Welcome to Dimitri Nion's homepage


 
 
Dr. Dimitri Nion

E-mail:  here
CV: [French] [English]

Research interests:  Signal Processing, Sensor Array Processing, Blind Source Separation, Linear and Multilinear Algebra, Tensor Decompositions, Batch and Adaptive Signal Processing, Optimization,  Telecommunications (MIMO, CDMA, Radars).



 new  Matlab codes  new
Joint Block Diagonalization: 

    [1]  A non-linear conjugate gradient algorithm for Non-Unitary Joint Block Diagonalization (JBD) and Joint Diagonalization (JD). [Code]
         
The Non-Unitary JBD problem is reformulated as a tensor decomposition. The latter decomposition is computed by a non linear conjugate gradient (NCG) algorithm.
          The JBD-NCG algorithm works for real or complex valued data and handles the symmetric or the hermitian symmetric cases.
          The exactly-determined case (matrix A is square), over-determined case (A is tall) and under-determined case (A is fat) are also handled.

Tensor decompositions: 


    [1]  Candecomp/Parafac (CP) decomposition (for tensors of order 3, 4 and 5). [Code]
         
CP model fitted via the Alternating Least Squares (ALS) algorithm coupled with line search.


    [2]  Block Component Decompositions (BCD).
[Code]
          BCD fitted via the Alternating Least Squares (ALS) algorithm coupled with line search.

Adaptive signal processing:


    [1]  Adaptive algorithms to track the Candecomp/Parafac (CP) decomposition of a third-order tensor.
[Code]
          Tracking the CP decomposition of a tensor X which has a dimension growing with time. Assume we are given the loading matrices A(t), B(t) and C(t) of the CP decomposition of X(t).
          At time t+1, X(t+1) is obtained from X(t) by appending a new observed slice in one of the 3 modes.
          The purpose is then to estimate the loadings A(t+1), B(t+1) and C(t+1) of the CP decomposition of X(t+1).
          This can be done in an efficient way via the adaptive algorithms parafac-SDT (Simultaneous Diagonalization Tracking) and parafac-RLST (Recursive Least Squares Tracking).


Algebraic signal processing tools:

   
[1]  Blind SIMO (Single Input Multiple Output) identification (Multichannel FIR filters identification). [Code]
          Given the M signals xm(t) = conv( hm(t) , s(t) ), where m=1,...,M is a channel index, estimate the M channel impulse responses hm(t) and the source signal s(t).

    [2]  Toeplitz structure recovery.
[Code]
          Factorization of a matrix X of the form X= H S where H is an unknown square unstructured matrix and S is an unknown Toeplitz matrix.

 
  [3]  Vandermonde structure recovery. [Code]
          Approximate a vector u by a Vandermonde vector v = [m, m ej a , m e2j a , ..., m e(P-1) j a].

   
[4]  Removing column-wise permutation and scaling ambiguity (e.g. to evaluate performance in blind source separation applications). [Code]
          Estimate the diagonal matrix D and the permutation matrix P that links two given matrices A and B such that : A = B  D  P (+Residual) and compute the error err = norm(A - B D P).

    [5] Removing block-wise permutation ambiguity.
[Code]
         Estimate the block-diagonal matrix D and the block-wise permutation matrix P that links two given matrices A and B such that : A = B  D  P (+Residual),
         where A=[A1, A2, ..., AR]  and  B=[B1, B2, ..., BR] are partitioned matrices. This is useful to assess performance of a technique that yields estimates of Span(Br), r=1,...,R, in an arbitrary order.


    [6]  Matrix inversion and pseudo-inversion for rank-1 updates.
[Code]
          Given Anew = Aold + c dT where c and d are vectors and given  Pold = pinv(Aold) , compute  Pnew = pinv(Anew) recursively, in an efficient way.

 Blind source separation (BSS):


     [1]  Separation of linear instantaneous mixtures via Second-Order-Statistics (SOS) and Candecomp/Parafac.
    
           [Code 1] A user-friendly matlab interface to illustrate the BSS problem with speech mixtures of 2 or 3 sources (Can be useful for educational purpose!)
          
[Code 2] Matlab code for an arbitrary number of sources and sensors.  
          
See also: a list of online available codes for Blind Source Separation [here] and  [here].          
           Consider M recorded signals 
xm(t) = am1 s1(t) + ... + amN sN(t) , m=1,...,M, that consist of linear combinations of unknown source signals sn(t), n=1,...,N.
           The mixing model can be compactly written as x(t) = A s(t). Given the observed vector x(t), the purpose is to:
           1- estimate the mixing matrix A.
           2- if A is full column-rank, then estimate the sources in the least squares sense: s(t) = pinv(A) x(t).
           Assuming the sources to be mutually uncorrelated, estimation of A boils down to a JAD (Joint Approximate Diagonalization) problem. The latter can be solved via Candecomp/Parafac (CP) which,
           contrary to classical JAD algorithms, does not necessarily require A to be tall and full column-rank; powerful uniqueness properties allow estimation of A even in several under-determined cases (more
           sources than sensors).
   

     [2]  Pure delayed mixtures : separation and localization via TDOAs (Time Differences of Arrival). [Code]
           Consider M recorded signals  xm(t) = am1 s1(t-dm1) + ... + amN sN(t-dmN) , m=1,...,M, that consists of linear combinations of unknown delayed source signals sn(t), n=1,...,N, where dmn is the
           propagation delay between source n and sensor m. The purpose is to:
           1- estimate the propagation delays relative to the reference sensor mref (TDOAs):  
dmn(rel)  =   dmn  -  dmref n 
           2- estimate the scaling factors relative to the reference sensor:  amn(rel)  =  amn / amref n
           3- exploit the TDOAs to localize the sources one by one (estimation of cartesian coordinates).
           Our technique is based on time-frequency analysis and consists of Alternating Least Squares (ALS) updates of the source and channel components interleaved with a Vandermonde structure enforcing
           strategy.


     [3] 
Separation of convolutive mixtures of speech signals. [Code]
          
Consider M recorded signals  xm = conv(hm1 , s1) + conv(hm2 , s2) + ... + conv(hmN , sN) , m=1,...,M, that consists of linear combinations of unknown source signals  sn, n=1,...,N, convolved with
           unknown FIR filters, where
hmn denotes the impulse response of the filter between source n and sensor m. The purpose is to exploit the multiple recordings to estimate the mixing channels, and to
           separate the sources.

           Our method is based on time-frequency analysis and Second-Order-Statistics (SOS) and consists of solving a Joint-Approximate-Diagonalization (JAD) problem independently at  each frequency via 
           Candecomp/Parafac (CP). Once the separation achieved, the frequency-dependent permutation ambiguity is corrected by exploiting properties of speech signals.

 
MIMO Radar (Multiple Input Multiple Output):

     [1]  Parafac-based localization in MIMO radar systems.
[Code]
           Localization of multiple targets in the same range via Candecomp/Parafac (CP) and ULA (Uniform Linear Array) steering vector recovery to estimate the Angle Of Departures (AODs) and Angles Of 
           Arrivals (AOAs). Comparison to Capon-based and to MUSIC-based radar-imaging localization techniques.


  


Publications

PhD. Thesis (in French)
D. Nion, Méthodes PARAFAC généralisées pour l'extraction aveugle de sources. Applications aux systèmes CDMA, Université de Cergy-Pontoise, october 2007. [pdf] [bibtex] [slides]

Journal Papers

[7]
D. Nion, A Tensor Framework for Non-Unitary Joint Block Diagonalization, IEEE Trans. on Signal Processing, Vol. 59, No.10, pp. 4585-4594, Oct. 2011. [pdf] [bibtex] [M-code]

[6] D. Nion and N. D. Sidiropoulos, Tensor Algebra and Multi-dimensional Harmonic Retrieval in Signal Processing for MIMO Radar, IEEE Trans. on Signal Processing, Vol. 58, No. 11, pp. 5693-5705, Nov. 2010. [pdf] [bibtex] [M-code]
[5] D. Nion, K. N. Mokios, N. D. Sidiropoulos and A. Potamianos, Batch and Adaptive PARAFAC-based Blind Separation of Convolutive Speech Mixtures, IEEE Trans. on Audio, Speech and Language Processing, Vol. 18, No. 6, pp. 1193-1207, August 2010. [pdf] [bibtex] [Audio Demo] [M-code]

[4] D. Nion and N. D. Sidiropoulos, Adaptive Algorithms to Track the PARAFAC decomposition of a Third-Order Tensor, IEEE Trans. on Signal Processing, Vol. 57, No. 6, pp. 2299-2310, June 2009. [pdf] [bibtex] [M-code]
[3] D. Nion and L. De Lathauwer, A Block-Component Model Based Blind DS-CDMA Receiver, IEEE Trans. on Signal Processing, Vol. 56, No. 11, pp. 5567-5579, Nov. 2008. [pdf] [bibtex]
[2] L. De Lathauwer and D. Nion, Decompositions of a Higher-Order Tensor in Block Terms - Part III: Alternating Least Squares Algorithms, SIAM Journal on Matrix Analysis and Applications (SIMAX), Vol. 30, No. 3, pp. 1067-1083, Sept 2008. [pdf] [bibtex] [M-code]
Companion papers:
Part I [pdf] [bibtex] and Part II [pdf] [bibtex]

[1] D. Nion and L. De Lathauwer, An Enhanced Line Search Scheme for Complex-Valued Tensor Decompositions. Application in DS-CDMA, Elsevier Signal Processing, Vol. 88, Issue 3, pp. 749-755, March 2008. [pdf] [bibtex] [M-code]


International Conferences with Proceedings

[8] D. Nion, B. Vandewoestyne, S. Vanaverbeke, K. Van Den Abeele, H. De Gersem and L. De Lathauwer, A time-frequency technique for blind separation and localization of pure delayed sources, Proc. LVA/ICA 2010, St. Malo, France,
Sept. 27-30, 2010. [pdf] [bibtex] [poster] [M-code]
[7] D. Nion and L. De Lathauwer, A link between the decomposition of a third-order tensor in rank-(L,L,1) terms and joint block diagonalization, Proc. CAMSAP 2009, Aruba, Dutch Antilles, 2009. [pdf]

[6] D. Nion and N. D. Sidiropoulos, A PARAFAC-Based Technique for Detection and Localization of Multiple Targets in a MIMO Radar System, Proc. IEEE International Conference on Acoustics, Speech & Signal Processing (ICASSP), pp. 2077-2080, Taipei, Taiwan, 2009. [pdf] [bibtex] [slides] [M-code]
[5] D. Nion and L. De Lathauwer,  Blind Receivers based on Tensor Decompositions. Application in DS-CDMA and over-sampled systems, Proc. 41th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, November 4-7, 2007. [pdf] [bibtex] [slides]
[4] D. Nion and L. De Lathauwer,  A Tensor-Based Blind DS-CDMA Receiver Using Simultaneous Matrix Diagonalization, Proc. IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Helsinki, Finland, June 17-20, 2007. [pdf] [bibtex] [poster]

[3] D. Nion and L. De Lathauwer,  Levenberg-Marquardt computation of the Block Factor Model for blind multi-user access in wireless communications, Proc. 14th European Signal Processing Conference (EUSIPCO), Florence, Italy, Sept. 4-8, 2006. [pdf] [bibtex] [slides]

[2] D. Nion and L. De Lathauwer,  Line Search computation of the Block Factor Model for blind multi-user access in wireless communications, Proc. IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC), Cannes, France, July 2-5, 2006. [pdf] [bibtex] [poster]
[1] D. Nion and L. De Lathauwer,  A Block Factor Analysis based receiver for blind multi-user access in wireless communications, Proc. IEEE International Conference on Acoustics, Speech & Signal Processing (ICASSP), Toulouse, France, May 15-19, 2006. [pdf] [bibtex] [poster]


National Conferences

[1] D. Nion and L. De Lathauwer,
Séparation et Egalisation aveugles de signaux CDMA par la décomposition en blocs d'un tenseur au moyen de l'algorithme de Levenberg-Marquardt, XXIème colloque GRETSI, Troyes, France, September 11-14, 2007. [pdf]




Invited talks and International conferences without proceedings

[6] D. Nion and L. De Lathauwer, The Joint Block Diagonalization (JBD) problem: a tensor framework, Workshop on Tensor Decompositions and Applications (TDA), Monopoli, Italy, Sept. 13-17, 2010. [pdf]

[5] D. Nion and L. De Lathauwer, Decomposing a Third-Order Tensor in rank-(L,L,1) terms by Means of Simultaneous Matrix Diagonalization, SIAM Conference on Applied Linear Algebra, Monterey, California, USA, October 26th-29th, 2009. [slides]

[4] D. Nion and L. De Lathauwer, Block Component Decompositions of a Tensor: Definition, Computation and Uniqueness, SIAM annual meeting, Denver, Colorado, USA, July 6th-8th 2009.

[3] D. Nion and L. De Lathauwer, The Decomposition of a Third-Order Tensor in R Block-Terms of rank-(L,L,1): Model, Algorithms, Uniqueness, Estimation of R and L, Three-way methods in Chemistry and Psychology (TRICAP) meeting, Nurià, Spain, June 14th-19th, 2009. [slides]

[2] D. Nion, Tensor Decompositions: Models, Applications, Algorithms, Uniqueness, seminar, I3S Laboratory, Sophia-Antipolis, France, December 11th 2008. [slides]

[1]  D. Nion and L. De Lathauwer, Generalized PARAFAC decompositions for blind multi-user access in wireless communications, Workshop on Tensor Decompositions and Applications (WTDA), Luminy, Marseille, France, Aug. 29th - Sept. 2nd, 2005.

       

Links
[1] PARAFAC. Tutorial and Applications. [here] or [here]. This tutorial is an excellent way to get familiar with the PARAFAC decomposition.
[2] Matlab code for PARAFAC, from KVL university website. 
[here]
[3] The Three-Mode Company. A company devoted to creating three-mode software and promoting three-mode data analysis.
[here]
[4] A list of online available codes for Blind Source Separation. Check [here] and  [here].

A non-exhaustive list of researchers' homepages involved in Multi-Way Analysis:

- Lieven De Lathauwer's homepage
- Nicholas D. Sidiropoulos' homepage
- Pierre Comon's homepage
- Rasmus Bro's homepage
- Richard A. Harshman's homepage
- Pieter M. Kroonenberg's homepage
- Henk A. L. Kier's homepage
- Alwin Stegeman's homepage
- André L. F. de Almeida's homepage
- Alex O. Vasilescu's homepage
- Martin Haardt's homepage
- Tamara G. Kolda's homepage
- Brett W. Bader's homepage