Properties of optimal solutions
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)
[32] Antoniadis A,
[30] Nikolova, M. and F.
Malgouyres. "Average
performance of the approximation in a dictionary using an ℓ0
objective", Comptes-rendus de l'Académie des sciences, Série I (Mathématiques), 347, 2009, pp. 565-570. (pdf)
[29] Nikolova, M. "Semi-explicit solution and
fast minimization scheme for an energy with L1-fitting and Tikhonov-like
regularization ", Journal of
Mathematical Imaging and Vision, Vol. 34, № 1, 2009, pp.
32-47 (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)
[25] Nikolova M., ''Model distortions in Bayesian MAP
reconstruction'', AIMS Journal on Inverse Problems and Imaging, vol. 1, N.
2, 2007, pp. 399-422 (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)
[21] Durand S. and Nikolova
M. ``Stability of the Minimizers of Least Squares with a
Non-Convex Regularization. Part I: Local Behavior'', Journal of
Applied Mathematics and Optimization, Vol. 53, n. 2, March 2006, pp.
185-208. (pdf)
[20] Durand S. and Nikolova
M. ``Stability of the Minimizers of Least Squares with a
Non-Convex Regularization. Part II: Global Behavior'', Journal of
Applied Mathematics and Optimization, Vol. 53, n. 3, May 2006, pp. 259-277.
(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)
[6] Nikolova M., ''Local
strong homogeneity of a regularized estimator'', SIAM Journal on Applied
Mathematics, vol. 61, no. 2, pp. 633-658, 2000. (pdf)
[5] Nikolova M., ''Thresholding
implied by truncated quadratic regularization'', IEEE Trans. on Signal
Processing, vol. 48, Dec. 2000, pp. 3437-3450.(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)
[38] Nikolova M., "Bounds on the minimizers of (nonconvex)
regularized least-squares", Scale Space and Variational
Methods in Computer Vision, Springer – Lecture notes in Computer science
LNCS 4485, ed. F. Sgallary, A. Murli, N. Paragios, 2007, pp. 496-507.
[37] Nikolova M.,
"Counter-examples for Bayesian MAP restoration", Scale Space and
Variational Methods in Computer Vision, Springer – Lecture notes in Computer
science LNCS 4485, ed. F. Sgallary, A. Murli, N. Paragios, 2007, pp. 140-152.
[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.
[31] Nikolova M., ``Minimization of
cost-functions with non-smooth data-fidelity terms to clean impulsive noise'', Int. workshop on
Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in
Computer Science, Springer-Verlag, pp. 391-406, 2003.
[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.
[23] Durand S. and M.
Nikolova, ``Stability of image restoration by minimizing regularized objective
functions'', IEEE Int. Conf. on Computer Vision / Workshop on Variational and
Level-Set Methods, pp. 73-80, Jul. 2001.
[22] Nikolova M., ``Smoothing of
outliers in image restoration by minimizing regularized objective functions
with non-smooth data-fidelity terms'', IEEE Int. Conf. on Image
Processing (ICIP), vol. 1, pp. 233-236n Oct. 2001.
[16] Nikolova M., ``Assumed and
effective priors in Bayesian MAP estimation'', IEEE Int. Conf. on
Acoustics, Speech and Signal Processing(ICASSP), Jun. 2000.
[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.
[13] Nikolova M., ``Local continuity and
thresholding using truncated quadratic regularization'', IEEE Workshop on
Higher Order Statistics, pp. 277-280, June 1999.
[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
[4] Nikolova M., ``Parameter selection
for a Markovian signal reconstruction with edge detection'', Proc. IEEE Int. Conf.
Acoust. Speech Signal Process.,
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
Antoniadis, A., Gijbels,
I. and M. Nikolova, "Penalized Likelihood
Regression for Generalized Linear Models with Nonquadratic
Penalties", submitted (pdf). Report
CMLA n.2008-07