Abstract
In this paper we study a Blind Source Separation (BSS) problem, and in particular we deal with document restoration. We consider the classical linear model. To this aim, we analyze the derivatives of the images instead of the intensity levels. Thus, we establish non-overlapping constraints on document sources. Moreover, we impose that the rows of the mixture matrices of the sources have sum equal to 1, in order to keep equal the lightnesses of the estimated sources and those of the data. Here we give a technique which uses the symmetric factorization, whose goodness is tested by the experimental results.
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References
Boccuto, A., Gerace, I., Giorgetti, V.: A blind source separation technique for document restoration. SIAM J. Imaging Sci. 12(2), 1135–1162 (2019)
Boccuto, A., Gerace, I., Giorgetti, V., Valenti, G.: A Blind Source Separation Technique for Document Restoration Based on Edge Estimation. http://viXra.org/abs/2201.0141 (2022)
Chan, T.-H., Ma, W.-K., Chi, C.-Y., Wang, Y.: A convex analysis framework for blind separation of non-negative sources. IEEE Trans. Signal Process. 56(10), 5120–5134 (2008)
Cichocki, A., Zdunek, R., Amari, S.-I.: New algorithms for non-negative matrix factorization in applications to blind source separation. In: Proceedings of the 2006 IEEE International Conference Acoustics, Speech and Signal Processing, Toulouse, France, pp. 1–4 (2006)
Comon, P.: Independent component analysis, a new concept? Signal Process. 36, 287–314 (1994)
Gillis, N.: Successive nonnegative projection algorithm for robust nonnegative blind source separation. SIAM J. Imaging Sci. 7(2), 1420–1450 (2014)
Gillis, N.: Sparse and unique nonnegative matrix factorization through data preprocessing. J. Mach. Learn. Res. 13, 3349–3386 (2012)
Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. Neural Netw. 10(3), 626–634 (1999)
Hyvärinen, A.: The fixed-point algorithm and maximum likelihood estimation for independent component analysis. Neural Process. Lett. 10(1), 1–5 (1999)
Hyvärinen, A., Oja, E.: A fast fixed-point algorithm for independent component analysis. Neural Comput. 9(7), 1483–1492 (1997)
Khaparde, A., Madhavilatha, M., Manasa, M.B.L., Pradeep Kumar, S.: FastICA algorithm for the separation of mixed images. WSEAS Trans. Signal Process. 4(5), 271–278 (2008)
Malik, R. K., Solanki, K.: FastICA based blind source separation for CT imaging under noise conditions. Int. J. Adv. Eng. Technol. 5(1), 47–55 (2012)
Ouedraogo, W.S.B., Souloumiac, A., Jaidane, M., Jutten, C.: Non-negative blind source separation algorithm based on minimum aperture simplicial cone. IEEE Trans. Signal Process. 62(2), 376–389 (2014)
Tonazzini, A., Gerace, I., Martinelli, F.: Multichannel blind separation and deconvolution of images for document analysis. IEEE Trans. Image Process. 19(4), 912–925 (2010)
Tonazzini, A., Gerace, I., Martinelli, F.: Document image restoration and analysis as separation of mixtures of patterns: from linear to nonlinear models. In: Gunturk, B.K., Li, X. (eds.) Image Restoration - Fundamentals and Advances, pp. 285–310. CRC Press, Taylor and Francis, Boca Raton (2013)
Tonazzini, A., Salerno, E., Bedini, L.: Fast correction of bleed-through distortion in greyscale documents by a blind source separation technique. Int. J. Doc. Anal. 10(1), 17–25 (2007)
Vavasis, S.: On the complexity of nonnegative matrix factorization. SIAM J. Optim. 20(3), 1364–1377 (2009)
Acknowledgments
This work was partially supported by University of Perugia, G.N.A.M.P.A. (Italian National Group of Mathematical Analysis, Probability and Applications) and I.N.d.A.M. (Italian National Institute of Higher Mathematics).
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Boccuto, A., Gerace, I., Giorgetti, V., Valenti, G. (2022). A Blind Source Separation Technique for Document Restoration Based on Image Discrete Derivative. In: Gervasi, O., Murgante, B., Hendrix, E.M.T., Taniar, D., Apduhan, B.O. (eds) Computational Science and Its Applications – ICCSA 2022. ICCSA 2022. Lecture Notes in Computer Science, vol 13375. Springer, Cham. https://doi.org/10.1007/978-3-031-10522-7_31
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DOI: https://doi.org/10.1007/978-3-031-10522-7_31
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