Abstract
Blind Source Separation (BSS) is a relevant problem in the signal processing research area, with a broad application sphere. In this work, we consider a BSS problem with recto–verso images subject to show–through and bleed–through effects; in particular, we suppose that the observed image is obtained using a two-step linear process: the recto and verso images are separately blurred using a blur operator with known coefficients and then mixed. Our algorithm, Blind Estimation Technique Imposing Smoothness and Non–Overlapping (BETIS–NO), built on top of previous work, computes the entries of the mixture matrix, which regulates the intensity of recto–verso mixing for the document reconstruction; the introduction of second–order discontinuities and additional constraints on source images, i.e., minimum entropy, non–Gaussianity, and correct overlapping, leads to improved quality of the reconstruction.
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References
Barros, A.K.: The independence assumption: dependent component analysis. In: Girolami, M. (eds.) Advances in Independent Component Analysis. Perspectives in Neural Computing. Springer, London (2000). https://doi.org/10.1007/978-1-4471-0443-8_4
Benlin, X., Fangfang, L., Xingliang, M., Huazhong, J.: Study on independent component analysis application in classification and change detection of multispectral images. In: The International Archives of the Photogrammetry, Remote Sensing, and Spatial Information Sciences, vol. 37, pp. 871–876 (2008)
Boccuto, A., Gerace, I.: Image reconstruction with a non-parallelism constraint. In: Proceedings of the International Workshop on Computational Intelligence for Multimedia Understanding, Reggio Calabria, Italy, 27–28 October 2016, pp. 1–5. IEEE Conference Publications (2016)
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., Martinelli, F.: Half-quadratic image restoration with a non-parallelism constraint. J. Math. Imaging Vis. 59(2), 270–295 (2017)
Boccuto, A., Gerace, I., Pucci, P.: Convex approximation technique for interacting line elements deblurring: a new approach. J. Math. Imaging Vis. 44(2), 168–184 (2012)
Cricco, F., De Santi, G., Gerace, I.: A deterministic algorithm for deblurring considering higher order smoothness constraints. In: Proceedings of the 2003 International Workshop on Spectral Methods and Multirate Signal Processing SMMSP2004, Vienna, Austria, 11/12 September 2004, pp. 325–332 (2004)
Cricco, F., Gerace, I.: An IMAP estimation for the joint separation and restoration of mixed degraded color images. In: Proceedings of the 7th Conference on Applied and Industrial Mathematics in Italy, Venice (Italy), 20–24 September 2004, pp. 260–269 (2004)
Cluni, F., Costarelli, D., Minotti, A.M., Vinti, G.: Applications of sampling Kantorovich operators to thermographic images for seismic engineering. J. Comput. Anal. Appl. 19(4), 602–617 (2015)
Discepoli, M., Gerace, I., Pandolfi, R.: Blind image restoration from multiple views by IMAP estimation. In: Modern Information Processing From Theory to Applications, pp. 441–452 (2006)
Evangelopoulos, X., Brockmeier, A. J., Mu, T., Goulermas, J. Y.: A graduated non-convexity relaxation for large-scale seriation. In: Proceedings of the 2017 SIAM International Conference on Data Mining, Houston, Texas (USA), pp. 462–470 (2017)
Fedeli, L., Gerace, I., Martinelli, F.: Unsupervised blind separation and deblurring of mixtures of sources. In: Proceedings of Knowledge-Based Intelligent Information and Engineering Systems. LNCS, Vietri sul Mare, Italy, vol. 4694, pp. 25–32 (2007)
Gerace, I., Cricco, F., Tonazzini, A.: An extended maximum likelihood approach for the robust blind separation of autocorrelated images from noisy mixtures. In: Puntonet, C.G., Prieto, A. (eds.) ICA 2004. LNCS, vol. 3195, pp. 954–961. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30110-3_120
Gerace, I., Pandolfi, R.: A color image restoration with adjacent parallel lines inhibition. In: Proceedings of the 12th International Conference on Image Analysis and Processing, 17–19 September 2003, Mantova, Italy, 6 p. (2003)
Gerace, I., Pandolfi, R., Pucci, P.: A new estimation of blur in the blind restoration problem. In: Proceedings of the 2003 International Conference on Image Processing, Barcelona, Spain, 14–17 September 2003, pp. 261–264 (2003)
Gillis, N.: Sparse and unique nonnegative matrix factorization through data preprocessing. J. Mach. Learn. Res. 13, 3349–3386 (2012)
Hazan, E., Levy, K.Y., Shalev-Shwartz, S.: On graduated optimization for stochastic non-convex problems. In: Proceedings of the 33rd International Conference on Machine Learning, New York, NY, USA, vol. 48, pp. 1–9, 2016. JMLR: W & CP (2016)
Hyvärinen, A.: Fast and robust fixed-point algorithms for independent component analysis. IEEE Trans. Neural Netw. 10, 626–634 (1999)
Hyvärinen, A.: Gaussian moments for noisy independent component analysis. IEEE Sig. Proc. Lett. 6, 145–147 (1999)
Kuruoglu, E., Bedini, L., Paratore, M.T., Salerno, E., Tonazzini, A.: Source separation in astrophysical maps using independent factor analysis. Neural Netw. 16(3–4), 479–491 (2003)
Leedham, G., Varma, S., Patankar, A., Govindaraju, V.: Separating text and background in degraded document images - a comparison of global thresholding techniques for multi-stage thresholding. In: Proceedings of the 8th International Workshop on Frontiers in Handwriting Recognition, Niagara on the Lake, Canada, pp. 244–249 (2002)
Liu, Z.-Y., Qiao, H.: GNCCP-graduated nonconvexity and concavity procedure. IEEE Trans. Pattern Anal. Mach. Intell. 36(6), 1258–1267 (2014)
Liu, Z.-Y., Qiao, H., Su, J.-H.: MAP inference with MRF by graduated non-convexity and concavity procedure. In: Loo, C.K., Yap, K.S., Wong, K.W., Teoh, A., Huang, K. (eds.) ICONIP 2014. LNCS, vol. 8835, pp. 404–412. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12640-1_49
Nikolova, M., Ng, M.K., Tam, C.-P.: On \(\ell _1\) data fitting and concave regularization for image recovery. SIAM J. Sci. Comput. 35(1), A397–A430 (2013)
Nikolova, M., Ng, M.K., Zhang, S., Ching, W.-K.: Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization. SIAM J. Imaging Sci. 1(1), 2–25 (2008)
Rowley-Brooke, R., Pitié, F., Kokaram, A.: A ground truth bleed-through document image database. In: Zaphiris, P., Buchanan, G., Rasmussen, E., Loizides, F. (eds.) TPDL 2012. LNCS, vol. 7489, pp. 185–196. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33290-6_21
Smith, T., Egeland, O.: Dynamical pose estimation with graduated non-convexity for outlier robustness. Model. Identif. Control (MIC) J. 43(2), 79–89 (2022)
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 & Francis, Boca Raton (2013)
Yang, H., Antonante, P., Tzoumas, V., Carlone, L.: Graduated non-convexity for robust spatial perception: from non-minimal solvers to global outlier rejection. IEEE Robot. Autom. Lett. 5(2), 1127–1134 (2020)
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Biondi, G., Boccuto, A., Gerace, I. (2023). Blind Source Separation of Color Noisy Blurred Images. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2023 Workshops. ICCSA 2023. Lecture Notes in Computer Science, vol 14108. Springer, Cham. https://doi.org/10.1007/978-3-031-37117-2_44
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