Showing papers on "Impulse noise published in 2020"
TL;DR: A new hyperspectral image denoising method is introduced that is able to cope with additive mixed noise, i.e., mixture of Gaussian noise, impulse noise, and stripes, and fully exploits a compact and sparse HSI representation based on its low-rank and self-similarity characteristics.
Abstract: This article introduces a new hyperspectral image (HSI) denoising method that is able to cope with additive mixed noise, i.e., mixture of Gaussian noise, impulse noise, and stripes, which usually corrupt hyperspectral images in the acquisition process. The proposed method fully exploits a compact and sparse HSI representation based on its low-rank and self-similarity characteristics. In order to deal with mixed noise having a complex statistical distribution, we propose to use the robust $\ell _1$ data fidelity instead of using the $\ell _2$ data fidelity, which is commonly employed for Gaussian noise removal. In a series of experiments with simulated and real datasets, the proposed method competes with state-of-the-art methods, yielding better results for mixed noise removal.
66 citations
TL;DR: A nonconvex regularized low-rank and sparse matrix decomposition (NonRLRS) method is proposed for HSI denoising, which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes.
Abstract: Hyperspectral images (HSIs) are often degraded by a mixture of various types of noise during the imaging process, including Gaussian noise, impulse noise, and stripes Such complex noise could plague the subsequent HSIs processing Generally, most HSI denoising methods formulate sparsity optimization problems with convex norm constraints, which over-penalize large entries of vectors, and may result in a biased solution In this paper, a nonconvex regularized low-rank and sparse matrix decomposition (NonRLRS) method is proposed for HSI denoising, which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes The NonRLRS aims to decompose the degraded HSI, expressed in a matrix form, into low-rank and sparse components with a robust formulation To enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions, a novel nonconvex regularizer named as normalized $\varepsilon $ -penalty, is presented, which can adaptively shrink each entry In addition, an effective algorithm based on the majorization minimization (MM) is developed to solve the resulting nonconvex optimization problem Specifically, the MM algorithm first substitutes the nonconvex objective function with the surrogate upper-bound in each iteration, and then minimizes the constructed surrogate function, which enables the nonconvex problem to be solved in the framework of reweighted technique Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method
64 citations
TL;DR: The proposed HSI denoising framework is modeled as a convolutional neural network (CNN) constrained non-negative matrix factorization problem, which has a relatively good performance on the removal of the Gaussian and mixed Gaussian impulse noises.
Abstract: Deep learning has been successfully introduced for 2D-image denoising, but it is still unsatisfactory for hyperspectral image (HSI) denoising due to the unacceptable computational complexity of the end-to-end training process and the difficulty of building a universal 3D-image training dataset. In this paper, instead of developing an end-to-end deep learning denoising network, we propose an HSI denoising framework for the removal of mixed Gaussian impulse noise, in which the denoising problem is modeled as a convolutional neural network (CNN) constrained non-negative matrix factorization problem. Using the proximal alternating linearized minimization, the optimization can be divided into three steps: the update of the spectral matrix, the update of the abundance matrix, and the estimation of the sparse noise. Then, we design the CNN architecture and proposed two training schemes, which can allow the CNN to be trained with a 2D-image dataset. Compared with the state-of-the-art denoising methods, the proposed method has a relatively good performance on the removal of the Gaussian and mixed Gaussian impulse noises. More importantly, the proposed model can be only trained once by a 2D-image dataset but can be used to denoise HSIs with different numbers of channel bands.
57 citations
03 Apr 2020
TL;DR: This paper proposes a novel approach to boost the performance of a real image denoiser which is trained only with synthetic pixel-independent noise data dominated by AWGN, and investigates Pixel-shuffle Down-sampling strategy to adapt the trained model to real noises.
Abstract: Discriminative learning based image denoisers have achieved promising performance on synthetic noises such as Additive White Gaussian Noise (AWGN). The synthetic noises adopted in most previous work are pixel-independent, but real noises are mostly spatially/channel-correlated and spatially/channel-variant. This domain gap yields unsatisfied performance on images with real noises if the model is only trained with AWGN. In this paper, we propose a novel approach to boost the performance of a real image denoiser which is trained only with synthetic pixel-independent noise data dominated by AWGN. First, we train a deep model that consists of a noise estimator and a denoiser with mixed AWGN and Random Value Impulse Noise (RVIN). We then investigate Pixel-shuffle Down-sampling (PD) strategy to adapt the trained model to real noises. Extensive experiments demonstrate the effectiveness and generalization of the proposed approach. Notably, our method achieves state-of-the-art performance on real sRGB images in the DND benchmark among models trained with synthetic noises. Codes are available at https://github.com/yzhouas/PD-Denoising-pytorch.
47 citations
TL;DR: The processing results of simulated data and real data indicate that the presented method well estimates the parameters of Class B modelled noise and shows that the Middleton Class B model is suitable for modelling the impulsive noise in shallow water.
Abstract: The statistical characteristic of ocean ambient noise plays an important role in developing underwater signal processors. Considering that the noise in shallow water shows the impulsive nature, non-Gaussian noise models are usually applied to model the ocean ambient noise. In this study, the ocean ambient noise is modelled by using the Middleton Class B model, which can be decomposed into Gaussian and non-Gaussian models. Then, the parameters of Class B model are estimated based on the least-square estimation method, which can be deduced by using the characteristic function of the Middleton Class B model. The processing results of simulated data and real data indicate that the presented method well estimates the parameters of Class B modelled noise. Besides, it further shows that the Middleton Class B model is suitable for modelling the impulsive noise in shallow water.
42 citations
TL;DR: Results show that the proposed filter significantly improves edges over exiting literature, and Peak Signal to Noise Ratio was improved by 1.2 dB in de-noising of medical images corrupted by medium to high noise densities.
Abstract: Image corruption is a common phenomenon which occurs due to electromagnetic interference, and electric signal instabilities in a system. In this letter, a novel multi procedure Min-Max Average Pooling based Filter is proposed for removal of salt, and pepper noise that betide during transmission. The first procedure functions as a pre-processing step that activates for images with low noise corruption. In latter procedure, the noisy image is divided into two instances, and passed through multiple layers of max, and min pooling which allow restoration of intensity transitions in an image. The final procedure recombines the parallel processed images from the previous procedures, and performs average pooling to remove all residual noise. Experimental results were obtained using MATLAB software, and show that the proposed filter significantly improves edges over exiting literature. Moreover, Peak Signal to Noise Ratio was improved by 1.2 dB in de-noising of medical images corrupted by medium to high noise densities.
35 citations
TL;DR: This paper interprets nonlocal similar patch-based denoising as a problem of low-rank recovery and introduces a new nonconvex surrogate for the $l_{0}$ -norm and finds the optimal solution of the optimization problems when the new norm is applied to low- rank recovery.
Abstract: Exemplar-based image denoising algorithms have shown great potential for image restoration with a multitude of existing models. In this paper, we interpret nonlocal similar patch-based denoising as a problem of low-rank recovery. This offers a physically plausible model and unifies several existing techniques in a single low-rank recovery framework. The framework can handle complex noise models, such as zero-mean Gaussian noise, impulse noise, and any other noise that can be approximated by mixing these two kinds of noise. Moreover, we introduce a new nonconvex surrogate for the $l_{0}$ -norm and find the optimal solution of the optimization problems when the new norm is applied to low-rank recovery. The experimental results with different kinds of noise confirm the effectiveness of the proposed low-rank recovery framework and the new norm.
35 citations
TL;DR: A novel Adaptive Switching Modified Decision Based Unsymmetric Trimmed Median Filter for noise reduction in gray scale MR Images which are affected by salt and pepper noise is proposed.
31 citations
TL;DR: The proposed Adaptive Cuckoo Search based bilateral filter denoising gives better results in terms of Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Feature Similarity Index (FSIM), Entropy and CPU time in comparison to traditional methods such as Median filter and RGB spatial filter.
Abstract: A satellite image transmitted from satellite to the ground station is corrupted by different kinds of noises such as impulse noise, speckle noise and Gaussian noise. The traditional methods of denoising can remove the noise components but cannot preserve the quality of the image and lead to over-blurring of the edges in the image. To overcome these drawbacks, this paper develops an optimized bilateral filter for image denoising and preserving the edges using different nature inspired optimization algorithms which can effectively denoise the image without blurring the edges in the image. Denoising the image using a bilateral filter requires the decision of the control parameters so that the noise is removed and the edge details are preserved. With the help of optimization algorithms such as Particle Swarm Optimization (PSO), Cuckoo Search (CS) and Adaptive Cuckoo Search (ACS), the control parameters in the bilateral filter are decided for optimal performance. It is observed that the proposed Adaptive Cuckoo Search based bilateral filter denoising gives better results in terms of Peak Signal to Noise Ratio (PSNR), Mean Square Error (MSE), Feature Similarity Index (FSIM), Entropy and CPU time in comparison to traditional methods such as Median filter and RGB spatial filter.
30 citations
TL;DR: A comprehensive study of the median filter and its different variants to reduce or remove the impulse noise from gray scale images is presented and the Extended median filter (EMF) and Modified BDND are best in terms of relative statistical ratios and pleasant visual results.
29 citations
TL;DR: The proposed method is effective and efficient, and exhibits better performance for the removal of mixed or unknown noise in images on graphs than other denoising algorithms in the literature.
Abstract: Image denoising technologies in a Euclidean domain have achieved good results and are becoming mature. However, in recent years, many real-world applications encountered in computer vision and geometric modeling involve image data defined in irregular domains modeled by huge graphs, which results in the problem on how to solve image denoising problems defined on graphs. In this paper, we propose a novel model for removing mixed or unknown noise in images on graphs. The objective is to minimize the sum of a weighted fidelity term and a sparse regularization term that additionally utilizes wavelet frame transform on graphs to retain feature details of images defined on graphs. Specifically, the weighted fidelity term with $\ell _{1}$ -norm and $\ell _{2}$ -norm is designed based on a analysis of the distribution of mixed noise. The augmented Lagrangian and accelerated proximal gradient methods are employed to achieve the optimal solution to the problem. Finally, some supporting numerical results and comparative analyses with other denoising algorithms are provided. It is noted that we investigate image denoising with unknown noise or a wide range of mixed noise, especially the mixture of Poisson, Gaussian, and impulse noise. Experimental results reported for synthetic and real images on graphs demonstrate that the proposed method is effective and efficient, and exhibits better performance for the removal of mixed or unknown noise in images on graphs than other denoising algorithms in the literature. The method can effectively remove mixed or unknown noise and retain feature details of images on graphs. It delivers a new avenue for denoising images in irregular domains.
TL;DR: The experimental results show that the trained model has better quality evaluation performance on noisy images than existing blind noise assessment models, while also outperforming general-purpose blind and full-reference image quality assessment methods.
Abstract: Noise that afflicts natural images, regardless of the source, generally disturbs the perception of image quality by introducing a high-frequency random element that, when severe, can mask image content. Except at very low levels, where it may play a purpose, it is annoying. There exist significant statistical differences between distortion-free natural images and noisy images that become evident upon comparing the empirical probability distribution histograms of their discrete wavelet transform (DWT) coefficients. The DWT coefficients of low- or no-noise natural images have leptokurtic, peaky distributions with heavy tails; while noisy images tend to be platykurtic with less peaky distributions and shallower tails. The sample kurtosis is a natural measure of the peakedness and tail weight of the distributions of random variables. Here, we study the efficacy of the sample kurtosis of image wavelet coefficients as a feature driving, an extreme learning machine which learns to map kurtosis values into perceptual quality scores. The model is trained and tested on five types of noisy images, including additive white Gaussian noise, additive Gaussian color noise, impulse noise, masked noise, and high-frequency noise from the LIVE, CSIQ, TID2008, and TID2013 image quality databases. The experimental results show that the trained model has better quality evaluation performance on noisy images than existing blind noise assessment models, while also outperforming general-purpose blind and full-reference image quality assessment methods.
TL;DR: Evaluations, based on t-distributed Stochastic Neighbor Embedding visualization, Receiver Operating Characteristic analysis, and saliency maps, demonstrate the reliability of the Inception-v3 deep CNN in classifying noisy skin lesion images.
TL;DR: The proposed noise adaptive information set based switching median (NAISM) filter is inspired from fuzzy switching median filter and works on the concept of information sets and can preserve image details better than the fuzzy filter.
TL;DR: A spatially adaptive image denoising via enhanced noise detection method (SAID-END) is proposed for grayscale and color images, which shows that the proposed method outperforms the existing denoizing methods when applied to graysscale andcolor images.
Abstract: Keeping in view the variety of the applications, image denoising still remains the unexplored territory for the researchers. There are many pros and cons in existing denoising algorithms. The two prime cons of image denoising algorithms are (i) Over and under detection of noisy pixels (ii) Low performance at high noise levels. So, in order to overcome these existing issues, a spatially adaptive image denoising via enhanced noise detection method (SAID-END) is proposed for grayscale and color images. The denoising is achieved using a two-stage sequential algorithm, the first stage ensures accurate noise estimation by eliminating over and under detection of noisy pixels. The second stage performs image restoration by considering non-noisy pixels in estimation of the original pixel value. To enhance the accuracy while denoising high-density impulse noise and artifacts, both noise estimation and restoration stages are using a spatially adaptive window (window expands to spatially connected area), the size of the window depends upon the noise level in the vicinity of the reference noisy pixel. The two stages of the proposed method are referred to as (i) Enhanced adaptive noise detection (ii) Non-corrupted pixel sensitive adaptive image restoration. The proposed method is evaluated by two test steps to ensure its versatility and robustness. In the first step, the proposed method is tested on a wide standard data set of color and grayscale images affected by impulse noise and artifacts. The results of proposed method are compared with well-known methods compatible for denoising impulse noise and artifacts. In the second step, the results of proposed method are compared with the recent state of the art algorithms for traditional test images. The result shows that the proposed method outperforms the existing denoising methods when applied to grayscale and color images.
TL;DR: Simulation results demonstrate that the proposed algorithms achieve faster convergence rate and better noise reduction performance compared with other investigated algorithms.
TL;DR: Experimental work showed that the proposed method can achieve low loss and root meansquare error during training, high peak signal to noise ratio, low mean square error, image quality assessment with good quality and mean absolute error for close prediction between denoised and original color images.
Abstract: Elimination of combined Gaussian and impulse noises in digital image processing with preservation of image details and suppression of noise are challenging problem. For this purpose, a new filter which is median filters combined with convolutional neural network for Gaussian and salt & pepper noises. The previous methods are application dependents; some used for impulse noise and other employed only for Gaussian noise. The elimination of Gaussian and impulse noise completed into two steps. First the detection of impulse noise with the rejection of noise by employed of 3 × 3 and 5 × 5 window size median filters. In the second step removal of Gaussian noise performed by residual learning denoising convolutional neural network. It is very favorable and the ability of learning and denoising performance in the field of digital image processing. Denoising convolutional neural network also has active Gaussian noise with an unknown level of noise. Experimental work showed that the proposed method can achieve low loss and root mean square error during training, high peak signal to noise ratio, low mean square error, image quality assessment with good quality and mean absolute error for close prediction between denoised and original color images.
TL;DR: The experimental outcomes demonstrate that the proposed approach is better than those existing methods in terms of standard signal-to-noise ratio (PSNR), relative error (ReErr), and visual quality.
TL;DR: A kernel affine projection-like algorithm (KAPLA) is proposed in reproducing kernel Hilbert space in non-Gaussian environments and provides good performance for nonlinear channel equalization in impluse-noise environments.
Abstract: A kernel affine projection-like algorithm (KAPLA) is proposed in reproducing kernel Hilbert space in non-Gaussian environments. The cost function for the developed algorithm is constructed by using the correntropy approach and Gaussian kernel to deal with nonlinear channel estimation. The devised algorithm can efficiently operate in the impulse noise. As a consequence, the proposed KAPLA algorithm provides good performance for nonlinear channel equalization in impluse-noise environments. Simulations results in different mixed noise environments verify the superior behavior of KAPLA compared to known algorithms.
TL;DR: The performance of the proposed denoising model is better than the other existing methods in terms of some quality assessment metrics.
Abstract: Although image denoising as a basic task of image restoration has been widely studied in the past decades, there are not many studies on mixed noise denoising. In this paper, we propose two structured dictionary learning models to recover images corrupted by mixed Gaussian and impulse noise. These two models can be merged as $\ell _{p}$ -norm fidelity plus $\ell _{q}$ -norm regularization. The fidelity term is used to fit image patches and the regularization term is employed for sparse coding. Particularly, we utilize proximal (and proximal linearized) alternating minimization methods as the main solvers to deal with these two models. We remove the Gaussian noise under the assumption that the uncorrupted image can be approximated with a linear representation under an appropriate orthogonal basis. We use different ways to remove impulse noise for these two models. The experimental results are reported to compare the existing methods and demonstrate the performance of the proposed denoising model is better than the other existing methods in terms of some quality assessment metrics.
TL;DR: The introduction of Mid-Value-Decision-Median in DP reduces the chances of selecting corrupted pixel for denoised image and results indicate that the IAMFA-II has better running time and equivalent output compared with DP, while IAM FA-I generates better output and has equivalent running time when compared withDP.
TL;DR: A novel SAP noise elimination method which employs a regression-based neuro-fuzzy network for highly corrupted gray scale and color images is proposed which has superior performance in terms of all comparison metrics.
Abstract: Salt and pepper (SAP) noise elimination is a crucial step for further image processing and pattern recognition applications. The main aim of this article is to propose a novel SAP noise elimination method which employs a regression-based neuro-fuzzy network for highly corrupted gray scale and color images. In the proposed method, multiple neuro-fuzzy filters trained with artificial bee colony algorithm is combined with a decision tree algorithm. The performance of the proposed filter is compared with a number of well known methods with respect to popular metrics including, structural similarity index, peak signal-to-noise ratio, and correlation on well known test images. The results reveal that the proposed filter has superior performance in terms of all comparison metrics.
TL;DR: In this article, a nonlinear constrained-PDE based on the fractional order tensor diffusion to approximate the clean image and also the impulse component in a mixture of Gaussian and impulse noise is proposed.
Abstract: In denoising problems, it is always hard to deal with a mixture of two noise densities. In this paper, we introduce a nonlinear constrained-PDE based on the fractional order tensor diffusion to approximate the clean image and also the impulse component in a mixture of Gaussian and impulse noise. Our model offers an ideal compromise between the edge preservation, staircasing creation and the loss of image contrasts. The proposed constrained-PDE is formulated using a variational model that features a L1 data discrepancy encoding the impulse noise and an L2 term of the clean image which is a solution of a high-order PDE. Then, a rigorous analysis of the existence of the solution to the proposed model is checked in a suitable functional framework. In addition, to solve the constrained-PDE, we consider an extension of the Primal-Dual algorithm to nonlinear operators with an accelerate Bregman iteration. Numerical experiments show that the proposed model produces pleasant results in terms of restoration quality and solution efficiency compared to some competitive regularizations.
TL;DR: The model of asynchronous impulsive noise of Middleton class-A noise and corresponding multipath fading channels in PLC is introduced, and the bit error rate (BER) performance of the MDCSK scheme over different channels is analyzed and found that the BER of the proposed scheme is by 2–3 orders of magnitude lower.
Abstract: Previous studies have shown that impulsive noise can weaken the performance of power line communication (PLC). Though DCSK can improve the performance in an order of magnitude comparing to the direct sequence differential phase shift keying (DS-DPSK), it is still a challenge to further improve the BER performance with signal redesign without the need of advanced and expensive extra noise suppression technologies. The paper introduces the model of asynchronous impulsive noise of Middleton class-A noise and corresponding multipath fading channels in PLC, and analyzes the bit error rate (BER) performance of the $M$ -ary differential chaos shift keying (MDCSK) scheme over different channels. Furthermore, a new replica piecewise frame of MDCSK (RP-MDCSK) is proposed to resist the impulse noise. In the proposed scheme, one piecewise of signals is transmitted first. Then, it replicates $pw$ times, which serves as the reference signal transmitted in the first half symbol period. The information-bearing signal combines the reference signal with its Hilbert transform in the second half. At the receiver, one piece of reference signals is extracted and then correlated with its corresponding information-bearing part. The BER expressions of the MDCSK and the proposed scheme are derived and analyzed over different channels, and verified by simulations. Comparing with the corresponding schemes, it is found that the BER of the proposed scheme is by 2–3 orders of magnitude lower.
TL;DR: This paper proposes a spatial non-local and local rank-constrained low-rank regularized Plug-and-Play model for mixed noise removal in HSIs, and develops an efficient algorithm for solving the proposed NLRPnP model by using the alternating direction method of multipliers method.
Abstract: Hyperspectral images (HSIs) are usually corrupted by various noises during the image acquisition process, e.g., Gaussian noise, impulse noise, stripes, deadlines and many others. Such complex noise severely degrades the data quality, reduces the interpretation accuracy of HSIs, and restricts the subsequent HSI applications. In this paper, a spatial non-local and local rank-constrained low-rank regularized Plug-and-Play (NLRPnP) model is presented for mixed noise removal in HSIs. Specifically, we first divide HSIs into local overlapping patches. Local rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise and a part of Gaussian noise, and to significantly preserve local structure and detail information in HSIs. Then the spatial non-local based denoiser is introduced to promote the non-local self-similarity and obviously depress the Gaussian noise. Without increasing the difficulty of solving optimization problems, we combine the local and non-local based methods into the Plug-and-Play framework, and develop an efficient algorithm for solving the proposed NLRPnP model by using the alternating direction method of multipliers method. Finally, several experiments are conducted in both simulated and real data conditions to illustrate the better performance of the proposed NLRPnP model than the existing state-of-the-art denoising models.
TL;DR: This review discusses in detail of Poisson and Impulse noise, as well as its causes and effect on the X-ray images, which create un-certainty for theX-ray inspection imaging system while discriminating objects and for the screeners as well.
Abstract: In this paper, we present a review of the research literature regarding applying X-ray imaging of baggage scrutiny at airport. It discusses multiple X-ray imaging inspection systems used in airports for detecting dangerous objects inside the baggage. Moreover, it also explains the dual energy X-ray image fusion and image enhancement factors. Different types of noises in digital images and noise models are explained in length. Diagrammatical representations for different noise models are presented and illustrated to clearly show the effect of Poisson and Impulse noise on intensity values. Overall, this review discusses in detail of Poisson and Impulse noise, as well as its causes and effect on the X-ray images, which create un-certainty for the X-ray inspection imaging system while discriminating objects and for the screeners as well. The review then focuses on image processing techniques used by different research studies for X-ray image enhancement, de-noising, and their limitations. Furthermore, the most related approaches for noise reduction and its drawbacks are presented. The methods that may be useful to overcome the drawbacks are also discussed in subsequent sections of this paper. In summary, this review paper highlights the key theories and technical methods used for X-ray image enhancement and de-noising effect on X-ray images generated by the airport baggage inspection system.
TL;DR: A new denoising model based on generative adversarial network (DeGAN) is proposed to remove mixed noise in images and a new joint loss function is designed to incorporate information from image features and human visual perception into the mixed noise elimination task, which further improves the image quality and the visual effect.
TL;DR: This work proposes a novel sparse unmixing method with the bandwise model (SUBM) to address the above mentioned problems simultaneously and the alternative direction method of multipliers (ADMM) is adopted for solving the proposed SUBM.
TL;DR: Compared with the mainstream denoising algorithms, the proposed method can detect and filter out the random-value impulse noise in the image more effectively and faster, while better retaining the edges and other details of the image.
Abstract: A two-stage denoising algorithm based on local similarity is proposed to process lowly and moderate corrupted images with random-valued impulse noise in this paper. In the noise detection stage, the pixel to be detected is centered and the local similarity between the pixel and each pixel in its neighborhood is calculated, which can be used as the probability that the pixel is noise. By obtaining the local similarity of each pixel in the image and setting an appropriate threshold, the noise pixels and clean pixels in the damaged image can be detected. In the image restoration stage, an improved bilateral filter based on local similarity and geometric distance is designed. The pixel detected as noise in the first stage is filtered and the new intensity value is the weighted average of all pixel intensities in its neighborhood. A large number of experiments have been conducted on different test images and the results show that compared with the mainstream denoising algorithms, the proposed method can detect and filter out the random-value impulse noise in the image more effectively and faster, while better retaining the edges and other details of the image.
TL;DR: Numerical experiments on five different kinds of mixed noise scenarios and one real world data have tested and demonstrated the superior denoising power of the proposed BFTV model compared with three state-of-the-art low-rank-based approaches.