Abstract
For images with sharp changes of intensity, the appropriate regularization is based on variational functionals. In order to minimize such a functional, the gradient descent approach can be used. In this paper, we analyze the performance of the gradient descent method in the frequency domain and show that the method converges to the sum of the original undistorted function and the kernel function of a linear distortion operator.
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The work was supported by the Ministry of Education and Science of Russian Federation, grant 2.1766.2014К and RFBR grant 13.01.00735.
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Makovetskii, A., Vokhmintsev, A., Kober, V., Kuznetsov, V. (2015). Frequency Analysis of Gradient Descent Method and Accuracy of Iterative Image Restoration. In: Khachay, M., Konstantinova, N., Panchenko, A., Ignatov, D., Labunets, V. (eds) Analysis of Images, Social Networks and Texts. AIST 2015. Communications in Computer and Information Science, vol 542. Springer, Cham. https://doi.org/10.1007/978-3-319-26123-2_11
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DOI: https://doi.org/10.1007/978-3-319-26123-2_11
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