Bilateral Total Variation for Compressive Sensing Image Reconstruction

The use of non-local self-similarity prior between image blocks can improve image reconstruction performance significantly. We propose a compressive sensing image reconstruction algorithm that combines bilateral total variation and nonlocal low-rank regularization to overcome over-smoothing and degradation of edge information which result from the prior reconstructed image. The proposed algorithm makes use of the preservation of image edge information by bilateral total variation operator to enhance the edge details of the reconstructed image. In addition, we use weighted nuclear norm regularization as a low-rank constraint for similar blocks of the image. To solve this convex optimization problem, the Alternating Direction Method of Multipliers (ADMM) is employed to optimize and iterate the algorithm model effectively. Experimental results show that the proposed algorithm can obtain better image reconstruction quality than conventional algorithms with using total variation regularization or considering the nonlocal structure of the image only. At 10% sampling rate, the peak signal-to-noise ratio gain is up to 2.39 dB in noiseless measurements compared with Nonlocal Low-rank Regularization (NLR-CS). Reconstructed image comparison shows that the proposed algorithm retains more high frequency components. In noisy measurements, the proposed algorithm is robust to noise and the reconstructed image retains more detail information.

Robust approach for blind separation of noisy mixtures of independent and dependent sources

In this paper, a new Blind Source Separation (BSS) method that handles mixtures of noisy independent/dependent sources is introduced. We achieve that by minimizing a criterion that fuses a separating part, based on Kullback–Leibler divergence for either dependent or independent sources, with a regularization part that employs the bilateral total variation (BTV) for the purpose of denoising the observations. The proposed algorithm utilizes a primal-dual algorithm to remove the noise, while a gradient descent method is implemented to retrieve the signal sources. Our algorithm has shown its effectiveness and efficiency and also surpassed the standard existing BSS algorithms.

Spatiotemporal Adaptive Nonuniformity Correction Based on BTV Regularization

The residual nonuniformity response, ghosting artifacts, and over-smooth effects are the main defects of the existing nonuniformity correction (NUC) methods. In this paper, a spatiotemporal feature-based adaptive NUC algorithm with bilateral total variation (BTV) regularization is presented. The primary contributions of the innovative method are embodied in the following aspects: BTV regularizer is introduced to eliminate the nonuniformity response and suppress the ghosting effects. The spatiotemporal adaptive learning rate is presented to further accelerate convergence, remove ghosting artifacts, and avoid over-smooth. Moreover, the random projection-based bilateral filter is proposed to estimate the desired target image more accurately which yields more details in the actual scene. The experimental results validated that the proposed algorithm achieves outstanding performance upon both simulated data and real-world sequence.

Robust Multi-Frame Super-Resolution Based on Spatially Weighted Half-Quadratic Estimation and Adaptive BTV Regularization.

Multi-frame image super-resolution focuses on reconstructing a high-resolution image from a set of low-resolution images with high similarity. Combining image prior knowledge with fidelity model, the Bayesian-based methods have been considered as an effective technique in super-resolution. The minimization function derived from maximum a posteriori probability (MAP) is composed of a fidelity term and a regularization term. In this paper, based on the MAP estimation, we propose a novel initialization method for super-resolution imaging. For the fidelity term in our proposed method, the half-quadratic estimation is used to choose error norm adaptively instead of using fixed and norms. Besides, a spatial weight matrix is used as a confidence map to scale the estimation result. For the regularization term, we propose a novel regularization method based on adaptive bilateral total variation (ABTV). Both the fidelity term and the ABTV regularization guarantee the robustness of our framework. The fidelity term is mainly responsible for dealing with misregistration, blur, and other kinds of large errors, while the ABTV regularization aims at edge preservation and noise removal. The proposed scheme is tested on both synthetic data and real data. The experimental results illustrate the superiority of our proposed method in terms of edge preservation and noise removal over the state-of-the-art algorithms.

A multiframe super-resolution technique based on a nonlocal Bregman distance of bilateral total variation term

In this paper, we propose a variational multiframe super-resolution (SR) model based on a nonlocal regularization term using Bregman distances. Since the SR algorithms always skip the complex spatial interactions within images, we introduce a nonlocal form of the bilateral total variation (BTV) regularization term which can take into consideration these interactions and also efficiently preserve strong edges and contours of the reconstructed high resolution (HR) image for our model. In addition, to avoid contrast loss and smoothing gray values in the SR process, we introduce Bregman distances which produce a more consistent model. Moreover, to resolve the obtained SR algorithm, we use a first-order primal dual algorithm to ensure that the convergence to the desired HR image can be achieved in a fast way. As a result, the proposed algorithm shows improved performance compared to other SR methods.

Multiframe super‐resolution based on a high‐order spatially weighted regularisation

Here, the authors propose a spatially weighted super-resolution (SR) algorithm, which takes into consideration the distribution of every information that characterise different image areas. The authors investigate to use a combined spatially weighted regularisation of the bilateral total variation and a second-order term increasing then the robustness of the proposed SR approach with respect to blur and noise degradations. In addition, the authors propose an iterative Bregman iteration algorithm to resolve the obtained optimisation SR problem. As a result, this regularisation is more efficient and easier to implement; moreover, it preserves well the smooth regions of the image and also sharp edges. Using different simulated and real tests, the authors prove the efficiency of the proposed algorithm compared to some SR methods.