Research
In October 2000 I started working on the unit group of non-commutative orders as an Aspirant FWO and obtained my Ph. D. in Mathematics on the 26th of March 2004. In the years thereafter I got more and more interested in applications of mathematics in image processing and hence I moved to IBBT/ETRO-IRIS in October 2007.
Currently, my research interests are in security and authentication of multimedia content, mostly still images (including digital representations of paintings) and (scalable) video. I am leading the ‘Multimedia Security and Authentication’ research group and our research can be divided into two main parts: Information Hiding and Digital Painting Analysis.
In particular, I am investigating the art and science of watermarking and steganography.
Cryptography (derived
from Greek "secret writing") or information hiding is considered to be a branch
of both mathematics and computer science, and is affiliated closely
with information theory, computer security, and engineering. Before
the modern era, cryptography was concerned solely with message confidentiality
(i.e., encryption) — conversion of messages from a comprehensible
form into an incomprehensible one, and back again at the other end,
rendering it unreadable by interceptors or eavesdroppers without secret
knowledge (namely, the key needed for decryption of that message). In
recent decades, the field has expanded beyond confidentiality concerns
to include techniques for message integrity checking, sender/receiver
identity authentication, digital signatures, interactive proofs, and
secure computation, amongst others. The goal of cryptanalysis
is to find some weakness or insecurity in a cryptographic scheme. Cryptology covers cryptography and cryptanalysis.
Watermarking is imperceptibly altering digital content to embed a message and hence is a branch of cryptography.
Steganography (or covert
writing) is the little sister of cryptography where even the
existence of a message is hidden so as to keep it confidential and was also first developed in ancient times. An early example,
from Herodotus, concealed a message - a tattoo on a slave's shaved head
- under the regrown hair. More modern examples of steganography include
the use of invisible ink, microdots, and watermarking
to conceal information. The goal of steganalysis is
to find some weakness or insecurity in a steganographic scheme. Steganology covers steganography and steganalysis.
For now it seems that no system of information hiding is totally
immune for attacks. However watermarking and steganography have their place in security,
they can in no way replace encryption, but are intended to supplement it. The application of watermarking
for use in detection of unauthorised, illegally copied material is continuously
being realised and developed.
Students:
Dieter Bardyn (Ph. D.)
Tim Dams (implementation - market study)
Robrecht Van Caenegem (Master)
Hui Jie (Master)
Projects:
Coördinator of the FWO-project Perceptuele hashing en semi-fragiele watermarking voor de ontdekking, opsoring, herkenning en selectieve authenticatie van multimediamateriaal, 2008-2011. Cooperation with COSIC (KULeuven).
Co-Promotor of the IM-Pact-project (International Media Pact) Digitale Archivering en verborgen informatie voor controle van intellectuele eigendomsrechten - DaVinci, 2008-2012. Cooperation with TILT (Universiteit Tilburg).
Links:
For an excellent introduction to information hiding we point the interested reader to
Data-Hiding Codes
Moulin, P.; Koetter, R.
Proceedings of the IEEE
Volume 93, Issue 12, Dec. 2005. Page(s):2083 - 2126
Fragile watermarking for authentication
On the other hand, I use signal processing for painting analysis, such as artist identification (authentication in particular), dating, style classification, registration of different acquisitions and inpainting.
Students:
Bruno Cornelis (Ph. D.)
Projects:
We are part of the Princeton Digital Painting Analysis - team led by Ingrid Daubechies (Princeton) and working on van Gogh paintings.
Links:
van Gogh Gallery
Workshop Image Processing for Artist Identification II - Amsterdam, 20-21 October 2008, van Gogh Museum, Amsterdam.
De slaapkamer, van Gogh, 1888
Past Research Events:
Lecture by Massimo Fornasier, Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria
(followed by FNRS contact group "Wavelets and Applications" @ULB)
When: dinsdag 13 januari 2009 9:00-9:50.
Location: VUB, ETRO, Pleinlaan 9, Marconi room
Title: A comparison of joint sparsity and total variation minimization algorithms in a real-life art restoration problem
Abstract:
On March 11, 1944, the famous Eremitani Church in Padua (Italy) was destroyed in an Allied bombing along with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. We contributed to the development of an efficient pattern recognition algorithm to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the colored fragments is only 77 m2, while the original area was of several hundreds.
This means that we can reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Moreover, is it possible to estimate how faithful such a restoration is?
In this talk we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. Then we review two models recently studied for the recovery of vector valued functions from incomplete data, with applications to the recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions, in particular wavelet or curvelet expansions, for the first functional and functional total variation for the second. We show numerical test on the real-life problem of the A. Mantegna’s frescoes and we compare the results due to the two methods.
Information about the speaker:
Massimo Fornasier’s recent research focuses on the numerical analysis of compressive algorithms (CA) for sparse solution of equations and inverse problems. In particular, he studies algorithms for problems in
- signal/image processing,
- modern data analysis, and
- adaptive numerical solution of PDE's
that exploit parsimonious expansions via redundant discretizations, adaptive compression, and randomness. Compressive algorithms are a new approach to efficient computing and take advantage of the property of solutions of certain PDE's and variational problems to be characterized by few major features which are recovered by adaptive nonlinear iterations. CA are fast, tend to use minimal number of degrees of freedom, and are simple. Their numerical analysis is challenging. CA are very successfully applied in several applied problems. The relevant mathematics includes applied harmonic analysis, functional analysis, probability theory, discrete and convex geometry, convex optimization, and calculus of variations. The main numerical techniques include iterative thresholding algorithms, operator compression, random alternating projections, subspace correction, and domain decomposition methods.
A tutorial lecture on Data Hiding
When:
Friday 10th July 2009, 16:30-18:00 and 18:30-20:00
Location:
VUB, ETRO, Pleinlaan 9, Marconi room
Abstract:
This tutorial reviews the theory and design of codes for hiding or embedding information in signals such as images, video, audio, graphics, and text. Such codes have also been called watermarking codes; they can be used in a variety of applications, including copyright protection for digital media, content authentication, media forensics, data binding, and covert communications. Some of these applications imply the presence of an adversary attempting to disrupt the transmission of information to the receiver; other applications involve a noisy, generally unknown, communication channel.
Our focus is on the mathematical models, fundamental principles, and code design techniques that are applicable to data hiding. The approach draws from basic concepts in information theory, coding theory, game theory and signal processing, and is illustrated with applications to the problem of hiding data in images.