Recently, many variational models involving high order derivatives have been widely used in image processing, because they can reduce staircase effects during noise elimination. However, it is very challenging to construct efficient algorithms to obtain the minimizers of original high order functionals. In this paper, we propose a new linearized augmented Lagrangian method for Euler's elastica image denoising model. We detail the procedures of finding the saddle-points of the augmented Lagrangian functional. Instead of solving associated linear systems by FFT or linear iterative methods (e.g., the Gauss-Seidel method), we adopt a linearized strategy to get an iteration sequence so as to reduce computational cost. In addition, we give some simple complexity analysis for the proposed method. Experimental results with comparison to the previous method are supplied to demonstrate the efficiency of the proposed method, and indicate that such a linearized augmented Lagrangian method is more suitable to deal with large-sized images.
In the current study, the deflection angle of columnar dendrites on the cross section of steel billets under mold electromagnetic stirring (M-EMS) was observed. A mathematical model was developed to define the effect of M-EMS on fluid flow and then to analyze the relationship between flow velocities and deflection angle. The model was validated using experimental data that was measured with a Tesla meter on magnetic intensity. By coupling the numerical results with the experimental data, it was possible to define a relationship between the velocities of the fluid with the deflection angle of high-carbon steel. The deflection angle of high-carbon steel reached maximum values from 18 to 23 deg for a velocity from 0.35 to 0.40 m/s. The deflection angles of low-carbon steel under different EM parameters were discussed. The deflection angle of low-carbon steel was increased as the magnetic intensity, EM force, and velocity of molten steel increased.
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