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This paper proposes an effective and robust method for image alignment and recovery on a set of linearly correlated data via Frobenius and L2,1 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 L2,1 norms. To attain this, affine transformations and Frobenius and L2,1 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.

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 ( . 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.

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.

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BackgroundCOVID 19 is becoming a global health problem, where strong intervention is needed. Thus, this paper addresses predictive models on COVID 19 in Africa, from which the government and others put a strong intervention in optimizing resources and necessary healthcare demand.MethodsPredictive models (Cubic polynomial and quadratic regression models) are considered based on the daily report of WHO, 2020 rampant data. The data were analyzed using R and STATA packages.ResultsThe result of the study has shown that the spatial and temporal pattern of this novel virus is varying, spreading and covering the entire world within a brief time. The result has shown that the fitting effect of 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 cubic algorithm is more robust in predicting the deaths and confirmed cases of COVID 19. There are also evidences that the source of the outbreak of the epidemic is related to Huanan Seafood from the whole market, fever (78%), cough (59%), fatigue (75%), headache (76%), and others are identified as the major symptoms of COVID 19. Moreover, the result of our study has shown the corona virus infection epidemic is increasing, which seeks a long-term plan to take an action in disease prevention and intervention programs.ConclusionThe trend of COVID 19 is increasing with an alarm rate, thus strong intervention is needed to mitigate the spread of this novel virus. This also can be done through reducing the spread of COVID 19 as persistent and strict self-isolation. The results acquired from this study also recommend that COVID-19 mortality and more cases might be engulfing in Africa due to lack of preparedness and giving strong awareness for the public.This pandemic will sustain to grow up, and peak to the highest for which a strong care and public health interventions practically implemented. Africans must go beyond theory preparations, strong awareness for the public and practical implementation is highly recommended. Highly recommended more sophisticated equipment to tackle the spread of the virus and safe the loss of the infected from deaths.