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Nonmydriatic retinal fundus images often suffer from quality issues and artifacts due to ocular or systemic comorbidities, leading to potential inaccuracies in clinical diagnoses. In recent times, deep learning methods have been widely employed to improve retinal image quality. However, these methods often require large datasets and lack robustness in clinical settings. Conversely, the inherent stability and adaptability of traditional unsupervised learning methods, coupled with their reduced reliance on extensive data, render them more suitable for real-world clinical applications, particularly in the limited data context of high noise levels or a significant presence of artifacts. However, existing unsupervised learning methods encounter challenges such as sensitivity to noise and outliers, reliance on assumptions like cluster shapes, and difficulties with scalability and interpretability, particularly when utilized for retinal image enhancement. To tackle these challenges, we propose a novel robust PCA (RPCA) method with low-rank sparse decomposition that also integrates affine transformations τ i , weighted nuclear norm, and the L 2 , 1 norms, aiming to overcome existing method limitations and to achieve image quality improvement unseen by these methods. We employ the weighted nuclear norm (L w , ∗) to assign weights to singular values to each retinal images and utilize the L 2 , 1 norm to eliminate correlated samples and outliers in the retinal images. Moreover, τ i is employed to enhance retinal image alignment, making the new method more robust to variations, outliers, noise, and image blurring. The Alternating Direction Method of Multipliers (ADMM) method is used to optimally determine parameters, including τ i , by solving an optimization problem. Each parameter is addressed separately, harnessing the benefits of ADMM. Our method introduces a novel parameter update approach and significantly improves retinal image quality, detecting cataracts, and diabetic retinopathy. Simulation results confirm our method's superiority over existing state-of-the-art methods across various datasets. [ABSTRACT FROM AUTHOR]

In this study, an effective robust PCA is developed for joint image alignment and recovery via L 2,1 norms and affine transformations. To alleviate the potential impacts of outliers, heavy sparse noises, occlusions, and illuminations, the L 2,1 norms along with affine transformations are taken into consideration. The determination of the parameters involved and the updating affine transformations is arranged in the form of a constrained convex optimization problem. To reduce the computation load, we also further decompose the error as sparse error and Gaussian noise; additionally, the alternating direction method of multipliers (ADMM) is considered to develop a new set of recursive equations to update the optimization parameters and the affine transformations iterative. The convergence of the derived updating equation is explained as well. Conducted simulations illustrate that the new method is superior to the baseline works in terms of precision on some public databases. [ABSTRACT FROM AUTHOR]

In this latest work, the Newly Modified Robust Tensor Principal Component Analysis (New RTPCA) using affine transformation and L 2,1 norms is proposed to remove the outliers and heavy sparse noises in signal processing. This process is done by decomposing the original data matrix as the low-rank heavy sparse noises. The determination of the potential variables is casted as constrained convex optimization problem, and the Alternating Direction Method of Multipliers (ADMM) method is considered to reduce the computational loads in an iterative manner. The simulation results validate the effectiveness of the new method as compared with that of the state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this work, we propose a novel method for head pose estimation and face recovery, particularly to solve the potential impacts of noises in signal processing to get an efficient and effective model that is more resilient with annoying effects through adding affine transformation with the low-rank robust subspace regression. Consequently, the corrupted images can be correctly recovered by affine transformations to render more best regression outcomes. Thereby, we need to search so as to get optimal parameters which can be regarded as convex constrained optimization techniques. Afterward, the alternating direction method for multipliers (ADMM) approach is considered and a new set of updated equations is well established so as to update the optimization parameters and affine transformations iteratively in a round-robin manner. Additionally, the convergence of these new updating equations is well scrutinized as well. Thus, the experimental simulations reveal that the proposed method outperforms the state-of-the-art works for head pose estimation and face recovery on some public databases. [ABSTRACT FROM AUTHOR]

In this paper, we developed a new robust part-based model for facial landmark localization and detection via affine transformation. In contrast to the existing works, the new algorithm incorporates affine transformations with the robust regression to tackle the potential effects of outliers and heavy sparse noises, occlusions and illuminations. As such, the distorted or misaligned objects can be rectified by affine transformations and the patterns of occlusions and outliers can be explicitly separated from the true underlying objects in big data. Moreover, the search of the optimal parameters and affine transformations is cast as a constrained optimization programming. To mitigate the computations, a new set of equations is derived to update the parameters involved and the affine transformations iteratively in a round-robin manner. Our way to update the parameters compared to the state of the art of the works is relatively better, as we employ a fast alternating direction method for multiplier (ADMM) algorithm that solves the parameters separately. Simulations show that the proposed method outperforms the state-of-the-art works on facial landmark localization and detection on the COFW, HELEN, and LFPW datasets. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel robust algorithm for image recovery via affine transformations, the weighted nuclear, L ∗ , w , and the L 2,1 norms. The new method considers the spatial weight matrix to account the correlated samples in the data, the L 2,1 norm to tackle the dilemma of extreme values in the high-dimensional images, and the L ∗ , w norm newly added to alleviate the potential effects of outliers and heavy sparse noises, enabling the new approach to be more resilient to outliers and large variations in the high-dimensional images in signal processing. The determination of the parameters is involved, and the affine transformations are cast as a convex optimization problem. To mitigate the computational complexity, alternating iteratively reweighted direction method of multipliers (ADMM) method is utilized to derive a new set of recursive equations to update the optimization variables and the affine transformations iteratively in a round-robin manner. The new algorithm is superior to the state-of-the-art works in terms of accuracy on various public databases. [ABSTRACT FROM AUTHOR]

In this work, a new robust regularized shrinkage regression method is proposed to recover and align high-dimensional images via affine transformation and Tikhonov regularization. To be more resilient with occlusions and illuminations, outliers, and heavy sparse noises, the new proposed approach incorporates novel ideas affine transformations and Tikhonov regularization into high-dimensional images. The highly corrupted, distorted, or misaligned images can be adjusted through the use of affine transformations and Tikhonov regularization term to ensure a trustful image decomposition. These novel ideas are very essential, especially in pruning out the potential impacts of annoying effects in high-dimensional images. Then, finding optimal variables through a set of affine transformations and Tikhonov regularization term is first casted as mathematical and statistical convex optimization programming techniques. Afterward, a fast alternating direction method for multipliers (ADMM) algorithm is applied, and the new equations are established to update the parameters involved and the affine transformations iteratively in the form of the round-robin manner. Moreover, the convergence of these new updating equations is scrutinized as well, and the proposed method has less time computation as compared to the state-of-the-art works. Conducted simulations have shown that the new robust method surpasses to the baselines for image alignment and recovery relying on some public datasets. [ABSTRACT FROM AUTHOR]

This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L 2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and L 2,1 norms. To attain this, affine transformations and Frobenius and L 2,1 norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works. [ABSTRACT FROM AUTHOR]

This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L 2,1 norms. The most popular and successful approach is to model the robust PCA problem as a low-rank matrix recovery problem in the presence of sparse corruption. The existing algorithms still lack in dealing with the potential impact of outliers and heavy sparse noises for image alignment and recovery. Thus, the new algorithm tackles the potential impact of outliers and heavy sparse noises via using novel ideas of affine transformations and Frobenius and L 2,1 norms. To attain this, affine transformations and Frobenius and L 2,1 norms are incorporated in the decomposition process. As such, the new algorithm is more resilient to errors, outliers, and occlusions. To solve the convex optimization involved, an alternating iterative process is also considered to alleviate the complexity. Conducted simulations on the recovery of face images and handwritten digits demonstrate the effectiveness of the new approach compared with the main state-of-the-art works. [ABSTRACT FROM AUTHOR]

In this study, predictive models are proposed to accurately estimate the confirmed cases and deaths due to of Corona virus 2019 (COVID-19) in Africa. The study proposed the predictive models to determine the spatial and temporal pattern of COVID 19 in Africa. The result of the study has shown that the spatial and temporal pattern of the pandemic is varying across in the study area. The result has shown that cubic model is best outperforming compared to the other six families of exponentials ( R 2 = 0.996 , F = 538.334 , D F 1 = 3 , D F 1 = 7 , b 1 = 13691.949 , b 2 = - 824.701 , b 1 = 12.956 ) . The adopted cubic algorithm is more robust in predicting the confirmed cases and deaths due to COVID 19. The cubic algorithm is more superior to the state of the art of the works based on the world health organization data. This also entails the best way to mitigate the expansion of COVID 19 is through persistent and strict self-isolation. This pandemic will sustain to grow up, and peak to the highest for which a strong care and public health interventions practically implemented. It is highly recommended for Africans must go beyond theory preparations implementations practically through the public interventions., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (© 2021 The Authors. Production and hosting by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.)