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«CURRICULUM VITAE MASSIMO FORNASIER 1. PERSONAL DATA, EDUCATION, CAREER, AND AVAILABILITY 2. SCIENTIFIC RESEARCH ACTIVITY 2.1 Research directions 2.2 ...»

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CURRICULUM VITAE

MASSIMO FORNASIER

1. PERSONAL DATA, EDUCATION, CAREER, AND AVAILABILITY

2. SCIENTIFIC RESEARCH ACTIVITY

2.1 Research directions

2.2 Synthesis of the scientific activity in approximation theory and numerical harmonic analysis

2.3 Synthesis of the scientific activity in digital signal and image processing

2.4 Synthesis of the scientific activity in numerical solution of (pseudo)differential equations

3. COMPLETE LIST OF PUBLICATION

4. CONFERENCE, SEMINAR, AND COURSE PARTICIPATION

4.1 Conference talks under invitation

4.2 Other conference communications

4.3 Research seminars

4.4 Participation to specializing schools and courses

5. RESEARCH PROJECT PARTICIPATION AND COORDINATION

6. DIDACTICAL ACTIVITY

7. ORGANIZATIONAL ACTIVITY

1. PERSONAL DATA, EDUCATION, AND CAREER

Place and date of birth: Feltre (BL) Italy, 6 July 1975.

Citizenship: Italian.

Domiciles in the last 3 years: Austria (23 months, Nov. 2002-Jun. 2003, Jan.2004-Mar. 2005), Germany (6 months), Italy (official residence).

Academic degrees: Research Doctoral degree in Computational Mathematics 17 February 2003 at University of Padova, Italy. Title of the thesis: Constructive Methods for Numerical Applications in Signal Processing and Homogenization Problems (no marks are given in Italy).

Laurea in Matematica (Master degree) 28 October 1999 at University of Padova, Italy, with mark 110/110 summa cum laude. Title of the thesis: A Method for the Representation and the Comparison of Digital Images Independently of Rotations. A Contribution to the Computer Assisted Reconstruction of the Art Frescoes in in the Eremitani Church in Padua (Italian).

Current positions: since 1st June 2003: research grant Wavelets e Frames in teoria della approssimazione in the discipline sector MAT/08-Numerical Analysis at the Department of Mathematical Methods and Models for the Applied Sciences, University of Rome "La Sapienza", Italy;

since 1st May 2004: Individual Marie Curie Fellowship (European Commission - Research Directorate-General) with title Flexible Time-Frequency Decompositions and Adaptive Treatment of Operator Equations by Frames at NuHAG (the Numerical Harmonic Analysis

Group), Faculty of Mathematics, University of Vienna, Austria (proposal FTFDORF-FP6Previous positions:

Jan.-Mar. 2004 Marie Curie Fellowship (Forschung Mitarbeiter) EU-network RTN HASSIP (Harmonic An

–  –  –

Other recent research activity and cooperation At AG Numerik/Wavelet-Analysis Group, Fachbereich Mathematik und Informatik der Philipps-Universitaet Marburg, Germany in the periods 8-12 March 2004, 23-26 June 2004, 16-27 August 2004, e 6-16 March 2005.

Communication skills: fluent English, good Spanish, native Italian. Basic French and German.

–  –  –

AVAILABILITY

Currently the candidate can continue his activity on the basis of the Individual Marie Curie Fellowship until the end of April 2006. From May 2006 he is available for research positions for at least three (3) years in Universities, Research Centres and Private Institutes.

2. SCIENTIFIC RESEARCH ACTIVITY

2.1 Research directions:

-Numerical harmonic analysis

-Time-frequency and wavelet methods

-Signal and image processing, and data analysis

-Numerical treatment of (pseudo-)differential equations by frame adaptive schemes

-Engineering and software applications for the conservation of cultural heritage (art fresco restoration), and numerical simulation During his research activity, the candidate has developed studies on frames, i.e. stable, redundant, and nonorthogonal expansions in Banach (function) spaces, and their applications in digital signal and image processing, and for the formulation of innovative schemes for the numerical solution of integral and differential equations.

Introduced by Duffin and Schaeffer in 1952 in studies related to nonharmonic Fourier series, frames play a crucial role in sampling theory, wavelet, and time-frequency (Gabor) analysis. They differ from bases since the coefficients of an expansion with respect to a frame are in general not unique, defining an intrinsic redundancy in the representation of functions (signals).

Such property can be in fact exploited in those applications where numerical stability, noise and error tolerance are fundamental. Among traditional and classical applications of frames, one can already count digital signal and image processing, data compression and restoration, data (wireless) transmission. Not yet much known are indeed the properties of such expansions as a tool of discretization for the numerical solution of integral and differential equations, and more general pseudodifferential equations. Recently the candidate has focused his attention on the latter research direction with expected potential applications in robust numerical simulation and regularized inverse problems for signal and image processing.





1) One important experience that has characterized the initial stage of his research activity (1999-2002) has been the development of numerical and software tools for digital image pattern recognition, and their concrete application in the computer assisted real restoration of frescoes by A. Mantegna et al. in the Ovetari Chapel of the Eremitani Church in Padova (Italy). Considered as one of the most important testimonials of the Italian Renaissance (1452), this art opera has been destroyed and fragmented during a dramatic bombing in the Second World War (11 March 1944). Of the masterpiece by Guariento, Antonio Vivarini, Giovanni D'Alemagna, Nicolò Pizolo, Bono da Ferrara, Ansuino da Forlì, and of course Andrea Mantegna circa 88000 fragments still survive now. More technical and historical details on “the state of the art” can be found in the booklet [P4].

The restoration of this huge incomplete puzzle has been attempted with traditional methods at the Restoration Central Institute in Rome for several years without reaching a complete mapping of the original positions of the fragments, due to the intrinsic difficulties of the problem.

During the cooperation at the Department of Physics “G. Galilei” in Padova (Italy) with Domenico Toniolo the candidate has developed a fast, robust, and efficient [2,7,P1-4,T1-2] image pattern recognition algorithm, based on (local) circular harmonic expansions (see in particular [7] for more mathematics details). One remarkable property of such numerical scheme is its invariance under mutual rotation and affine transformation of the images to compare, which is fundamental for the detection of a fragment.

In 1999 an experimentation of the algorithm on 1000 sample real fragments has been conducted, for the localization of the fragment image by comparison with an old gray level picture of the fresco dated to 1920. The results described in the technical report [P2] showed and confirmed the potential efficiency of such method, motivating then the proposal of a large scale project for the complete mapping of the positions of all the fragments. This project has involved as (publicprivate) sponsors and promoting agencies the University of Padova, the Soprintendenza per il Patrimonio Storico Artistico e Demoetnoantropologico del Veneto, the Fondazione Cassa di Risparmio di Padova e Rovigo and the Curia Vescovile di Padova. The project has been funded with c.a. 525000 Euro, with the constitution of a dedicated laboratory for digital image processing in art restoration (the Mantegna Project Laboratory, Via Carlo Dottori 7/B, Padova, Italy) where, since 22 October 2001, circa 35 people has been involved for the realization of the computer assisted mapping of the fragment positions. This stage of the project has been concluded on 23 December 2004. During 2005 the Laboratory will be dedicated to the organization of the huge amount of data produced in the last three years of research activity in order to present officially the results of the project in 2006 during the important exhibition that will be organized in Padova for the Mantegna's anniversary. The special edition of a book dedicated to the Mantegna Project activity is also planned.

Inspired by the fresco problem, in [12] a new method for vector valued signal restoration is introduced. In particular such method have been applied in order to reconstruct the colors of the missing parts of the fresco from the given colors of the detected fragments and the tracks given by the gray level of the pictures of the frescoes dated to 1920.

Such technique is based both on nonuniform sampling methods and on the minimization of suitable variational problems.

It is expected in 2005 a cooperation with Riccardo March (IAC-CNR, Rome, Italy) for the extension of the variational problem to BV vector valued functions, by using Gamma-convergence methods (introduced by De Giorgi in the early 1970's). As a consequence of this investigation, a new approach to the quasi-characterization of BV functions by wavelet coefficients is expected, the latter being a long standing problem in harmonic analysis of BV space.

2) This initial experience has partially inspired the successive scientific production of the candidate in approximation theory and numerical harmonic analysis, and specifically in the frame theory of (generalization of) Gabor and wavelet expansions. The latter are expansions with respect to functions defined respectively by dilation and translation (wavelets) and by modulation and translation (Gabor frames) of a given analysing function, as powerful tools of time/spacescale/frequency function (signal) analysis.

In [1,3] a general method to construct structured frames (i.e., generated by application of suitable operators) in Hilbert spaces has been introduced, and later applied in [4] for the formulation of intermediate frames between Gabor and wavelet ones, by application of suitable combinations of modulations, translations, and dilations.

This study has been motivated by the fact that, even if similar, wavelet and Gabor frame theories have been developed in the last years almost independently each other. Therefore, the contribution [4] has been an attempt to formulate a unified theory of such expansions (see also [10]) and for the introduction of new and possibly more flexible tools for applications in signal processing and in the discretization of operators.

The study of the approximation properties of such expansions and their use in specific problems (signal approximation or equation discretization) require to define which is the class of representable functions by such expansions. Such theoretical question has motivated the introduction and the development of the intrinsic localization of frame theory [6], i.e. the theory of frames with Gramian matrix endowed with special off-diagonal decay properties. This concept has been first introduced by Groechenig and successively generalized by the candidate for its application in several theoretical

contexts, e.g., see [6,8,10,11-12,T2], and in numerical analysis [9,14]:

Such localized frames, that include the class introduced in [4] (except for some generalization of the concept of localization, see [8]) allow the characterization of canonically associated Banach spaces (of representable functions).

Moreover the fact that they are naturally endowed with an extra off-diagonal decay structure which measures the approximation properties allows the development of efficient numerical methods for the discretization of operators and the solution of operator equations [9]. Such theory has shown interesting relations with the spectral theory of involutive Banach algebras of matrices, leading to some original results even in this direction, included in [6] too.

The theory of intrinsically localized frames has been further generalized in [8] for the characterization by flexible Gaborwavelet frames [4] of so called alpha-modulation spaces (introduced at the beginning of the 90's by P. Groebner and H.

G. Feichtinger), as an intermediate class of more classical function spaces known as modulation spaces and Besov spaces.

Such classical spaces can be derived as coorbit spaces (in the terminology by Feichtinger and Groechenig) associated to (square) integrable Heisenberg and Affine group representations respectively. A coorbit space Co(Y) is essentially the retract space by the representation coordinate transform of a given space Y. Alpha modulation spaces cannot be described as associated to any square integrable representation of the crossed Heisenberg-Affine group.

This observation (derivable from studies by Torresani et al.) has motivated the generalization of the coorbit space theory as described in the paper [12]: One assumes the existence of suitable (still rather generic, no group structure is assumed in the background) continuous frames and (by generalizing the intrinsic localization of frame theory) one can associate canonically generalized coorbit spaces. In [12] it is also shown that for suitably localized continuous frames one can extract by sampling a sub-frame which is discrete still characterizing the same class of coorbit spaces.

Such studies and investigations has been realized, since the period of the Research Doctorate at the University of Padova, in the context of international cooperations, especially in the European area.

In particular, since 1999-2000, a strong relation of cooperation has been developed with NuHAG, Faculty of Mathematics, University of Vienna, Austria (coordinated by Hans Georg Feichtinger). First on the basis of regular short term visits, and then in the context of the European Research Network RNT HASSIP (Harmonic Analysis and Statistics for Signal and Image Processing), and by the recent award to the candidate by the European Commission of an Intra-European Individual Marie Curie Fellowship entitled Flexible Time-Frequency Decompositions and Adaptive Treatment of Operator Equations by Frames.



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