Accurate task execution time estimation is vital for efficient and dependable operation of safety-critical systems. However, modern automotive functions' complexity challenges conventional estimation methods. To address this, we propose a novel technique that combines execution time and job sequence data using a multi-layer perceptron (MLP) neural network. Leveraging MLP's capabilities, our approach achieves impressive 99.7% prediction accuracy with a mere 38.33 μs latency. Integrating our technique into safety-critical systems optimizes resource allocation and scheduling, enhancing performance and reliability. Importantly, our method extends beyond automotive systems, finding potential in diverse safety-critical domains. By precisely estimating task execution time, we enhance operational efficiency and decision-making in complex systems.

EIT problem is a typical inverse problem with serious ill-posedness. In general, regularization techniques are necessary for such ill-posed inverse problems. To overcome ill-posedness, the total variation (TV) regularization is widely used and it is also successfully applied to EIT. For realtime monitoring, a fast and robust image reconstruction algorithm is required. By exploiting recent advances in optimization, we propose a first-order TV algorithm for EIT, which simply consists of matrix-vector multiplications and in which the sparse structure of the system can be easily exploited. Furthermore, a typical smoothing parameter to overcome nondifferentibility of the TV term is not needed and a closed form solution can be applied in part using soft thresholding. It shows a fast reconstruction in the beginning. Numerical experiments using simulated data and real experimental data support our claim.

The fully developed speckle (multiplicative noise) naturally appears in coherent imaging systems, such as synthetic aperture radar. Since the speckle is multiplicative, it is difficult to interpret observed data. Total variation (TV) based variational models have recently been used in the removal of the speckle because of the strong edge preserving property of TV and reasonable computational cost. However, the fidelity term (or negative log-likelihood) of the original variational model [G. Aubert and J.-F. Aujol, SIAM J. Appl. Math., 68 (2008), pp. 925--946], which appears on maximum a posteriori (MAP) estimation, is not convex. Recently, the logarithmic transformation and the $m$th root transformation have been proposed to relax the nonconvexity. It is empirically observed that the $m$th root transform based variational model outperforms the log transform based variational model. However, the performance of the $m$th root transform based model critically depends on the choice of $m$. In this paper, we propose the two-level convex relaxed variational model; i.e., we relax the original variational model by using the $m$th root transformation and the concave conjugate. We also adapt the two-block nonlinear Gauss--Seidel method to solve the proposed model. The performance of the proposed model does not depend on the choice of $m$, and the model shows overall better performance than the logarithmic transformed variational model and the $m$th root transformed variational model.

Speckles (multiplicative noise) in synthetic aperture radar (SAR) make it difficult to interpret the observed image. Due to the edge-preserving feature of total variation (TV), variational models with TV regularization have attracted much interest in reducing speckles. Algorithms based on the augmented Lagrangian function have been proposed to efficiently solve speckle-reduction variational models with TV regularization. However, these algorithms require inner iterations or inverses involving the Laplacian operator at each iteration. In this paper, we adapt Tseng's alternating minimization algorithm with a shifting technique to efficiently remove the speckle without any inner iterations or inverses involving the Laplacian operator. The proposed method is very simple and highly parallelizable; therefore, it is very efficient to despeckle huge-size SAR images. Numerical results show that our proposed method outperforms the state-of-the-art algorithms for speckle-reduction variational models with a TV regularizer in terms of central-processing-unit time.

In coherent imaging systems, such as the synthetic aperture radar (SAR), the observed images are contaminated by multiplicative noise. Due to the edge-preserving feature of the total variation (TV), variational models with TV regularization have attracted much interest in removing multiplicative noise. However, the fidelity term of the variational model, based on maximum a posteriori estimation, is not convex, and so, it is usually difficult to find a global solution. Hence, the logarithmic function is used to transform the nonconvex variational model to the convex one. In this paper, instead of using the log, we exploit the m th root function to relax the nonconvexity of the variational model. An algorithm based on the augmented Lagrangian function, which has been applied to solve the log transformed convex variational model, can be applied to solve our proposed model. However, this algorithm requires solving a subproblem, which does not have a closed-form solution, at each iteration. Hence, we propose to adapt the linearized proximal alternating minimization algorithm, which does not require inner iterations for solving the subproblems. In addition, the proposed method is very simple and highly parallelizable; thus, it is efficient to remove multiplicative noise in huge SAR images. The proposed model for multiplicative noise removal shows overall better performance than the convex model based on the log transformation.

In synthetic aperture radar (SAR), the observed image is corrupted by the speckle (multiplicative noise). The variational models with the total variation (TV) regularization have attracted much interest in reducing the speckle due to the edge preserving feature of TV. Recently, several TV regularized convex variational models, such as the maximum a posteriori (MAP) model for a log-transformed image and the I divergence model, have been proposed. In this paper, we adapt Tseng's alternating minimization algorithm to solve the proposed shifted speckle reduction variational models with TV. The algorithm for the proposed shifted variational models does not require any inner iteration or inversion involving the Laplacian operator that is required in recent algorithms based on an augmented Lagrangian framework. Hence, the proposed method is very simple and highly parallelizable and so efficient to despeckle huge SAR images.

Frame-based image restoration by using the balanced approach has been developed over the last decade. Many recently developed algorithms for image restoration can be viewed as an acceleration of the proximal forward-backward splitting algorithm. Accelerated proximal gradient (APG) algorithms studied by Nesterov, Nemirovski, and others have been demonstrated to be efficient in solving various regularized convex optimization problems arising in compressed sensing, machine learning, and control. In this paper, we adapt the APG algorithm to solve the $\ell_1$-regularized linear least squares problem in the balanced approach in frame-based image restoration. This algorithm terminates in $O(1/\sqrt{\epsilon})$ iterations with an $\epsilon$-optimal solution, and we demonstrate that this single algorithmic framework can universally handle several image restoration problems, such as image deblurring, denoising, inpainting, and cartoon-texture decomposition. Our numerical results suggest that the APG algorithms are efficient and robust in solving large-scale image restoration problems. The algorithms we implemented are able to restore $512\times512$ images in various image restoration problems in less than 50 seconds on a modest PC. We also compare the numerical performance of our proposed algorithms applied to image restoration problems by using one frame-based system with that by using cartoon and texture systems for image deblurring, denoising, and inpainting.