Nezam Mahdavi-Amiri

Saeedeh Rezaee, Nezam Mahdavi-Amiri

Nowadays, due to advanced digital imaging technologies and internet accessibility to the public, the number of generated digital images has increased dramatically. Thus, the need for automatic image enhancement techniques is quite apparent. In recent years, deep learning has been used effectively. Here, after introducing some recently developed works on image enhancement, an image enhancement system based on convolutional neural networks is presented. Our goal is to make an effective use of two available approaches, convolutional neural network and bilateral grid. In our approach, we increase the training data and the model dimensions and propose a variable rate during the training process. The enhancement results produced by our proposed method, while incorporating 5 different experts, show both quantitative and qualitative improvements as compared to other available methods.

Negin Bagherpour, Nezam Mahdavi-Amiri

Nonlinear matrix equations arise in many practical contexts related to control theory, dynamical programming and finite element methods for solving some partial differential equations. In most of these applications, it is needed to compute a symmetric and positive definite solution. Here, we propose new iterative algorithms for solving three different types of nonlinear matrix equations. We have recently proposed a new algorithm for solving positive definite total least squares problems. Making use of an iterative process for inverse of a matrix, we convert the nonlinear matrix equation to an iterative linear one, and, in every iteration, we apply our algorithm for solving a positive definite total least squares problem to solve the linear subproblem and update the newly defined variables and the matrix inverse terms using appropriate formulas. Our proposed algorithms have a number of useful features. One is that the computed unknown matrix remains symmetric and positive definite in all iterations. As the second useful feature, numerical test results show that in most cases our proposed approach turns to compute solutions with smaller errors within lower computing times. Finally, we provide some test results showing that our proposed algorithm converges to a symmetric and positive definite solution in Matlab software environment on a PC, while other methods fail to do so.