Optimization in Image Processing

University of Macau

State Key Laboratory of Analog and Mixed-Signal VLSI

Workshop on

Optimization in Image Processing

15th May 2014

2:40pm – 3:10pm       Talk 1

Digital Assisted High Performance ADCs

Speaker: Dr. Yan ZHU, Assistant Professor, State Key Laboratory of Analog and Mixed-Signal VLSI, University of Macau



Digitally assisted analog technique is increasingly needed in further circuit and system designs, as FinFET and FD-SOI replace planar CMOS technology at the advanced process nodes of 20nm and beyond. The intrinsic feature of these new devices are lowering the barrier between the analog and the digital worlds, allowing unprecedented performance to be achieved by assisting analog circuit with digital techniques (e.g calibration and run-time control). The objective of talk is to discuss practical design consideration in high–performance ADCs in scaled CMOS process, established circuit technique that take advantage of scaled CMOS process technique.




Yan Zhu (S’10- M’12) received the B.Sc. degree in electrical engineering and automation from Shanghai University, Shanghai, China, in 2006, and the M.Sc. and Ph.D. degrees in electrical and electronics engineering from the University of Macau Macao, China, in 2009 and 2011, respectively. She is now an Assistant Professor with the State Key Laboratory of Analog and Mixed-Signal VLSI, University of Macau, Macao, China. She received the Chipidea Microelectronics Prize and Macao Scientific and Technological R&D for Postgraduates Award – Postgraduate Level in 2012 for outstanding Academic and Research achievements in Microelectronics, as well as the Student Design Contest award in A-SSCC 2011. Her research interests include low-power and wideband high-speed Nyquist A/D converters, digitally assisted data converter designs and ultra sound image sensor. She has involved in more than 15 research projects for low-power and high-performance ADC; published more than 25 technical journals and conference papers in her field of interests and held 4 US patents.



15th May 2014

3:10pm – 3:50pm       Talk 2

Fast Hue and Range Preserving Histogram Specification: Theory and New Algorithms for Color Image Enhancement

Speaker: Prof. Mila NIKOLOVA, Centre of Mathematics and Applications (CMLA), Department of Mathematics, ENS Cachan, France; Research Director, 2nd class, CNRS



Color image enhancement is a complex and challenging task in digital imaging with abundant applications. Preserving the hue of the input image is crucial in a wide range of situations. We propose simple image enhancement algorithms which conserve the hue and preserve the range (gamut) of the R, G, B channels in an optimal way. In our setup, the intensity input image is transformed into a target intensity image whose histogram matches a specified, well-behaved histogram. We derive a new color assignment methodology where the resulting enhanced image fits the target intensity image. We analyse the obtained algorithms in terms of chromaticity improvement and compare them with the unique and quite popular histogram based hue and range preserving algorithm of Naik and Murthy. Numerical tests confirm our theoretical results and show that our algorithms perform much better than the Naik-Murthy algorithm. In spite of their simplicity, they compete with well-established alternative methods for images where hue-preservation is desired.

Joint work with G. Steidl, University of Kaiserslautern


About Speaker:


Academic Qualification:

2006 Habilitation to Supervise Research in Mathematics, University Paris 6, France.

1995 PhD in Signal and Image Processing from the Université Paris-Sud, France.

Work Experience:

1995–1996  Post-Doc at the Direction des Etudes et Recherches d’EDF (Electricité de France)

1996-1998 Assistant Professor, Department of Mathematics and Informatics, University René Descartes, Paris, France.

1998–1999  Lecturer, Ecole Normale Supérieure de Télécommunications (ENST), France.

1999–2009  Senior Research Fellow, 1st class, CNRS (National Center for Scientific Research), competitive recruitement 1999.

2001–now   Permanent CNRS civil servant.

Research duties performed at:

1999–2003  ENST – Paris

2003–now  Centre of Mathematics and Applications (CMLA), Department of Mathematics, ENS Cachan, France

2009–now   Research Director, 2nd class, CNRS, competitive promotion, 2009.

Honors and Awards: IEEE Senior Member (since 2008), Michel Monpetit Prize of the French Academy of Sciences (2010), Allowance for scientific excellence 2011-2015 (inaugurated in 2009), Plenary Talk – Annual Meeting of the German Mathematical Society (DMV) 2012, Plenary Speaker – SIAM Conference on Imaging Science 2008

Editorship: IEEE Transactions on Image Processing (1999–2003), IEEE Signal Processing Letters (2007–2010), Numerical Functional Analysis and Optimization (2007–) SIAM Journal on Imaging Sciences (2008–), Journal of Mathematical Imaging and Vision (2014–).

Reviewer for Journals and Funding Agencies: Reviewer for 60 different academic journals; Hong Kong Research Grants Council.

Publications: Papers in refereed journals: 41 (among which sole author 13); Papers in proceedings and book chapters: 46 (among which sole author 21); Invited Presentations in International Conferences: 36.

Professional activities: see http://mnikolova.perso.math.cnrs.fr/

ISI Web of Knowledge (October 2013):


- 4 highly cited papers (last 10 years).

- Citation Ranking: Engineering (13 papers, 353 citations), Mathematics (16 papers, 289 citations), All fields (78 papers, 1041 citations)



15th May 2014

3:50pm – 4:30pm       Talk 3

Disparity and Optical Flow Partitioning Using Extended Potts Priors

Speaker: Prof. Gabriele STEIDL, Professor, Department of Mathematics, University of Kaiserslautern, Germany



This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notation of asymptotically level stable functions we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of minimizers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method.


This is joint work with X. Cai, (University of Cambridge), J.H. Fitschen (University of Kaiserslautern), and M. Nikolova (CMLA, ENS Cachan, CNRS).



Gabriele Steidl received her PhD and Habilitation in Mathematics from the University of Rostock, Germany, in 1988 and 1991, respectively. From 1993 to 1996, she held a position as assistant professor of Applied Mathematics at the University of Darmstadt, Germany. From 1996 to 2010, she was full professor at the Department of Mathematics and Computer Science, University of Mannheim, Germany. Since 2011, she is Professor at the Department of Mathematics at the University of Kaiserslautern, Germany. She was a visiting researcher at the University of Debrecen (Hungary), the University of Zürich (Switzerland), the Banach Center Warsaw (Poland), the ENS Cachan and the University Paris Est (France). Her research interests include applied and computational harmonic analysis and convex analysis with applications in image processing.



15th May 2014

4:40pm – 5:20pm       Talk 4

An Adaptive Finite Element Method for Total Variation Based Image Denoising

Speaker: Prof. Michael HINTERMÜLLER, Department of Mathematics, Humboldt-Universität zu Berlin; Head of Research Group, Applied Mathematics Group



The first order optimality system of a total variation regularization based variational model with L2-data-fitting in image denoising (L2-TV problem) can be expressed as an elliptic variational inequality of the second kind. For a finite element discretization of the variational inequality problem, an a posteriori error residual based error estimator is derived and its reliability and (partial) efficiency are established. The results are applied to solve the L2-TV problem by means of the adaptive finite element method. The adaptive mesh refinement relies on the newly derived a posteriori error estimator and on an additional heuristic providing a local variance estimator to cope with noisy data. The numerical solution of the discrete problem on each level of refinement is obtained by a superlinearly convergent algorithm based on Fenchel-duality and inexact semismooth Newton techniques and which is stable with respect to noise in the data. Numerical results justifying the advantage of adaptive finite elements solutions are presented.


About Speaker:

2013       Vice Speaker of the Einstein-Center for Mathematics Berlin

2011       Member of the Council of the DFG-Research Center MATHEON

2010       Scientist-in-Charge of MATHEON Application Area C

2009       Member of the 'Junge Kurie' of the Austrian Academy of Sciences

2008      MATHEON-Research Professor and W3-Professor in Applied Mathematics, Humboldt - University of Berlin 

2007       Chair in Applied Mathematics, University of Sussex 

2005       START award by BMWF (Austrian Federal Ministry of Science and Research) 

2004       Associate Professor, Department of Mathematics, University of Graz 

2003       Visiting Associate Professor, Rice University 

2000       Assistant Professor, Department of Mathematics, University of Graz 

1997       Research Assistant, SFB "Optimization & Control", University of Graz 


2003       Habilitation in Mathematics, University of Graz 

1997       Dr. techn. degree, University of Linz 

1994       Diploma in Technical Mathematics, University of Linz 



15th May 2014

5:20pm – 6:00pm       Talk 5

Image Deblurring with Krylov Subspace Methods

Speaker: Prof. Per Christian HANSEN, Professor of Scientific Computing, Technical University of Denmark; Head of HD-Tomo Research Project



Image deblurring, i.e., reconstruction of a sharper image from a blurred and noisy one, involves the solution of a large and very ill-conditioned system of linear equations, and regularization is needed in order to compute a stable solution. Krylov subspace methods are often ideally suited for this task: their iterative nature is a natural way to handle such large-scale problems, and the underlying Krylov subspace provides a convenient mechanism to regularized the problem by projecting it onto a low-dimensional "signal subspace" adapted to the particular problem.  In this talk we consider the three Krylov subspace methods CGLS, MINRES, and GMRES.  We describe their regularizing properties, and we discuss some computational aspects such as preconditioning and stopping criteria.


Per Christian Hansen received the PhD and DrTechn degrees from the Technical University of Denmark in 1985 and 1996, respectively. He has previously worked at Copenhagen University and the Danish university computing center UNI-C.  He is now professor of scientific computing at the Technical University of Denmark.  He has worked with numerical regularization algorithms for 25+ years and published 4 books and 85+ papers on the subject, moreover he is the author of 6 software packages for ill posed and rank deficient problems.



16th May 2014

11:00am – 11:40am    Talk 6

Alternating Direction Optimization for Image Restoration Problems

Speaker: Prof. Mário A. T. FIGUEIREDO, Professor,  Department of Electrical and Computer Engineering, Instituto Superior Técnico (IST); Co-coordinator (with R. Valadas), Networks and Multimedia Research Area, Instituto de Telecomunicações; Group Coordinator, Pattern and Image Analysis, Instituto de Telecomunicações



This talk will review our recent work on the application of the alternating direction method of multipliers (ADMM) to several imaging inverse problems. We will show how ADMM provides an efficient and modular optimization tool, which allows addressing a wide variety of problems (namely, image restoration under Gaussian, Poisson, or multiplicative noise) using several types of regularizers (namely total variation, frame-based analysis, frame-based synthesis, or hybrid/balanced analysis-synthesis), and formulations (constrained or unconstrained optimization). We will also describe very recent work on the use of ADMM for blind deconvolution and in dealing efficiently with non-periodic boundary conditions. 



Mario A. T. Figueiredo received MSc, PhD, and "Agregado" degrees in electrical and computer engineering, both from Instituto Superior Tecnico (IST), the engineering school of the University of Lisbon, in 1990, 1994, and 2004. Since 1994, he has been with the faculty of the Department of Electrical and Computer Engineering, IST, where he is now a full Professor. He is also area coordinator and group leader at Instituto de Telecomunicacoes, a private non-profit research institute.


His research interests include image processing and analysis, pattern recognition, statistical learning, and optimization. M. Figueiredo is a Fellow of the IEEE and of the IAPR. He received the 1995 Portuguese IBM Scientific Prize, the 2008 UTL/Santander-Totta Scientific Prize, the 2011 IEEE Signal Processing Society Best Paper Award, the 2014 IEEE W. R. G. Baker Award, and several conference best paper awards. He is/was associate editor of several journals (among others, the IEEE Transactions on Image Processing, the IEEE Transactions on Pattern Analysis and Machine Intelligence, the SIAM Journal on Imaging Sciences, the Journal of Mathematical Imaging and Vision). He served on program and prganizing committees of several conferences and workshops; namely, he co-chaired the 2001 and 2003 Workshops on Energy Minimization Methods in Computer Vision and Pattern Recognition, co-organized all the editions (2011-2014) of the Lisbon Machine Learning School, and is the technical program chair of the 2014 European Signal Processing Conference. 



16th May 2014

11:40am – 12:20pm    Talk 7

Alternating Projection, Ptychography and High Dimensional Phase Retrieval

Speaker: Dr. Hau-tieng WU, Mathematics Department, Stanford University



We demonstrate the global convergence of the alternating projection algorithm which has been open for 40+ years. Additionally, for the ptychographic imaging problem, we discuss phase synchronization and connection graph Laplacian as well as their theoretical properties, and show how to construct an accurate initial guess to accelerate convergence speed to handle the big imaging data in the coming new light source era. This is a joint work with Stefano Marchesini and Yu-Chao Tu.



Hau-tieng Wu obtained his Ph.D. from Mathematics department at Princeton Uniersity in 2011. He worked with Ingrid Daubechies and Amit Singer for his thesis. After graduation, he worked as a postdoctor researcher in PACM at Princeton University continuing his work with Amit Singer for 1 year, and now he is in Mathematics department at Stanford University. Starting from July 1, 2014, he will be an assistant professor in Mathematics department at Toronto University. Before coming to mathematics, he obtained his M.D. degree from National Yang-Ming University in 2003 and practiced as a residency doctor for 1+ years in the Taipei Veterans General Hospital, Taiwan.