◄back◄ ◄homepage◄

About Sparsity

A. Journal Articles

[36] F. Malgouyres and M. Nikolova, "Average performance of the sparsest approximation using a general dictionary", to appear in Numerical Functional Analysis and Optimization (NFAO)   (pdf)

[30] Nikolova, M. and F. Malgouyres. "Average performance of the approximation in a dictionary using an  ℓ₀ objective", to appear in Comptes-rendus de l'Académie des sciences, Série I (Mathématiques), (pdf)

[29] Nikolova, M. "Semi-explicit solution and fast minimization scheme for an energy with L1-fitting and Tikhonov-like regularization ", to appear in Journal of Mathematical Imaging and Vision, (pdf) Report CMLA n.2008-06.

 [27] Nikolova M., M. Ng, S. Zhang and W-K. Ching, "Efficient reconstruction of piecewise constant images using nonsmooth nonconvex minimization", SIAM Journal on Imaging Sciences, vol. 1, n. 1, Mar. 2008, pp. 2-25. (pdf)

[26] Nikolova M., ''Analytical bounds on the minimizers of (nonconvex) regularized least-squares'', AIMS Journal on Inverse Problems and Imaging, 2007, vol. 1, N.4, 2007, pp. 661-677 (pdf)

[22] Chan Tony, Selim Esedoglu and Mila Nikolova, "Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models, SIAM J. on Applied Mathematics, vol. 66, n. 5, 2006, pp.1632-1648. (pdf)

[19] Haoying Fu H., M. Ng, M. Nikolova and J. Barlow, "Efficient minimization methods of mixed ℓ₁ - ℓ₁ and ℓ₂ - ℓ₁ norms for image restoration", SIAM Journal on Scientific computing, Vol. 27, No 6, 2006, pp 1881-1902. (pdf)

[18] Alberge F., M. Nikolova and P. Duhamel, "Blind Identification / Equalization using Deterministic Maximum Likelihood and a partial prior on the input'', IEEE Trans. on Signal Processing, Vol. 54, Issue 2, Feb. 2006, pp. 724- 737. (pdf)

[15] Nikolova M., ''Analysis of the recovery of edges in images and signals by minimizing nonconvex regularized least-squares'', SIAM Journal on Multiscale Modeling and Simulation, vol. 4, N. 3, 2005, pp. 960-991 (pdf)

[11] Nikolova M., ''A variational approach to remove outliers and impulse noise'', Journal of Mathematical Imaging and Vision, vol. 20, no. 1-2, 2004, pp. 99-120. (pdf)

[10] Nikolova M., ''Weakly constrained minimization. Application to the estimation of images and signals involving constant regions'', Journal of Mathematical Imaging and Vision,  no. 2, vol. 21, Sep. 2004, pp. 155-175. (pdf)

[8] Nikolova M., ''Minimizers of cost-functions involving non-smooth data-fidelity terms. Application to the processing of outliers'', SIAM Journal on Numerical Analysis vol. 40, no. 3, 2002, pp. 965-994. (pdf)

[7] Alberge F., P. Duhamel and M. Nikolova, "Adaptive solution for blind identification / equalization using deterministic maximum likelihood'',  IEEE Trans. on Signal Processing, vol. 50, no 4, April 2002, pp. 923-936. (pdf)

[6] Nikolova M., ''Local strong homogeneity of a regularized estimator'', SIAM Journal on Applied Mathematics, vol. 61, no. 2, pp. 633-658, 2000. (pdf)

[2] Nikolova M., ''Homogénéité forte d'une solution régularisée'', Comptes-rendus de l'Académie des sciences, Paris, t. 325, Série I (Mathématiques), p. 665-670, 1997. (ps)

B. Peer Reviewed Proceedings Papers

[39] Malgouyres, F. and M. Nikolova, "Average performance of the sparsest approximation in a dictionary ", Int. Workshop SPARS’09, April 2009. (pdf)

[36] Nikolova M., "Restoration of edges by minimizing non-convex cost-functions", IEEE Int. Conf. on Image Processing (ICIP), vol. II, pp. 786-789, Sept. 2005.

[35] Chan T., S. Esedoglu and M. Nikolova, "Finding the Global Minimum for Binary Image Restoration", IEEE Int. Conf. on Image Processing (ICIP), vol. I, pp. 121-124, Sept. 2005.

[33] Fu H., M. Ng, Mila Nikolova, J. L. Barlow, W.-K. Ching, "Fast algorithms for ℓ₁ norm/mixed ℓ₁ and ℓ₂ norms for image restoration”. ICCSA, vol. 4, pp. 843-851, 2005.

[29] Nikolova M., ``Efficient removing of impulsive noise based on an ℓ₁-ℓ₂ cost-function'', IEEE Int. Conf. on Image Processing (ICIP), vol. 1, pp. 14-17, Sep. 2003. (pdf)

[24] Nikolova M., ``Image restoration by minimizing objective functions with non-smooth data-fidelity terms'', IEEE Int. Conf. on Computer Vision / Workshop on Variational and Level-Set Methods, pp. 11-18, Jul. 2001. 

[14] Nikolova M., ``Locally homogeneous images as minimizers of an objective function'', IEEE Int. Conf. on Image Processing, Oct. 1999, vol.2, pp. 11-15, invited paper.

[10] Nikolova M., ``Estimation of binary images using convex criteria'', Proc. of IEEE Int. Conf. on Image Processing (ICIP), Oct. 1998. (pdf)

[8] Nikolova M., ``Estimation of signals containing strongly homogeneous zones'', Proc. of IEEE Stat. Signal and Array Proc., Sept. 1998.

[7] Nikolova M., ``Reconstruction of locally homogeneous images'', European Signal Proc. Conf., Sept. 1998.

[6] Nikolova M., ``Regularisation functions and estimators'', Proc. of IEEE Int. Conf. on Image Processing (ICIP), Nov. 1996, pp. 457-460.

[5] Nikolova M., ``Non convex regularization and the recovery of edges'', Proc. IEEE Workshop on Nonlinear Signal and Image Processing., Greece, June. 1995, pp. 1042-1045.

C. Reports

Malgouyres, F. and M. Nikolova, "Average performance of the sparsest approximation using a general dictionary", submitted, (pdf),  HAL-00260707, Report CMLA n.2008-08