This paper proposes an effective and robust algorithm for image alignment on a set of linearly correlated ata. The new algorithm modifies the Robust Algorithm for Sparse and Low rank decomposition (RASL) by utilizing the prior information of partial column rank. To attain this, an extra term is incorporated in the decomposition of data matrix, which enables the new approach to be more resilient to errors, outliers and occlusions. The problem is cast as a constrained optimization problem, which is then solved by convex program. A new set of equations are also derived to update the variables involved in a round-robin manner. Conducted simulations on the recovery of aligned face images and handwritten digits reveal the effectiveness of the new algorithm compared with the main state-of-the-art works.

In this paper, we propose a novel robust algorithm for image recovery via affine transformations and the L2,1 norm. To be robust against miscellaneous adverse effects such as occlusions, outliers and heavy sparse noise, the new algorithm integrates affine transformations with low-rank plus sparse decomposition, where the low-rank component lies in a union of disjoint subspaces, so the distorted or misaligned images can be rectified to render more faithful image representation. In addition, the L2,1 norm is employed to remove the correlated samples across the images, enabling the new approach to be more resilient to outliers and large variations in the images. The determination of the variables involved and the affine transformations is cast as a convex optimization problem. To alleviate the computational complexity, the Alternating 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 convergence of the developed updating equations is addressed and experimentally validated as well. Conducted simulations demonstrate that the new algorithm is superior to the state-of-the-art works in terms of accuracy on some public databases.

Background: Antenatal care (ANC) reduces maternal and newborn mortalities and makes it easier to find infections early and prevent them from progressing. This study aimed to identify factors affecting ANC utilization in Ethiopia via the count regression model. Methods: The data for the study was drawn from the 2019 Ethiopian Mini Demographic and Health Survey dataset. Count regression models, such as Poisson, Negative Binomial (NB), Zero-Inflated Poisson (ZIP), and Zero-Inflated Negative Binomial (ZINB) models, were used to determine the factors influencing ANC utilization. Results: A total of 3962 women were included in the study. Only about 42% of women used the WHO-recommended number of ANC of a minimum of four visits. The ZIP model was outperforming to fit the data as compared to other count regression models. Rural residence (IRR=0.8832, 95% CI: 0.8264–0.9440), being resident of the Somalia region (IRR=0.4762, 95% CI: 0.3919–0.5785), SNNPR (IRR=0.8716, 95% CI: 0.7913–0.9600), and Gambela Region (IRR=0.7830, 95% CI: 0.7063–0.8680), being Muslim (IRR=0.9384, 95% CI: 0.8876–0.9921) decrease the ANC utilization. Contrarily, Addis Ababa residence (IRR=1.1171, 95% CI: 1.0181–1.2259), primary education (IRR=1.1278, 95% CI: 1.0728–1.1855), secondary and higher education (IRR=1.2357, 95% CI: 1.1550–1.3220), middle wealth index (IRR=1.0855, 95% CI: 1.0095–1.1671) and rich wealth index (IRR=1.0941, 95% CI: 1.0152–1.1790) increase the ANC utilization. Conclusion: The ZIP model best fitted the data compared to others. The study revealed that being poor, rural resident, uneducated, Somalia region resident, SNNPR resident, Gambela region resident, and Muslim were factors associated with lower ANC utilization. Thus, health education is needed to be given for mothers with no education. In addition, building a strong awareness-creation program regarding ANC is required for rural residents so as to improve the level of ANC utilization in Ethiopia.

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 ${\tau }_i$, 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 $\left(L_{w,\ast }\right)$ 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, ${\tau }_i$ 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 ${\tau }_i$, 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.

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.