Monday, August 20, 2018

SPORCO: Convolutional Dictionary Learning - implementation -



Brendt sent me the following a few days ago: 

Hi Igor,
We have two new papers on convolutional dictionary learning as well as some recent related code. Could you please post an announcement on Nuit Blanche?
Brendt
Sure Brendt ! It is already mentioned in the Advanced Matrix Factorization Jungle Page as this is an awesome update to the previous announcement.



"Convolutional Dictionary Learning: A Comparative Review and New Algorithms", available from http://dx.doi.org/10.1109/TCI.2018.2840334 and https://arxiv.org/abs/1709.02893, reviews existing batch-mode convolutional dictionary learning algorithms and proposes some new ones with significantly improved performance. Implementations of all of the most competitive algorithms are included in the Python version of the SPORCO library at https://github.com/bwohlberg/sporco .

"First and Second Order Methods for Online Convolutional Dictionary Learning", available from http://dx.doi.org/10.1137/17M1145689 and https://arxiv.org/abs/1709.00106, extends our previous work and proposes some new algorithms for online convolutional dictionary learning that we believe outperform existing alternatives. Implementations of all of the new algorithms are included in the
Matlab version of the SPORCO library at http://purl.org/brendt/software/sporco and the first order algorithm is also included in the Python version of the SPORCO library at https://github.com/bwohlberg/sporco . A very recent addition to the Python version is the ability to exploit the SPORCO-CUDA extension to greatly accelerate the learning process.



Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the convolutional sparse coding problem, the corresponding dictionary learning problem is substantially more challenging. Furthermore, although a number of different approaches have been proposed, the absence of thorough comparisons between them makes it difficult to determine which of them represents the current state of the art. The present work both addresses this deficiency and proposes some new approaches that outperform existing ones in certain contexts. A thorough set of performance comparisons indicates a very wide range of performance differences among the existing and proposed methods, and clearly identifies those that are the most effective.


Convolutional sparse representations are a form of sparse representation with a structured, translation invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to all training images during the learning process, which results in very high memory usage and severely limits the training data that can be used. Very recently, however, a number of authors have considered the design of online convolutional dictionary learning algorithms that offer far better scaling of memory and computational cost with training set size than batch methods. This paper extends our prior work, improving a number of aspects of our previous algorithm; proposing an entirely new one, with better performance, and that supports the inclusion of a spatial mask for learning from incomplete data; and providing a rigorous theoretical analysis of these methods.


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Thursday, July 26, 2018

CfP: Call for Papers: Special Issue on Information Theory Applications in Signal Processing

Sergio just sent me the following:
Dear Igor,
Could you please announce in nuit blanche the following call for contributions to our Special Issue.
Best resgards,
Sergio
Sure Sergio !
Dear colleagues, 
We are currently leading a Special Issue entitled "Information Theory Applications in Signal Processing" for the journal Entropy (ISSN 1099-4300, IF 2.305). A short prospectus is given at the volume website: 
We would like to invite you to contribute a review or full research paper for publication in this Special Issue after standard peer-review procedure in Open access form.
The official deadline for submission is 30 November 2018. However, you may send your manuscript at any time before the deadline. We can organize a very fast peer-review, if accepted, the paper will be published immediately. Please also feel free to distribute this call for papers to colleagues and collaborators.
You can contact with the assistant editor Ms. Alex Liu (alex.liu@mdpi.com) to solve any question or doubt.
Thank you in advance for considering our invitation.
Sincerely,
Guest Editors:
Dr. Sergio Cruces (http://personal.us.es/sergio/)
Dr. Rubén Martín-Clemente (http://personal.us.es/ruben/)
Dr. Wojciech Samek (http://iphome.hhi.de/samek/)




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Monday, July 23, 2018

Rank Minimization for Snapshot Compressive Imaging - implementation -



Yang just sent me the following:

Hi Igor,

I am writing regarding a paper on compressive sensing you may find of interest, co-authored with Xin Yuan, Jinli Suo, David Brady, and Qionghai Dai. We get exciting results on snapshot compressive imaging (SCI), i.e., encoding each frame of an image sequence with a spectral-, temporal-, or angular- variant random mask and summing them pixel-by-pixel to form one-shot measurement. Snapshot compressive hyperspectral, high-speed, and ligh-field imaging are among representatives.

We combine rank minimization to exploit the nonlocal self-similarity of natural scenes, which is widely acknowledged in image/video processing and alternating minimization approach to solve this problem. Results of both simulation and real data from four different SCI systems, where measurement noise is dominant, demonstrate that our proposed algorithm leads to significant improvements (>4dB in PSNR) and more robustness to noise compared with current state-of-the-art algorithms.

Paper arXiv link: https://arxiv.org/abs/1807.07837.
Github repository link: https://github.com/liuyang12/DeSCI.

Here is an animated demo for visualization and comparison with the state-of-the-art algorithms, , i.e., GMM-TP (TIP'14), MMLE-GMM (TIP'15), MMLE-MFA (TIP'15), and GAP-TV (ICIP'16).
Thanks,
Yang (y-liu16@mails.tsinghua.edu.cn)


Thanks Yang !

Snapshot compressive imaging (SCI) refers to compressive imaging systems where multiple frames are mapped into a single measurement, with video compressive imaging and hyperspectral compressive imaging as two representative applications. Though exciting results of high-speed videos and hyperspectral images have been demonstrated, the poor reconstruction quality precludes SCI from wide applications.This paper aims to boost the reconstruction quality of SCI via exploiting the high-dimensional structure in the desired signal. We build a joint model to integrate the nonlocal self-similarity of video/hyperspectral frames and the rank minimization approach with the SCI sensing process. Following this, an alternating minimization algorithm is developed to solve this non-convex problem. We further investigate the special structure of the sampling process in SCI to tackle the computational workload and memory issues in SCI reconstruction. Both simulation and real data (captured by four different SCI cameras) results demonstrate that our proposed algorithm leads to significant improvements compared with current state-of-the-art algorithms. We hope our results will encourage the researchers and engineers to pursue further in compressive imaging for real applications.

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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
schemes and adversarial learning methods.
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,

-Vlad

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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Monday, July 09, 2018

Nuit Blanche in Review (February - June 2018)


It's been five months, already, here is what we featured on Nuit Blanche since the last Nuit Blanche in Review (Janvier 2018). During that time, Mila Nikolova left us. Here are some other things that happened.

Implementations


Meetings:


Posters:

In-depth

Book:

Video:

job:

Around the blogs:
conferences
Paris Machine Learning meetups:
IA en France
Other

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.
Link: https://www.springer.com/la/book/9783319786735
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.





  • [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. Maitre``Rééchantillonnage de données 3D laser aéroporté en milieu urbain''Congrès Vision par Ordinateeur ORASIS, pp. 75-82, Mai 2003.
  • [27] M. Nikolova and M. Ng``Comparison 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. Nikolova``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. 
  • [24] S. Durand 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.
  • [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. Duhamel``Adaptive 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. Nikolova``Local 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. Nikolova``Blind 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-Djafari``Discontinuity 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. Idier``Inversion 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-Djafari``Maximum 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  (pdf).
  • [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 (pdf).
  •  [31] M. Nikolova, "One-iteration dejittering of digital video images", Journal of Visual Communication and Image Representation, Vol. 20, 2009, pp. 254-274  (pdf).
  • [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(pdf)
  • M. Nikolova, ``Energy Minimization Methods'', Chapter 5, pp. 138-186, Handbook of Mathematical Methods in Imaging, editor: Otmar ScherzerSpringer 2011, first edition(pdf)
  • 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


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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