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This paper deals with novel mathematical methods to locate the edges of heated planar objects employing simple photodiodes. Thereby, both the lateral edge position and the axial distance of the object can be determined. Furthermore, a method which allows the estimation of the rotation angle of the investigated object is discussed. In contrast to an infrared camera, photodiodes and the required electronic components are insensitive to mechanical vibrations commonly experienced in industrial fabrication processes. Nevertheless, the limited spatial resolution of such photodiode ensemble demands for a signal-processing-based resolution enhancement, which is presented in this paper. By means of simulation results, the efficiency of the novel methods is verified. [ABSTRACT FROM AUTHOR]

Regularization methods for the solution of ill-posed inverse problems can be successfully applied if a right estimation of the regularization parameter is known. In this paper, we consider the L1-regularized image deblurring problem and evaluate its solution using the iterative forward–backward splitting method. Based on this approach, we propose a new adaptive rule for the estimation of the regularization parameter that, at each iteration, dynamically updates the parameter value, following the evolution of the objective functional. The iterative algorithm automatically stops, without requiring any assumption about the perturbation process, when the parameter has reached a seemingly near optimal value. In spite of the fact that the optimality of this value has not yet been theoretically proved, a large number of numerical experiments confirm that the proposed rule yields restoration results competitive with those of the best state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract: The weighted least-squares solutions of coupled singular matrix equations are too difficult to obtain by applying matrices decomposition. In this paper, a family of algorithms are applied to solve these problems based on the Kronecker structures. Subsequently, we construct a computationally efficient solutions of coupled restricted singular matrix equations. Furthermore, the need to compute the weighted Drazin and weighted Moore–Penrose inverses; and the use of Tian''s work and Lev-Ari''s results are due to appearance in the solutions of these problems. The several special cases of these problems are also considered which includes the well-known coupled Sylvester matrix equations. Finally, we recover the iterative methods to the weighted case in order to obtain the minimum D-norm G-vector least-squares solutions for the coupled Sylvester matrix equations and the results lead to the least-squares solutions and invertible solutions, as a special case. [Copyright &y& Elsevier]