On a nonlinear mean and its application to image compression using multiresolution schemes

Numerical Algorithms - Tập 71 Số 4 - Trang 729-752 - 2016
Sergio Amat1, Jacques Liandrat2, Juan Ruiz3, Juan Carlos Trillo1
1Universidad Politécnica de Cartagena / Technical University of Cartagena
2Institut de Mathématiques de Marseille
3Universidad de Alcalá - University of Alcalá

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Tài liệu tham khảo

Amat, S., Cherif, H., Trillo, J.C.: Denoising using Linear and nonlinear multiresolutions. Eng. Comput. 22(7), 877–891 (2005)

Amat, S., Ruiz, J., Trillo, J.C.: Denoising using linear and nonlinear multiresolutions II: Cell-average framework and color images. Eng. Comput. 26(7), 806–827 (2009)

Amat, S., Dadourian, K., Liandrat, J.: Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms. Adv. Comput. Math. 34(3), 253–277 (2011)

Amat, S., Dadourian, K., Liandrat, J.: On a nonlinear subdivision scheme avoiding Gibbs oscillations and converging towards C s functions with s > 1. Math. Comp. 80(274), 959–971 (2011)

Amat, S., Dadourian, K., Liandrat, J.: Analysis of a class of nonlinear subdivision schemes and associated multiresolution transforms. Adv. Comput. Math. 34(3), 253–277 (2011)

Amat, S., Donat, R., Liandrat, J., Trillo, J.C.: Analysis of a new nonlinear subdivision scheme. Applications in image processing. Found. Comput. Math. 6(2), 193–225 (2006)

Amat, S., Donat, R., Liandrat, J., Trillo, J.C.: A fully adaptive multiresolution scheme for image processing. Math. Comput. Modell 46(1–2), 2–11 (2007)

Amat, S., Liandrat, J.: On the stability of the PPH nonlinear multiresolution. Appl. Comp. Harm. Anal. 18(2), 198–206 (2005)

Amat, S., Liandrat, J., Ruiz, J., Trillo, J.C. S e → $\vec {e}$ MA J. 60, 75–92 (2012)

Aràndiga, F., Donat, R.: Nonlinear multi-scale decomposition: The approach of A.Harten. Numer. Algorithms 23, 175–216 (2000)

Binev, P., Dahmen, W., DeVore, R., Dyn, N.: Adaptive approximation of curves. Approximation theory: a volume dedicated to Borislav Bojanov, pp. 43–57. Prof. M. Drinov Acad Publ. House, Sofia (2004)

Chambolle, A., DeVore, R.A., Lee, N., Lucier, B.J.: Nonlinear wavelet image processing: variational problem, compression and noise removal through wavelet shrinkage. IEEE Trans. Image Process. 7, 319–335 (1998)

Cohen, A.: Theoretical, Applied and Computational Aspects of Nonlinear approximation. (English Summary) Multiscale Problems and Methods in Numerical Simulations, vol. 1–29, Lecture Notes in Math, pp. 1825. Springer, Berlin (2003)

Cohen, A., DeVore, R., Petrushev, P., Xu, H.: Nonlinear approximation and the space BV(R 2). Amer. J. Math. 121(3), 587–628 (1999)

Cohen, A., Dyn, N., Matei, B.: Quasi linear subdivision schemes with applications to ENO interpolation. Appl. Comput. Harmonic Anal. 15, 89–116 (2003)

Daubechies, I., Runborg, O., Sweldens, W.: Normal multiresolution approximation of curves. Const. Approx. 20(3), 399–463 (2004)

Donoho, D.L., Johnstone, I.: Ideal spatial adaptation by wavelet shrinkage. Biometrika 81, 425–455 (1994)

Gottlieb, D., Shu, C.-W.: On the Gibbs phenomenon and its resolution. SIAM Rev. 39(4), 644–668 (1997)

Harten, A.: Multi resolution representation of data II. SIAM J. Numer. Anal. 33(3), 1205–1256 (1996)

Harten, A., Yad-Shalom, I.: Fast multiresolution algorithms for matrix-vector multiplications. SIAM J. Numer. Anal. 31, 1191–1218 (1994)

Matei, B.: Smoothness characterization and stability in nonlinear multiscale framework: theoretical results. Asymptot. Anal. 41(3–4), 277–309 (2005)

Oswald, P.: Smoothness of nonlinear median-interpolation subdivision. Adv. Comput. Math. 20(4), 401–423 (2004)

Rabbani, M., Jones, P.W.: Digital Image Compression Techniques. Tutorial Text, Society of Photo-Optical Instrumentation Engineers (SPIE), TT07 (1991)