Welcome to Dr. Dimitri Nion's
homepage
Last
update: october 2010
|
Matlab codes |
[1] A non-linear conjugate gradient algorithm for Non-Unitary Joint Block Diagonalization (JBD) and Joint Diagonalization (JD). [Link]
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). [Link]
CP model fitted via the Alternating Least Squares (ALS) algorithm coupled with line search.
[2] Block Component Decompositions (BCD). [Link]
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. [Link]
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). [Link]
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. [Link]
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. [Link]
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). [Link]
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. [Link]
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. [Link]
Given Anew = Aold
Blind source separation (BSS):
[1] Separation of linear instantaneous mixtures via Second-Order-Statistics (SOS) and Candecomp/Parafac.
[Link 1] A user-friendly matlab interface to illustrate the BSS problem with speech mixtures of 2 or 3 sources (Useful for a quick demo).
[Link 2] Matlab code for an arbitrary number of sources and sensors.
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). [Link]
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. [Link]
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. [Link]
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) |
|
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.