## Thursday, July 19, 2018

### CSJob: PhD and Postdoc positions KU Leuven: Optimization frameworks for deep kernel machines

Johan let me know of the following positions in his group:

Dear Igor,
could you please announce this on nuit blanche.
many thanks,
Johan

Sure thing Johan !

PhD and Postdoc positions KU Leuven: Optimization frameworks for deep kernel machines
The research group KU Leuven ESAT-STADIUS is currently offering 2 PhD and 1 Postdoc (1 year, extendable) positions within the framework of the KU Leuven C1 project Optimization frameworks for deep kernel machines (promotors: Prof. Johan Suykens and Prof. Panos Patrinos).
Deep learning and kernel-based learning are among the very powerful methods in machine learning and data-driven modelling. From an optimization and model representation point of view, training of deep feedforward neural networks occurs in a primal form, while kernel-based learning is often characterized by dual representations, in connection to possibly infinite dimensional problems in the primal. In this project we aim at investigating new optimization frameworks for deep kernel machines, with feature maps and kernels taken at multiple levels, and with possibly different objectives for the levels. The research hypothesis is that such an extended framework, including both deep feedforward networks and deep kernel machines, can lead to new important insights and improved results. In order to achieve this, we will study optimization modelling aspects (e.g. variational principles, distributed learning formulations, consensus algorithms), accelerated learning
The PhD and Postdoc positions in this KU Leuven C1 project (promotors: Prof. Johan Suykens and Prof. Panos Patrinos) relate to the following  possible topics:
-1- Optimization modelling for deep kernel machines
-2- Efficient learning schemes for deep kernel machines
-3- Adversarial learning for deep kernel machines
For further information and on-line applying, see
https://www.kuleuven.be/personeel/jobsite/jobs/54740654" (PhD positions) and
https://www.kuleuven.be/personeel/jobsite/jobs/54740649" (Postdoc position)
(click EN for English version).
The research group ESAT-STADIUS http://www.esat.kuleuven.be/stadius at the university KU Leuven Belgium provides an excellent research environment being active in the broad area of mathematical engineering, including data-driven modelling, neural networks and machine learning, nonlinear systems and complex networks, optimization, systems and control, signal processing, bioinformatics and biomedicine.

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## Friday, July 13, 2018

### Phase Retrieval Under a Generative Prior

Vlad just sent me the following:
Hi Igor,

I am writing regarding a paper you may find of interest, co-authored with Paul Hand and Oscar Leong. It applies a deep generative prior to phase retrieval, with surprisingly good results! We can show recovery occurs at optimal sample complexity for gaussian measurements, which in a sense resolves the sparse phase retrieval O(k^2 log n) bottleneck.

https://arxiv.org/pdf/1807.04261.pdf

Best,

Thanks Vlad ! Here is the paper:

Phase Retrieval Under a Generative Prior by Paul Hand, Oscar Leong, Vladislav Voroninski
The phase retrieval problem asks to recover a natural signal y0Rn from m quadratic observations, where m is to be minimized. As is common in many imaging problems, natural signals are considered sparse with respect to a known basis, and the generic sparsity prior is enforced via 1 regularization. While successful in the realm of linear inverse problems, such 1 methods have encountered possibly fundamental limitations, as no computationally efficient algorithm for phase retrieval of a k-sparse signal has been proven to succeed with fewer than O(k2logn) generic measurements, exceeding the theoretical optimum of O(klogn). In this paper, we propose a novel framework for phase retrieval by 1) modeling natural signals as being in the range of a deep generative neural network G:RkRn and 2) enforcing this prior directly by optimizing an empirical risk objective over the domain of the generator. Our formulation has provably favorable global geometry for gradient methods, as soon as m=O(kd2logn), where d is the depth of the network. Specifically, when suitable deterministic conditions on the generator and measurement matrix are met, we construct a descent direction for any point outside of a small neighborhood around the unique global minimizer and its negative multiple, and show that such conditions hold with high probability under Gaussian ensembles of multilayer fully-connected generator networks and measurement matrices. This formulation for structured phase retrieval thus has two advantages over sparsity based methods: 1) deep generative priors can more tightly represent natural signals and 2) information theoretically optimal sample complexity. We corroborate these results with experiments showing that exploiting generative models in phase retrieval tasks outperforms sparse phase retrieval methods.

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## Tuesday, July 10, 2018

### #ICML2018 Tutorial: Toward theoretical understanding of deep learning, Sanjeev Arora

Sanjeev is giving a tutorial at ICML entitled Toward theoretical understanding of deep learning. the presentation and all the references are all on this page. (and yes compressive sensing shows up in different parts)

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## Friday, June 29, 2018

### Book: Dictionary Learning Algorithms and Applications

Paul sent me the following earlier this month:

Hi Igor,
I am a keen reader of your blog and just wanted to let you know that professor Dumitrescu and I just wrote a book about dictionary learning. Perhaps your other readers might be interested as well.
Short description:

This book covers all the relevant dictionary learning algorithms, presenting them in full detail and showing their distinct characteristics while also revealing the similarities. It gives implementation tricks that are often ignored but that are crucial for a successful program. Besides MOD, K-SVD, and other standard algorithms, it provides the significant dictionary learning problem variations, such as regularization, incoherence enforcing, finding an economical size, or learning adapted to specific problems like classification. Several types of dictionary structures are treated, including shift invariant; orthogonal blocks or factored dictionaries; and separable dictionaries for multidimensional signals. Nonlinear extensions such as kernel dictionary learning can also be found in the book. The discussion of all these dictionary types and algorithms is enriched with a thorough numerical comparison on several classic problems, thus showing the strengths and weaknesses of each algorithm. A few selected applications, related to classification, denoising and compression, complete the view on the capabilities of the presented dictionary learning algorithms. The book is accompanied by code for all algorithms and for reproducing most tables and figures.

Keep up the good work,
Paul Irofti

Thanks Paul !

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## Monday, June 25, 2018

### Mila Nikolova

Mila Nikolova is no longer with us.  Here is some of her work, a large part of it has had an important impact in compressive sensing and signal processing.

• Least squares regularized or constrained by L0: relationship between their global minimizers”  invited speaker – SIAM Minisymposium on Trends in the Mathematics of Signal Processing and Imaging – Joint Mathematics Meetings 2016, Seattle
• Image reconstruction from linear attenuating operators”
• Inverse Modelling in Inverse Problems using Optimization” –Tutorial 5 hrsSummer School 2014: Inverse Problems and Image Processing, Institute of Applied Physics and Computational Mathematics, Old yard, 14-17 July, Beijing,China(abstract) (lectures)
• "Non Convex Minimization using Convex Relaxation. Some Hints to Formulate Equivalent Convex Energies"
• "Graph Cut, Convex Relaxation and Continuous Max-flow Problems" with E. Bae and X.C. Tai, SIAM Conf. on Imaging Science, Hong Kong 2014
• Fast Hue and Range Preserving Histogram Specification: Theory and New Algorithms for Color Image Enhancement – Invited Speaker University of Macau 2014 (slides)
•  Inverse Modelling using Optimization” – 3 Tutorials, IPAMUCLA, Los Angeles, July 2013: abstract, Part I
• “ℓ1 - Concave versus 1 – TV energies: Questions and challenges”, Invited Speaker, Convex Relaxation Methods for Geometric Problems in Scientific Computing", Institute for Pure and Applied Mathematics (IPAM), UCLA, Los Angeles, February 2013 (slides)
• “ℓ1 Data Fidelity with Concave Regularization: Challenges”, Invited Speaker,  (slides)
• MATHEMAICS IN IMAGING (Inverse modelling to solve imaging tasks using optimization)”, Plenary TalkAnnual Meeting of the German Mathematical Society (DMV) 2012
• “Fast dejittering for digital video images using local non-smooth and non-convex functionals”, Imaging with Modulated/Incomplete Data (SFB Workshop), July 2010, Graz Austria
• Qualitative features of the minimizers of energies and implications on modelling”, Invited Plenary SpeakerSIAM Conference on Imaging Science 2008  (slides)
• Average performance of the sparsest approximation in terms of an orthogonal basis”, Invited Speaker, Rencontre: Approximation, modélisation géométrique et applications, Lumini 2008   (slides)
• “Average performance of the sparsest approximation using a general dictionary”, Mathematical and Algorithmical Challenges for Modeling and Analyzing Modern Data Sets, 21-25 April 2008 HKBU - Hong Kong (slides)
• "What Energy to Minimize?" –  EUSIPCO 2007  (slides)
• "Counter-examples for Bayesian MAP restoration", Variational and PDE Level Set Methods, September 1st - 3rd, 2006Obergurgl, Austria
• "Recovery of edges in signals and images by minimizing nonconvex regularized least-squares"- Mathematical Image Analysis and ProcessingBanff Research Station, Octobre 2004 (slides)

• [49] P. Arias and M. Nikolova, “Below the Surface of the Non-Local Bayesian Image Denoising Method”, Scale-Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science10302, Springer, 2017, pp. 208--220 (pdf)
• [48] J. Fehrenbach, M. Nikolova, G. Steidl, and P. Weiss, ”Bilevel Image Denoising using Gaussianity tests”. in J.-F. Aujol, M. Nikolova, N. Papadakis (Eds.) : Scale-Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science 9087, Springer, Berlin, 2015, pp. 117–128.
•  [47]  J. H. Fitschen, M. Nikolova, F. Pierre, and G. Steidl, ”A Variational Model for Color Assignment”, in J.-F. Aujol, M. Nikolova, N. Papadakis (Eds.) : Scale-Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science 9087, Springer, Berlin, 2015, pp. 437–448.
• [46]  M. Nikolova, "A fast algorithm for exact histogram specification. Simple extension to colour images", Scale Space and Variational Methods in Computer Vision, June 2013 (pdf).
• [45]  M. Nikolova, "Either fit to data entries or to locally to prior: the minimizers of energies with nonsmooth nonconvex data fidelity and regularization ", Scale Space and Variational Methods in Computer Vision, June 2011.
• [44]  M. Nikolova, "Should we search for a global minimizer of least squares regularized with an ℓ0 penalty to get the exact solution of an under determined linear system?", Scale Space and Variational Methods in Computer Vision, June 2011.
• [43]  R. Chan, M. Nikolova and Y.-W. Wen, "A variational approach for exact histogram specification ", Scale Space and Variational Methods in Computer Vision, June 2011.
• [42]  M. Nikolova, "Fast dejittering for digital video images ", Scale Space and Variational Methods in Computer Vision, Eds. X.-C. Tai, K. Morken, M. Lysaker, K.-A. Lie, LNCS 5567, Springer, pp. 439-451, 2009.  (pdf)
• [41] Durand S., J. Fadili and M. Nikolova, "Multiplicative noise clearing via a variational method involving curvelet coefficients ", Scale Space and Variational Methods in Computer Vision, Eds. X.-C. Tai, K. Morken, M. Lysaker, K.-A. Lie, LNCS 5567, Springer, pp. 282-294,, 2009. (pdf)
• [40] F. Malgouyres. and M. Nikolova, "Average performance of the sparsest approximation in a dictionary ", Int. Workshop SPARS’09, April 2009. (pdf)
• [39] M. Nikolova, "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.
• [38] M. Nikolova, "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.
• [37] M. Nikolova"Restoration of edges by minimizing non-convex cost-functions"IEEE Int. Conf. on Image Processing (ICIP), vol. II, pp. 786-789, Sept. 2005.
• [36] T 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.
• [35] R. H. Chan, C. Ho, C.W. Leung and M. Nikolova, "Minimization of detail-preserving regularization functional by Newton’s method with continuation”IEEE Int. Conf. on Image Processing (ICIP), vol. 1, pp. 125-128, Sept. 2005.
• [34] Fu H., M. Ng, M. 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.
• [33] Durand S. and M. Nikolova, "Restoration of wavelet coefficients by minimizing a specially designed objective function''IEEE Int. Conf. on Computer Vision / Workshop on Variational and Level-Set Methods, vol. 2, pp. 145-152, Oct. 2003. (pdf)
• [32]  M. Nikolova, 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.
• [31] Kornprobst, P., R. Peeters, M. Nikolova, R. Deriche, M. Ng and P. Van Hecke. A super-resolution framework  for fMRI sequences and its impact on resulting activation maps''Medical Image Computing and Computer-Assisted Intervention (MICCAI), LNCS 2879, pp. 117-127, 2003. (pdf)
• [30] M. Nikolova, Efficient removing of impulsive noise based on an 1-2 cost-function''IEEE Int. Conf. on Image Processing (ICIP), vol. 1, pp. 14-17, Sep. 2003. (pdf)
• [29] Deriche, R., P. Kornprobst, M. Nikolova and Michael Ng. Half-quadratic regularization for MRI image restoration''IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), vol. VI, pp. 585-588, 2003.
• [28] S. Zinger, M. Nikolova, M. Roux and H. MaitreRééchantillonnage de données 3D laser aéroporté en milieu urbain''Congrès Vision par Ordinateeur ORASIS, pp. 75-82, Mai 2003.
• [27] M. Nikolova and M. NgComparison of the main forms of half-quadratic regularization''IEEE Int. Conf. on Image Processing(ICIP), vol. 1, pp. 349-352, Oct. 2002.
• [26] S. Zinger, M. Nikolova, M. Roux and H. Maitre, 3D resampling for airborne laser data of urban areas''Proceedings of ISPRS, vol. XXXIV, n. 3A, pp. 418-423, 2002.
• [25] M. NikolovaImage 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.
• [24] S. Durand and M. NikolovaStability 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.
• [23] M. Nikolova, 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.
• [22] M. Nikolova and M. Ng, Fast image reconstruction algorithms combining half-quadratic regularization and preconditioning''IEEE Int. Conf. on Image Processing, vol. 1, pp. 277-280, Oct. 2001.
• [21] M. Nikolova and A. Hero III, Segmentation of a road from a vehicle-mounted imaging radar and accuracy of the estimation''Proc. of IEEE Intelligent Vehicles Symposium, pp. 284-289, Oct. 2000.
• [20] F. Alberge, P. Duhamel and M. Nikolova, Low cost adaptive algorithm for blind channel identification and symbol estimation''EUSIPCO (Finland), pp. 1549-1552, Sept. 2000. (pdf)
• [19] F. Roullot, A. Herment, I. Bloch, M. Nikolova and E. Mousseaux, Regularized reconstruction of 3D high-resolution magnetic resonance images from acquisitions of anisotropically degraded resolutions''15th Int. Conf. on Pattern Recognition, vol. 3, pp. 346-349, 2000.
• [18] F. Roullot, A. Herment, I. Bloch, M. Nikolova and E. Mousseaux, Reconstruction regularise d’images de resonance magnétique 3D de haute resolution à partir d’acquisitions anisotropes''RFIA (Paris, France), vol. II, pp. 59-68, 2000.
• [17] M. Nikolova, Assumed and effective priors in Bayesian MAP estimation''IEEE Int. Conf. on Acoustics, Speech and Signal Processing(ICASSP), Jun. 2000, vol. 1, pp. 305-308. (pdf)
• [16] F. Alberge, M. Nikolova and P. DuhamelAdaptive Deterministic Maximum Likelihood using a quasi-discrete prior''IEEE Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP), Jun. 2000.
• [15] M. Nikolova, Locally homogeneous images as minimizers of an objective function''IEEE Int. Conf. on Image Processing, Oct. 1999, vol.2, pp. 11-15, invited paper.
• [14] M. NikolovaLocal continuity and thresholding using truncated quadratic regularization''IEEE Workshop on Higher Order Statistics, pp.  277-280, June 1999.
• [13] M. Nikolova and A. Hero III, Noisy word recognition using denoising and moment matrix discriminants''IEEE Workshop on Higher Order Statistics, June 1999.
• [12] F. Alberge, P. Duhamel and M. NikolovaBlind identification / equalization using deterministic maximum likelihood and a partial information on the input''IEEE Workshop on Sig. Proc. Advances in Wireless Communications, May 1999.
• [11] M. Nikolova, Estimation of binary images using convex criteria''Proc. of IEEE Int. Conf. on Image Processing (ICIP), Oct. 1998. (pdf)
• [10] M. Nikolova and A. Hero III, Segmentation of road edges from a vehicle-mounted imaging radar'', Proc. of IEEE Stat. Signal and Array Proc., Sept. 1998. (pdf)
• [9] M. Nikolova, Estimation of signals containing strongly homogeneous zones''Proc. of IEEE Stat. Signal and Array Proc., Sept. 1998.
• [8] M. Nikolova, Reconstruction of locally homogeneous images''European Signal Proc. Conf., Sept. 1998.
• [7] M. Nikolova, Regularisation functions and estimators''Proc. of IEEE Int. Conf. on Image Processing (ICIP), Nov. 1996, pp. 457-460.
• [6] M. Nikolova, Non convex regularization and the recovery of edges''Proc. IEEE Workshop on Nonlinear Signal and Image Processing., Greece, June. 1995, pp. 1042-1045.
• [5] M. Nikolova, Parameter selection for a Markovian signal reconstruction with edge detection'', Proc. IEEE Int. Conf. Acoust. Speech Signal Process., Detroit, Apr. 1995, pp. 1804-1807. (pdf)
• [4] M. Nikolova, Markovian reconstruction in computed imaging and Fourier synthesis''IEEE Int. Conf. on Image Processing (ICIP), Nov. 1994, pp. 690-694.
• [3] M. Nikolova and A. Mohammad-DjafariDiscontinuity reconstruction from linear attenuating operators using the weak-string model''European Signal Proc. Conf(EUSIPCO), Sept. 1994, pp. 1062-1065. (pdf)
• [2] M. Nikolova, A. Mohammad-Djafari and J. IdierInversion of large-support ill-conditionned linear operators using a Markov model with a line process''Proc. IEEE Int. . Acoust. Speech Signal Process(ICASSP)Adelaide, Apr. 1994, vol. V, pp. 357-360.
• [1] M. Nikolova and A. Mohammad-DjafariMaximum entropy image reconstruction in eddy current tomography''pp. 273–278, in Proc. of the 12th Int. MaxEntWorkshop, Maximum Entropy and Bayesian Methods, 1992.

• [50] D.-C. Soncco, C. Barbanson, M. Nikolova, A. Almansa, and Y. Ferrec, “Fast and Accurate Multiplicative Decomposition for Fringe Removal in Interferometric Images”, IEEE Trans. Computational Imaging, Jun., 2017, vol. 3, issue 2, pp. 187 – 201, doi 10.1109/TCI.2017.2678279(pdf)
• [49] X. Cai, R. Chan, M. Nikolova, and T. Zeng, “A Three-stage Approach for Segmenting Degraded Color Images: Smoothing, Lifting and Thresholding (SLaT)”, Journal of Scientific Computing, 2017, doi 10.1007/s10915-017-0402-2 (pdf)
• [48] F. Laus, M. Nikolova, J. Persch, and G. Steidl, “A nonlocal denoising algorithm for manifold-valued images using second order statistics”, SIAM Journal on Imaging Science, vol. 10, issue 1, (2017), pp. 416448
• [47]  J.-F. Aujol, M. Nikolova, and N. Papadakis, “Guest Editorial: Scale-Space and Variational Methods”, J Math Imaging Vis (2016) 56:173–174.
• [46] M. Nikolova"Relationship between the optimal solutions of least squares regularized with L0-norm and constrained by k-sparsity", Appl. Comput. Harmon. Anal., vol. 41, issue 1, July 2016, pp. 237 - 265 (pdf)
•
• [45] X. Cai, J.-H. Fitschen, M. Nikolova, G. Steidl and M. Storath"Disparity and Optical Flow Partitioning Using Extended Potts Priors", Information and Inference : A Journal of the IMAvol 4, issue 1, March 2015, pp. 43-62  (pdf)
•
• [44] R. Chan, H-X. Liang, S.Wei, M. Nikolova and X-C. Tai, "High-order Total Variation Regularization Approach for Axially Symmetric Object Tomography from a Single Radiograph", Inverse Problems and Imaging, vol. 9, n. 1, 2015 (pdf)
•
• [43] M. Nikolova and G. Steidl"Fast ordering algorithm for exact histogram specification", IEEE Trans. on Image Processing, Dec. 2014, vol. 23, n. 12, pp. 5274-5283 (pdf)
•
• [42] M. Nikolova and G. Steidl"Fast Hue and Range Preserving Histogram Specification: Theory and New Algorithms for Color Image", IEEE Trans. on Image Processing, Sep. 2014, vol. 23, n. 9, pp. 4087-4100 (pdf)
• [41] M. Nikolova"Description of the minimizers of least squares regularized with norm. Uniqueness of the global minimizer", SIAM J. on Imaging Sciences, 2013, vol. 6, n. 2, pp. 904-937 (pdf)
• [40] F. Bauss, M. Nikolova and G. Steidl, " Fully smoothed   1- TV models: Bounds for the minimizers and parameter choice ", Journal of Mathematical Imaging and Vision, online Feb 2013  (pdf)
• [39] M. Nikolova, Y-W. Wen and R. Chan, "Exact Histogram Specifcation for Digital Images Using a Variational Approach", online November 2012, Journal of Mathematical Imaging and Vision, 2013, vol. 46, n. 3, pp. 309-325  (pdf)
• [38] M. Nikolova, M. Ng and C. P. Tam, "On 1 Data Fitting and Concave Regularization for Image Recovery", SIAM J. on Scientific Computing, vol. 35, n. 1, pp. A397-A430, online Jan 2013  (pdf).
• [37] M. Nikolova, "Solve exactly an underdetermined linear system by minimizing least squares with an 0 penalty",
• Comptes-rendus de l’Académie des sciences, Série I (Mathématiques) 349, Nov. 2011, pp. 1145-1150 (pdf)
•  [36] F. Malgouyres and M. Nikolova, "Average performance of the sparsest approximation using a general dictionary", Numerical Functional Analysis and Optimization (NFAO), 32(7), pp. 768-805, 2011 (pdf)
• [35] A. Antoniadis, I. Gijbels and M. Nikolova, "Penalized Likelihood Regression for Generalized Linear Models with Nonquadratic Penalties ", Annals of the Instutute of Statistical Mathematics, June 2011, vol. 63, n. 3, pp. 585-615
• [34] M. Nikolova, M. Ng and C. P. Tam, "A Fast Nonconvex Nonsmooth Minimization Method for Image Restoration and Reconstruction", IEEE Trans. on ImageProcessingVol. 19, .n 12, Dec. 2010  (pdf).
• [33] S. Durand S., J. Fadili and M. Nikolova, "Multiplicative noise removal using L1 fidelity on frame coefficients", Journal of Mathematical Imaging and Vision, (Online 2009), Mar. 2010, vol. 36, n. 3, pp. 201-226  (pdf).
• [32] Cai J.-F., R. Chan and M. Nikolova. "Fast Two-Phase Image Deblurring under Impulse Noise ", Journal of Mathematical Imaging and Vision, (Online 2009), Jan. 2010, vol. 36, n. 1, pp. 46-53
•  [31] M. Nikolova, "One-iteration dejittering of digital video images", Journal of Visual Communication and Image Representation, Vol. 20, 2009, pp. 254-274
• [30] M. Nikolova 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] M. Nikolova. "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)
• [28] Cai J-F., R. Chan and  M. Nikolova, “Two phase methods for deblurring images corrupted by impulse plus Gaussian noise ", AIMS Journal on Inverse Problems and Imaging, Vol. 2, n. 2, April 2008, pp. 187-204. (pdf)
• [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] M. Nikolova, ''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)
• [24] Durand S. and M. Nikolova, "Denoising of frame coefficients using ℓ1 data-fidelity term and edge-preserving regularization", SIAM Journal on Multiscale Modeling and Simulation, vol. 6, n. 2, 2007, pp.547-576 (pdf)
• [23] Nikolova M. and R. Chan, "The equivalence of Half-Quadratic Minimization and the Gradient Linearization Iteration'', IEEE Trans. on Image Processing, June 2007, vol. 16, n. 6, pp. 1623-1627 (pdf).
• [22] Chan Tony, Selim Esedoglu and Mila Nikolova, "Algorithms for Finding Global Minimizers of Image Segmentation and Denoising ModelsSIAM 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)
• [19] Haoying Fu H., M. Ng, M. Nikolova and J. Barlow, "Efficient minimization methods of mixed ℓ- ℓ1 and ℓ- 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)
• [17] Nikolova M. and M. Ng, "Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery'', SIAM Journal on Scientific computing, vol. 27, No. 3, 2005, pp. 937-966. (pdf)
• [16] Chan R., Chung-Wa Ho and M. Nikolova, "Salt-and-Pepper Noise Removal by Median-type Noise Detector and Detail-Preserving Regularization", IEEE Trans. on Image Processing, Vol. 14, No. 10, Oct. 2005, pp. 1479-1485. (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)
• [14] Chan R., C. Hu and M. Nikolova, "An Iterative Procedure for Removing Random-Valued Impulse Noise",  IEEE Signal Processing Letters, 11 (2004), 921-924. (pdf)
• [13] Chan R., C.W. Ho and M. Nikolova, "Convergence of Newton's Method for a Minimization Problem in Impulse Noise Removal'', J. Comput. Math., vol. 22, 2004, pp. 168-177. (pdf)
• [12] R. Peeters, P. Kornprobst, M. Nikolova, S. Sunaert, T. Vieville, G. Malandain, R. Deriche, O. Fougeras, M. Ng and P. Hecke,  "The use of superresolution techniques to reduce slice thickness in functional MRI'', International Journal of Imaging Systems and Technology, Vol. 14, No. 3, 2004. (pdf)DOI : 10.1002/ima.20016
• [11] Nikolova M., ''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)
• [9] Roullot E., A. Herment, I. Bloch, A. Cesare, M. Nikolova and E. Mousseaux, "Modeling anisotropic undersampling of magnetic resonance angiographies and reconstruction of a high-resolution isotropic volume using half-quadratic regularization techniques'', Signal Processing, vol. 84,  2004, pp. 743-762. (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)
• [5] Nikolova M., ''Thresholding implied by truncated quadratic regularization'', IEEE Trans. on Signal Processing, vol. 48, Dec. 2000, pp. 3437-3450.(pdf)
• [4] Nikolova M., "Markovian reconstruction using a GNC approach'', IEEE Trans. on Image Processing , vol. 8, no. 9, Sept. 1999, pp. 1204-1220(pdf)
• [3] Nikolova M., Idier J. and Mohammad-Djafari A., "Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF'', IEEE Trans. On Image Processing, vol. 8, no. 4, pp. 571-585, April 1998. (pdf)
• [2] Nikolova M., ''Estimées localement fortement homogènes = Locally strongly homogeneous estimates'', Comptes-rendus de l'Académie des sciences, Série I (Mathématiques), Paris, vol. 325, n. 6, p. 665-670, 1997. (pdf)
• [1] Nikolova M. and A. Mohammad-Djafari, "Eddy Current Tomography Using a Markov model'', Signal Processing, vol. 49, no. 2, 1996. (ps)

Book

• J.-F. Aujol, M. Nikolova, N. Papadakis (Eds.)Scale-Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science 9087, Springer, Berlin, 2015 (link)

Book chapters

• M. Nikolova, Energy Minimization Methods'', Chapter 5, Handbook of Mathematical Methods in Imaging, editor: Otmar ScherzerSpringer 2014, second edition, DOI 10.1007/978-3-642-27795-5 5-3
• M. Nikolova, Energy Minimization Methods'', Chapter 5, pp. 138-186, Handbook of Mathematical Methods in Imaging, editor: Otmar ScherzerSpringer 2011, first edition
• Nikolova M. and A. Mohammad-Djafari, Maximum Entropy Image Reconstruction in Eddy Current Tomography'', in Maximum entropy and Bayesian methods, A. Mohammad-Djafari & G. Demoment eds. Kluwer Academic Publ., 1993, pp.273-278.
• Zorgati R. and M. Nikolova, Eddy Current Imaging: An Overview'', in Studies in Applied Electromagnetics and Magnetics 9, Non-Destructive Testing of MaterialsKenzomiya et al. eds., IOS Press., 1996, 8 p.
• Nikolova M. « Inversion de données pour le contrôle non destructif : une synthèse des travaux du groupe P21 » - Direction des études et Recherches, EDF, Notes de la DER - EDF, Rapport EDF/DER/HP-21/96/013, Sept. 1996, 112 p., diffusion externe.
• Mohammad-Djafari A., H. Carfantan and M. Nikolova, New advances in Bayesian calculation for linear and non linear inverses problems, in Maximum entropy and Bayesian methods, Berg-en-Dal, Kluwer Academic Publ., 1996.

Habilitation to direct research, 2006

• "Functionals for signal and image reconstruction: properties of their minimizers and applications)  (résumé)

PhD Thesis

• Nikolova M. « Inversion markovienne de problèmes linéaires mal-posés. Application à l'imagerie tomographique », Université de Paris Sud, Février 1995. Thèse soutenue avec la mention très honorable et les félicitations du jury.

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