Pierre Vandergheynst
EPFL STI IEL LTS2
ELE 235 (Bâtiment ELE)
Station 11
1015 Lausanne
+41 21 693 56 45
+41 21 693 26 01
Office:
ELE 235
EPFL
>
STI
>
IEM
>
LTS2
Web site: Web site: https://lts2.epfl.ch/
EPFL STI IEM LTS2
ELD 241 (Bâtiment ELD)
Station 11
1015 Lausanne
+41 21 693 56 45
Office:
ELE 235
EPFL
>
VPA-AVP-DLE
>
AVP-DLE-EDOC
>
EDCB-GE
Web site: Web site: https://go.epfl.ch/phd-edcb
Fields of expertise
data science
machine learning
computational harmonic analysis
inverse problems
compressive sensing
computer vision
machine learning
computational harmonic analysis
inverse problems
compressive sensing
computer vision
Mission
Data nowadays come in overwhelming volume. In order to cope with this deluge, we explore and use the benefits of geometry and symmetry in higher dimensional data. But volume is not the only problem: data models are also increasingly complex, mixing various components. We thus use redundant dictionaries as a dimensionality reduction tool to dig out information from complicated high-dimensional datasets and multichannel signals, or to model complex behaviours in more classical signals. Finally data can also be complex because they are collected on surfaces, or more generally manifolds, or because they are not scalar-valued. We thus explore extensions of Computational Harmonic Analysis in higher dimensions, in complex geometries or for non-scalar data.Visit our lab web pages.
Biography
Pierre Vandergheynst received the M.S. degree in physics and the Ph.D. degree in mathematicalphysics from the Université catholique de Louvain, Louvain-la-Neuve, Belgium, in 1995 and 1998, respectively. From 1998 to 2001, he was a Postdoctoral Researcher with the Signal Processing Laboratory, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland. He was Assistant Professor at EPFL (2002-2007), where he is now a Full Professor of Electrical Engineering and, by courtesy, of Computer and Communication Sciences. As of 2015, Prof. Vandergheynst serves as EPFL’s Vice-Provost for Education.
His research focuses on harmonic analysis, sparse approximations and mathematical data processing in general with applications covering signal, image and high dimensional data processing, computer vision, machine learning, data science and graph-based data processing.
He was co-Editor-in-Chief of Signal Processing (2002-2006), Associate Editor of the IEEE Transactions on Signal Processing (2007-2011), the flagship journal of the signal processing community and currently serves as Associate Editor of Computer Vision and Image Understanding and SIAM Imaging Sciences. He has been on the Technical Committee of various conferences, serves on the steering committee of the SPARS workshop and was co-General Chairman of the EUSIPCO 2008 conference.
Pierre Vandergheynst is the author or co-author of more than 70 journal papers, one monograph and several book chapters. He has received two IEEE best paper awards. Professor Vandergheynst is a laureate of the Apple 2007 ARTS award and of the 2009-2010 De Boelpaepe prize of the Royal Academy of Sciences of Belgium.
Awards
2023 : IEEE SIGNAL PROCESSING MAGAZINE BEST PAPER AWARD : IEEE
2022 : Signal Processing Society Best Paper Award : IEEE
Publications
Infoscience publications
Recent publications (2009-present)
Interpreting and comparing neural activity across systems by geometric deep learning
NATURE METHODS. 2025. DOI : 10.1038/s41592-024-02581-3.MARBLE: interpretable representations of neural population dynamics using geometric deep learning
Nature methods. 2025. DOI : 10.1038/s41592-024-02582-2.Graph rewiring for long range-aware protein learning
38th Annual Conference on Neural Information Processing Systems, Vancouver Convention Center, Canada, 2024-12-10 - 2024-12-15.Exploring “dark-matter” protein folds using deep learning
Cell systems. 2024. DOI : 10.1016/j.cels.2024.09.006.Graph learning for capturing long-range dependencies in protein structures
2024. Machine Learning for Computational Biology, Seattle, 2024-09-05 - 2024-09-06.Molecular set representation learning
Nature Machine Intelligence. 2024. DOI : 10.1038/s42256-024-00856-0.Beyond fine-tuning: LoRA modules boost near-OOD detection and LLM security
2024. ICLR 2024 Workshop on Secure and Trustworthy Large Language Model, Vienna, Austria, May 11, 2024.Safe Deep Neural Networks
Lausanne, EPFL, 2024. DOI : 10.5075/epfl-thesis-10384.Beyond fine-tuning: LoRA modules boost near-OOD detection and LLM security
2024. 7th Deep Learning Security and Privacy Workshop, San Francisco, CA, May 23, 2024.Infusing structured knowledge priors in neural models for sample-efficient symbolic reasoning
Lausanne, EPFL, 2024. DOI : 10.5075/epfl-thesis-10642.Towards improving full-length ribosome density prediction by bridging sequence and graph-based representations
2024. 19th Machine Learning in Computational Biology meeting, Seattle, WA, USA, 2024-09-05 - 2024-09-06.Interpretable Inflammation Landscape of Circulating Immune cells
2023Probabilistic methods for neural combinatorial optimization
Lausanne, EPFL, 2023. DOI : 10.5075/epfl-thesis-10221.Interpretable statistical representations of neural population dynamics and geometry
arXiv. 2023. DOI : 10.48550/arxiv.2304.03376.Finding information-rich electrocardiographic biomarkers to characterize atrial fibrillation
Lausanne, EPFL, 2023. DOI : 10.5075/epfl-thesis-10284.RosettaSurf-A surface-centric computational design approach
Plos Computational Biology. 2022. DOI : 10.1371/journal.pcbi.1009178.Plasma-based Electroacoustic Actuator for Broadband Sound Absorption
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-9784.Leveraging topology, geometry, and symmetries for efficient Machine Learning
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-7398.Auditory externalization of a remote microphone signal
Lausanne, EPFL, 2022. DOI : 10.5075/epfl-thesis-8959.Generalised Implicit Neural Representations
2022. 36th Conference on Neural Information Processing Systems (NeurIPS 2022), New Orleans, Louisiana, USA, November 28 - December 9, 2022.Representation Learning for Multi-relational Data
Lausanne, EPFL, 2021. DOI : 10.5075/epfl-thesis-8654.Sound Field Reconstruction in a room through Sparse Recovery and its application in Room Modal Equalization
Lausanne, EPFL, 2021. DOI : 10.5075/epfl-thesis-8394.Musical Source Separation
2020Social Network Architectures of Disinformation
2020On the Experimental Transferability of Spectral Graph Convolutional Networks
2020Geometric deep learning for medium-range weather prediction
2020What is Trending on Wikipedia? Capturing Trends and Language Biases Across Wikipedia Editions
2020. The Web Conference 2020, Taipei, Taiwan, April 20-24, 2020. DOI : 10.1145/3366424.3383567.On Vacuous and Non-Vacuous Generalization Bounds for Deep Neural Networks.
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7437.Sparse and Parametric Modeling with Applications to Acoustics and Audio
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7215.Dynamic pattern recognition in large-scale graphs with applications to social networks
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7633.On the optimal sampling design for the Graph Total Variation decoder: recovering piecewise-constant graph signals from a few vertex measurements
Lausanne, EPFL, 2020. DOI : 10.5075/epfl-thesis-7219.Fourier could be a data scientist: From graph Fourier transform to signal processing on graphs
Comptes Rendus Physique. 2019. DOI : 10.1016/j.crhy.2019.08.003.Spherical Convolutionnal Neural Networks: Empirical Analysis of SCNNs
2019A Graph-structured Dataset for Wikipedia Research
2019. Companion Proceedings of the 2019 World Wide Web Conference (WWW '19 Companion), San Francisco, CA, USA, May 13-17, 2019. DOI : 10.1145/3308560.3316757.Learning Representations of Source Code from Structure and Context
2019Graph Laplacians for Rotation Equivariant Convolutional Neural Networks
2019Tensor Robust Pca On Graphs
2019. 44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, ENGLAND, May 12-17, 2019. p. 5406 - 5410. DOI : 10.1109/ICASSP.2019.8682990.Anomaly detection in the dynamics of web and social networks
2019. The Web Conference 2019, San Francisco, California, USA, May 13-17, 2019. p. 1290 - 1299. DOI : 10.1145/3308558.3313541.Spectrally approximating large graphs with smaller graphs
2018. International Conference in Machine Learning (ICML), Stockholmsmässan, Sweden, July 10-15, 2018.Joint Estimation Of The Room Geometry And Modes With Compressed Sensing
2018. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, CANADA, Apr 15-20, 2018. p. 6882 - 6886. DOI : 10.1109/ICASSP.2018.8462655.Graph Signal Processing: Overview, Challenges and Applications
Proceedings of the IEEE. 2018. DOI : 10.1109/JPROC.2018.2820126.Random sampling of bandlimited signals on graphs
Applied and Computational Harmonic Analysis. 2018. DOI : 10.1016/j.acha.2016.05.005.Computational Thinking and Thinking Computationally
Dia-logos, Ramon Llull's Method of Thought and Artistic Practice; Minneapolis: University of Minnesota Press, 2018.Fast Approximate Spectral Clustering for Dynamic Networks
2018. International Conference in Machine Learning (ICML), Stockholmsmässan, Sweden, July 10-15, 2018.Robust and Efficient Data Clustering with Signal Processing on Graphs
Lausanne, EPFL, 2018. DOI : 10.5075/epfl-thesis-8184.Global and Local Uncertainty Principles for Signals on Graphs
APSIPA Transactions on Signal and Information Processing. 2018. DOI : 10.1017/ATSIP.2018.2.Distributed Signal Processing via Chebyshev Polynomial Approximation
IEEE Transactions on Signal and Information Processing over Networks. 2018. DOI : 10.1109/TSIPN.2018.2824239.FMA: A Dataset For Music Analysis
2017. 18th International Society for Music Information Retrieval Conference, Suzhou, China, October 23-28, 2017.Scalable Low-rank Matrix and Tensor Decomposition on Graphs
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7958.Stationary signal processing on graphs
IEEE Transactions on Signal Processing. 2017. DOI : 10.1109/Tsp.2017.2690388.Localization of Sound Sources in a Room with One Microphone
2017. Wavelets and Sparsity XVII, San Diego, California, USA, August 6-9, 2017. DOI : 10.1117/12.2271249.Compressive Embedding and Visualization using Graphs
2017Graph-based structures in data science : fundamental limits and applications to machine learning
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7644.Geometric deep learning: going beyond Euclidean data
IEEE Signal Processing Magazine. 2017. DOI : 10.1109/Msp.2017.2693418.Graph-based Methods for Visualization and Clustering
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7952.Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems
Neuroimage. 2017. DOI : 10.1016/j.neuroimage.2017.04.015.From recommender systems to spatio-temporal dynamics with network science
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7428.Towards Stationary Time-Vertex Signal Processing
2017. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), New Orleans, LA, MAR 05-09, 2017. p. 3914 - 3918. DOI : 10.1109/ICASSP.2017.7952890.Structured Sequence Modeling with Graph Convolutional Recurrent Networks
2017.Locating Temporal Functional Dynamics of Visual Short-Term Memory Binding using Graph Modular Dirichlet Energy
Scientific Reports. 2017. DOI : 10.1038/srep42013.System, device, and method for contextual knowledge retrieval and display
WO2017187401 . 2017.Graph Based Sinogram Denoising for Tomographic Reconstructions
2016.PCA using graph total variation
2016. 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shanghai, China, 20-25 March 2016. p. 4668 - 4672. DOI : 10.1109/ICASSP.2016.7472562.Learning Laplacian Matrix in Smooth Graph Signal Representations
IEEE Transactions on Signal Processing. 2016. DOI : 10.1109/TSP.2016.2602809.Low-Rank Matrices on Graphs: Generalized Recovery & Applications
2016Room Modal Equalisation with Electroacoustic Absorbers
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7166.Multilinear Low-Rank Tensors on Graphs & Applications
2016.Vertex-Frequency Analysis on Graphs
Applied And Computational Harmonic Analysis. 2016. DOI : 10.1016/j.acha.2015.02.005.Song Recommendation with Non-Negative Matrix Factorization and Graph Total Variation
2016. 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shanghai, China, March 20-25. p. 2439 - 2443. DOI : 10.1109/ICASSP.2016.7472115.Fast Robust PCA on Graphs
IEEE Journal of Selected Topics in Signal Processing. 2016. DOI : 10.1109/Jstsp.2016.2555239.From data to structures : graph learning under smoothness assumptions and applications in data science
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7302.An Algorithm Architecture Co-Design for CMOS Compressive High Dynamic Range Imaging
Ieee Transactions On Computational Imaging. 2016. DOI : 10.1109/Tci.2016.2557073.Source Localization on Graphs via l1 Recovery and Spectral Graph Theory
2016. 12th IEEE Image, Video, and Multidimensional Signal Processing (IVMSP) Workshop 2016, Bordeaux, France, July 11-12, 2016. DOI : 10.1109/IVMSPW.2016.7528230.Compressive Spectral Clustering
2016. 33rd International Conference on Machine Learning (ICML), New York, USA, June 19-24. p. 1002 - 1011.Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering
2016. Advances in Neural Information Processing Systems 29, Barcelona, Spain, December 5-10, 2016.Compressed Sensing and Adaptive Graph Total Variation for Tomographic Reconstructions
2016A Multiscale Pyramid Transform for Graph Signals
IEEE Transactions on Signal Processing. 2016. DOI : 10.1109/TSP.2015.2512529.Localisation et identification spectrale conjointe de sources large bande par parcimonie groupée
2016. Congrès Français d'Acoustique, Le Mans, France, April 2016.Principal Patterns on Graphs: Discovering Coherent Structures in Datasets
IEEE Transactions on Signal and Information Processing over Networks. 2016. DOI : 10.1109/TSIPN.2016.2524500.Tensor low-rank and sparse light field photography
Computer Vision And Image Understanding. 2016. DOI : 10.1016/j.cviu.2015.11.004.Accelerated Spectral Clustering Using Graph Filtering of Random Signals
2016. 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016), Shanghai, China. p. 4094 - 4098. DOI : 10.1109/ICASSP.2016.7472447.Spatial hearing rendering in wireless microphone systems for binaural hearing aids
Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7221.Compressive PCA for Low-Rank Matrices on Graphs
Ieee Transactions On Signal And Information Processing Over Networks. 2016. DOI : 10.1109/Tsipn.2016.2631890.MATHICSE Technical Report : Accelerated filtering on graphs using Lanczos method
2015Ultra-low-power ECG front-end design based on compressed sensing
2015. 2015 Design, Automation and Test in Europe Conference (DATE ‘15), Grenoble, France, March 9-13, 2015. p. 671 - 676. DOI : 10.7873/DATE.2015.1098.Structure Modeling of High Dimensional Data : New Algorithms and Applications
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6590.A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method
2015. 10th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Hong Kong, PEOPLES R CHINA, JAN 13-16, 2015. p. 350 - 363. DOI : 10.1007/978-3-319-14612-6_26.Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
IEEE Transactions on Signal Processing. 2015. DOI : 10.1109/Tsp.2015.2424203.ShapeNet: Convolutional Neural Networks on Non-Euclidean Manifolds
2015.Learning class-specific descriptors for deformable shapes using localized spectral convolutional networks
Computer Graphics Forum. 2015. DOI : 10.1111/cgf.12693.Structured Auto-Encoder with application to Music Genre Recognition
2015Robust Principal Component Analysis on Graphs
2015. International Conference on Computer Vision (ICCV) 2015, Santiago, Chile, December 11-18, 2015. p. 2812 - 2820. DOI : 10.1109/ICCV.2015.322.Laplacian Matrix Learning for Smooth Graph Signal Representation
2015. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brisbane, Australia, April, 2015. p. 3736 - 3740. DOI : 10.1109/ICASSP.2015.7178669.Exploring information retrieval using image sparse representations : from circuit designs and acquisition processes to specific reconstruction algorithms
Lausanne, EPFL, 2015. DOI : 10.5075/epfl-thesis-6587.Accelerated filtering on graphs using Lanczos method
2015Graph-based denoising for time-varying point clouds
2015. 3DTV Conference 2015, Lisbon, Portugal, July 8-10, 2015. DOI : 10.1109/3DTV.2015.7169366.Enhanced Matrix Completion with Manifold Learning
International BASP Frontiers Workshop 2015, Villars-sur-Ollon, Switzerland, January 25 - 30, 2015.Mapping resting-state dynamics on spatio-temporal graphs: a combined functional and diffusion MRI approach
2015. 23rd International Symposium on Magnetic Resonance in Medicine (ISMRM), Toronto.Random sampling of bandlimited signals on graphs
2015Random Sampling of Bandlimited Signals on Graphs
NIPS2015 Workshop on Multiresolution Methods for Large Scale Learning, Montréal, December 12th, 2015.Dynamic activation patterns in brain MRI data
2015. 25th Colloque Gretsi, Lyon.Graph-based Image Inpainting
2014Robust image reconstruction from multi-view measurements
SIAM Journal on Imaging Sciences. 2014. DOI : 10.1137/120902586.On spin scale-discretised wavelets on the sphere for the analysis of CMB polarisation
2014. p. 64 - 67. DOI : 10.1017/S1743921314011107.Matrix Completion on Graphs
2014. Neural Information Processing Systems 2014, Workshop "Out of the Box: Robustness in High Dimension", Montreal, Canada, December 8-13, 2014.Numerical experiments with MALDI Imaging data
Advances In Computational Mathematics. 2014. DOI : 10.1007/s10444-013-9325-0.Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds
IEEE Transactions on Signal Processing. 2014. DOI : 10.1109/TSP.2013.2295553.Matrix Completion on Graphs
UCL - Duke Workshop on Sensing and Analysis of High-Dimensional Data (SAHD 2014), London, England, September 4-5, 2014.Ultra low power design of hardware efficient CS-Based compression scheme in WBSN
2014. CT-Energy Community Workshop, Barcelona, Spain, April 23-25, 2014.A Compressed Sensing Framework for Magnetic Resonance Fingerprinting
Siam Journal On Imaging Sciences. 2014. DOI : 10.1137/130947246.Compressed Quantitative MRI: Bloch Response Recovery through iterated projection
2014. IEEE International Conference on Accoustics, Speech and Signal Processing (ICASSP), Florence, Italy. DOI : 10.1109/ICASSP.2014.6854937.Robust Real-time Pedestrians Detection in Urban Environments with a Network of Low Resolution Cameras
Transportation Research Part C: Emerging Technologies. 2014. DOI : 10.1016/j.trc.2013.11.019.Compressed sensing : a universal energy-efficient compression scheme for biosignals on wireless body sensor nodes
Lausanne, EPFL, 2014. DOI : 10.5075/epfl-thesis-6340.Audio Steganography using Convex Demixing
2014Multi-View Signal Processing and Learning on Graphs
Lausanne, EPFL, 2014. DOI : 10.5075/epfl-thesis-6213.Compact Low-Power Cortical Recording Architecture for Compressive Multichannel Data Acquisition
IEEE Transactions on Biomedical Circuits and Systems. 2014. DOI : 10.1109/TBCAS.2014.2304582.A Convex Solution to Disparity Estimation from Light Fields via the Primal-Dual Method
2014. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Hong Kong, China.Approximate Compressed Sensing: Ultra-Low Power Biosignal Processing via Aggressive Voltage Scaling on a Hybrid Memory Multi-core Processor
2014. International Symposium on Low Power Electronics and Design (ISLPED 2014), La Jolla, California, USA, August 11-13, 2014. p. 40 - 45. DOI : 10.1145/2627369.2627629.From Bits to Images: Inversion of Local Binary Descriptors
IEEE Transactions on Pattern Analysis and Machine Intelligence. 2014. DOI : 10.1109/TPAMI.2013.228.Efficient compressive sampling strategies and novel reconstruction methods with applications in MRI
Lausanne, EPFL, 2014. DOI : 10.5075/epfl-thesis-6036.Robust Image Reconstruction from Multiview Measurements
Siam Journal On Imaging Sciences. 2014. DOI : 10.1137/120902586.Hardware-Software Inexactness in Noise-aware Design of Low-Power Body Sensor Nodes
2014. Designing with Uncertainty - Opportunities & Challenges, York, United Kingdom, March 17-19 , 2014.Reverberant Audio Source Separation via Sparse and Low-Rank Modeling
IEEE Signal Processing Letters. 2014. DOI : 10.1109/LSP.2014.2303135.Robust visual tracking using feature selection
2014Power-Efficient Joint Compressed Sensing of Multi-Lead ECG Signals
2014. 39th International Conference on Acoustics, Speech and Signal Processing (ICASSP 2014), Florence, Italy, May 5-9 2014. p. 4409 - 4412. DOI : 10.1109/ICASSP.2014.6854435.System and method for media library navigation and recommendation
WO2014002064 . 2014.Joint image registration and reconstruction from compressed multi-view measurements
2013. Conference on Wavelets and Sparsity XV. DOI : 10.1117/12.2023916.Interconnected Network of Cameras
2013. IS&T/SPIE Electronic Imaging, Burlingame, California, USA, February 3, 2013. DOI : 10.1117/12.2004736.S2LET: A code to perform fast wavelet analysis on the sphere
Astronomy & Astrophysics. 2013. DOI : 10.1051/0004-6361/201220729.compressive source separation for hyperspectral imaging
2013Power-Efficient CMOS Image Acquisition System based on Compressive Sampling
2013. 56th IEEE International Midwest Symposium on Circuits and Systems, Columbus, Ohio, USA, August 4-7, 2013. p. 1367 - 1370. DOI : 10.1109/MWSCAS.2013.6674910.Non-convex optimization for robust multi-view imaging
International Biomedical and Astronomical Signal Processing (BASP) Frontiers workshop, Villars-sur-Ollon, Switzerland, January, 2013.The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
IEEE Signal Processing Magazine. 2013. DOI : 10.1109/Msp.2012.2235192.Clustering on Multi-Layer Graphs via Subspace Analysis on Grassmann Manifolds
2013. IEEE Global Conference on Signal and Information Processing, Austin, Texas, USA, December 3-5, 2013. p. 993 - 996. DOI : 10.1109/GlobalSIP.2013.6737060.On the Sparsity of Wavelet Coefficients for Signals on Graphs
2013. Conference on Wavelets and Sparsity XV. DOI : 10.1117/12.2022850.Inference of Mobility Patterns via Spectral Graph Wavelets
2013. IEEE ICASSP, Vancouver, Canada, May 26-31, 2013. p. 3118 - 3122. DOI : 10.1109/ICASSP.2013.6638232.On the computation of directional scale-discretized wavelet transforms on the sphere
2013. Wavelets and Sparsity XV, San Diego, August 26-29, 2013. DOI : 10.1117/12.2022889.Patch-based methods for variational image processing problems
Lausanne, EPFL, 2013. DOI : 10.5075/epfl-thesis-5693.Compressive Source Separation: Theory and Methods for Hyperspectral Imaging
IEEE Transactions on Image Processing. 2013. DOI : 10.1109/Tip.2013.2281405.Column-Separated Compressive Sampling Scheme for Low Power CMOS Image Sensors
2013. 11th IEEE International New Circuits and Systems (NEWCAS) Conference, Paris, France, June 16-19, 2013. DOI : 10.1109/NEWCAS.2013.6573620.The PANOPTIC Camera: A Plenoptic Sensor with Real-Time Omnidirectional Capability
Journal of Signal Processing Systems for Signal, Image and Video Technology. 2013. DOI : 10.1007/s11265-012-0668-4.Sparse Reverberant Audio Source Separation via Reweighted Analysis
IEEE Transactions on Audio Speech and Language Processing. 2013. DOI : 10.1109/Tasl.2013.2250962.Sparse Binary Features for Image Classification
2013Sparse image reconstruction on the sphere: implications of a new sampling theorem
IEEE Transactions on Image Processing. 2013. DOI : 10.1109/TIP.2013.2249079.Joint Low-rank and Sparse Light Field Modeling for Dense Multiview Data Compression
2013. ICASSP. p. 3831 - 3835. DOI : 10.1109/ICASSP.2013.6638375.Joint reconstruction of misaligned images from incomplete measurements for cardiac MRI
2013. 10th International Conference on Sampling Theory and Applications (SAMPTA), Bremen, Germany, July 2013.Non-convex optimization for robust multi-view imaging
2013. International Biomedical and Astronomical Signal Processing (BASP) Frontiers workshop, Villars-sur-Ollon, Switzerland, January, 2013.High Frame-Rate Low-Power Compressive Sampling CMOS Image Sensor Architecture
23rd Great Lakes Symposium on VLSI, Paris, France, May 2-3, 2013.Compressive Image Acquisition in Modern CMOS IC Design
International Journal of Circuit Theory and Applications. 2013. DOI : 10.1002/cta.1969.Traitement du signal sur les graphes
2013 GRETSI Symposium, Brest, France, September 3-6, 2013.Image reconstruction of non-planar scenes from compressed multi-view measurements
2013. Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS 2013), Lausanne, 2013.Multichannel Blind Deconvolution Using Low-rank and Sparse Decomposition
2013. SPARS, 2013.Compressive Multichannel Cortical Signal Recording
2013. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Vancouver, Canada, May 26-31, 2013. p. 4305 - 4309. DOI : 10.1109/ICASSP.2013.6638472.Method to compensate the effect of the rolling shutter effect
US8350922 ; US2011267514 . 2013.Robust joint reconstruction of misaligned images using semi-parametric dictionaries
ICML Workshop on Sparsity, Dictionaries and Projections in Machine Learning and Signal Processing, Edinburgh, June 30, 2012.Compressive Sampling Strategies for Multichannel Signals : Theory and Applications
Lausanne, EPFL, 2012. DOI : 10.5075/epfl-thesis-5378.Design and Exploration of Low-Power Analog to Information Conversion Based on Compressed Sensing
IEEE Journal of Emerging and Selected Topics in Circuits and Systems. 2012. DOI : 10.1109/JETCAS.2012.2220253.A Real-time Multi-camera System with Omnidirectional Image Reconstruction Capability
ICCP2012, Seattle, WA, USA, April 27-29, 2012.Robust joint reconstruction of misaligned images using semi-parametric dictionaries
Workshop on Sparsity, Localization and Dictionary Learning, London, June 26, 2012.Robust joint reconstruction of misaligned images using semi-parametric dictionaries
2012. ICML Workshop on Sparsity, Dictionaries and Projections in Machine Learning and Signal Processing, Edinburgh, Scotland, June 30, 2012.Sparse Approximation Using M-Term Pursuit and Application in Image and Video Coding
IEEE Transactions on Image Processing. 2012. DOI : 10.1109/TIP.2011.2181525.Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices
2012Analyse de données en grande dimension sur graphes et réseaux
Journée Mathématiques et Grandes Dimensions, Polytech Lyon, December 10, 2012.Joint trace/TV norm minimization: A new efficient approach for spectral compressive imaging
2012. IEEE International Conference on Image Processing (ICIP 2012). p. 933 - 936. DOI : 10.1109/ICIP.2012.6467014.Foreground Silhouette Extraction robust to Sudden Changes of background Appearance
2012. IEEE International conference on Image Processing, Orlando, Florida, USA, September 30 - October 3, 2012. DOI : 10.1109/ICIP.2012.6467088.Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques
EURASIP Journal on Advances in Signal Processing. 2012. DOI : 10.1186/1687-6180-2012-6.Plenoptic Spherical Sampling
2012. 2012 IEEE International Conference on Image Processing, Disney Coronado Springs Resort, Florida, USA, September 30, October 3, 2012. p. 357 - 360. DOI : 10.1109/ICIP.2012.6466869.FREAK: Fast Retina Keypoint
2012. IEEE Conference on Computer Vision and Pattern Recognition, Rhode Island, Providence, USA, June 16-21, 2012. p. 510 - 517. DOI : 10.1109/CVPR.2012.6247715.Light Field Compressive Sensing
2012. 1st International Traveling Workshop for Interacting Sparse Models and Technology, Marseille, France.Compressed Sensing of Simultaneous Low-Rank and Joint-Sparse Matrices
2012Spread spectrum magnetic resonance imaging
IEEE Transactions on Medical Imaging. 2012. DOI : 10.1109/TMI.2011.2173698.Beyond Bits: Reconstructing Images from Local Binary Descriptors
2012. 21st International Conference on Pattern Recognition (ICPR), Tsukuba Science City, Japan, November 11-15, 2012. p. 935 - 938.Doubly sparse models for multiple filter estimation in sparse echoic environments
2012Clustering with Multi-Layer Graphs: A Spectral Perspective
IEEE Transactions on Signal Processing. 2012. DOI : 10.1109/Tsp.2012.2212886.SCOOP: A Real-Time Sparsity Driven People Localization Algorithm
Journal Of Mathematical Imaging And Vision. 2012. DOI : 10.1007/s10851-012-0405-4.Audio-Visual Object Extraction using Graph Cuts
2012Light Field Compressive Sensing in Camera Arrays
2012. The 37th International Conference on Acoustics, Speech, and Signal Processing, Kyoto, Japan, March 25 - 30, 2012. p. 5413 - 5416. DOI : 10.1109/ICASSP.2012.6289145.A Windowed Graph Fourier Transform
2012. IEEE Statistical Signal Processing Workshop, Ann Arbor, Michigan, USA, August 5-8, 2012. p. 133 - 136. DOI : 10.1109/SSP.2012.6319640.On localisation and uncertainty measures on graphs
2012Light Field Tensor Recovery
2012. IEEE International Conference on Image Processing, Orlando, Florida, USA.Hyperspectral Image Compressed Sensing Via Low-Rank And Joint-Sparse Matrix Recovery
2012. The 37th International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2012). p. 2741 - 2744. DOI : 10.1109/ICASSP.2012.6288484.Omnidirectional Light Field Analysis and Reconstruction
Lausanne, EPFL, 2012. DOI : 10.5075/epfl-thesis-5483.Image transform for video coding
US8300693 ; US2006159179 . 2012.Automatic online delineation of a multi-lead electrocardiogram bio signal
US2014148714 ; EP2654557 ; WO2012085841 . 2012.Omnidirectional sensor array system
US10362225 ; US2018220070 ; US9876953 ; US2014146132 ; WO2012056437 . 2012.Hardware Implementation of an Omnidirectional Camera with Real-Time 3D Imaging Capability
2011. 3DTV-Conference 2011, Antalya, Turkey, 16-18 May. DOI : 10.1109/3DTV.2011.5877192.Classification via Incoherent Subspaces
Rejecta Mathematica. 2011.Guaranteed recovery of a low-rank and joint-sparse matrix from incomplete and noisy measurements
SPARS11, Edinburgh, UK, June 27-29, 2011.On Variable Density Compressive Sampling
IEEE Signal Processing Letters. 2011. DOI : 10.1109/LSP.2011.2163712.Implications for compressed sensing of a new sampling theorem on the sphere
2011. 4th Workshop on Signal Processing with Adaptive Sparse Structured Representations, Edinburgh, Scotland, 27-30 June, 2011.Wavelets on graphs via spectral graph theory
Applied and Computational Harmonic Analysis. 2011. DOI : 10.1016/j.acha.2010.04.005.Spread Spectrum for Universal Compressive Sampling
2011. 4th Workshop on Signal Processing with Adaptive Sparse Structured Representations, Edinburgh, June 27-30, 2011.Sampling theorems and compressive sensing on the sphere
2011. Conference on Wavelets and Sparsity XIV, San Diego, CA, August 21-25, 2011. DOI : 10.1117/12.893481.Compressed Sensing for Real-Time Energy-Efficient ECG Compression on Wireless Body Sensor Nodes
IEEE Transactions on Biomedical Engineering Bme. 2011. DOI : 10.1109/TBME.2011.2156795.Accelerated MR imaging with spread spectrum encoding
2011. International Society for Magnetic Resonance in Medicine (ISMRM) conference, Montreal, May 7-13, 2011.Chebyshev polynomial approximation for transductive learning on graphs
2011Vision-Based Scene Understanding with Sparsity Promoting Priors
Lausanne, EPFL, 2011. DOI : 10.5075/epfl-thesis-5070.Audio-driven Nonlinear Video Diffusion
2011Unsupervised Extraction of Audio-Visual Objects
2011. IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011. p. 2284 - 2287. DOI : 10.1109/ICASSP.2011.5946938.A Regularization Framework for Mobile Social Network Analysis
2011. International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011. p. 2140 - 2143. DOI : 10.1109/ICASSP.2011.5946750.Guaranteed recovery of a low-rank and joint-sparse matrix from incomplete and noisy measurements (Abstract)
2011. Workshop on Signal Processing with Adaptive Sparse Structured Representations (SPARS11), Edinburgh, UK, June 2011.Audio-Visual Fusion : New Methods and Applications
Lausanne, EPFL, 2011. DOI : 10.5075/epfl-thesis-4962.Hardware Implementation of an Omnidirectional Camera with Real-time 3D Imaging Capability
3DTV 2011, Antalya, Turkey, May 16-18, 2011.Chebyshev Polynomial Approximation for Distributed Signal Processing
2011. IEEE International Conference on Distributed Computing in Sensor Systems (DCOSS), Barcelona, Spain, June 27-29, 2011. DOI : 10.1109/DCOSS.2011.5982158.A Laplacian pyramid scheme in graph signal processing
2011Structured Sparsity Models for Compressively Sensed Electrocardiogram Signals: A Comparative Study
2011. Biomedical Circuits and Systems Conference (BioCAS), 2011 IEEE, San Diego, CA, USA, November 10-12, 2011. DOI : 10.1109/BioCAS.2011.6107743.Methods for Clustering Multi-Layer Graphs in Mobile Networks
Interdisciplinary Workshop on Information and Decision in Social Networks, MIT, Cambridge, Massachusetts, USA, May 31-June 1, 2011.A Variational Framework for Structure from Motion in Omnidirectional Image Sequences
Journal of Mathematical Imaging and Vision. 2011. DOI : 10.1007/s10851-011-0267-1.Real-Time Compressed Sensing-Based Electrocardiogram Compression on Energy Constrained Wireless Body Sensors
2011. International Symposium on Circuits and Systems (ISCAS'11), Rio de Janeiro, Brazil, May 15 - 18, 2011. p. 1744 - 1747. DOI : 10.1109/ISCAS.2011.5937920.Semi-Supervised Learning with Spectral Graph Wavelets
2011. International Conference on Sampling Theory and Applications (SampTA), Singapore, May 2-6, 2011.Fully non-local super-resolution via spectral hashing
2011. 2011 International Conference on Acoustics, Speech and Signal Processing (ICASSP), Prague, Czech Republic, May 22-27, 2011. p. 1137 - 1140. DOI : 10.1109/ICASSP.2011.5946609.FAST TV-L1 OPTICAL FLOW FOR INTERACTIVITY
2011. IEEE International Conference on Image Processing (ICIP) 2011, Brussels, Belgium, September 11-14, 2011. p. 1885 - 1888. DOI : 10.1109/ICIP.2011.6115836.Scalable Feature Extraction for Coarse-to-Fine JPEG2000 Image Classification
IEEE Transactions on Image Processing. 2011. DOI : 10.1109/TIP.2011.2126584.Sparsity Driven People Localization with a Heterogeneous Network of Cameras
Journal of Mathematical Imaging and Vision. 2011. DOI : 10.1007/s10851-010-0258-7.Fast orthogonal sparse approximation algorithms over local dictionaries
Signal Processing. 2011. DOI : 10.1016/j.sigpro.2011.01.004.Image modeling with nonlocal spectral graph wavelets
Image Processing and Analysing With Graphs: Theory and Practice; CRC Press, 2011.Spread spectrum for interferometric and magnetic resonance imaging
2010. IEEE International Conference on Acoustic, Speech, and Signal Processing (ICASSP), Dallas, March 14–19, 2010. p. 2802 - 2805. DOI : 10.1109/ICASSP.2010.5496198.Audio-based nonlinear video diffusion
2010. IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP), Dallas, March 14-19, 2010. p. 2486 - 2489. DOI : 10.1109/ICASSP.2010.549489.Wavelet transform on manifolds: old and new approaches
Applied and Computational Harmonic Analysis. 2010. DOI : 10.1016/j.acha.2009.10.002.Compressed Sensing: When sparsity meets sampling
Optical and Digital Image Processing - Fundamentals and Applications; Wiley-Blackwell, 2010.Wavelets on the Sphere
Four Short Courses on Harmonic Analysis; Boston: Birkhäuser, 2010. p. 131 - 174.Parallel Spread Spectrum MR Imaging
2010Fast Structure from Motion for Planar Image Sequences
2010. 2010 European Signal Processing Conference, Aalborg, August 23-27 2010.Estimating and Learning the Trajectory of Mobile Phones
2010Multichannel Compressed Sensing via Source Separation for Hyperspectral Images
2010. Eusipco 2010, Aalborg, Denmark, 23-27 August, 2010.Blind Audio-Visual Source Separation based on Sparse Redundant Representations
IEEE Transactions on Multimedia. 2010. DOI : 10.1109/TMM.2010.2050650.An optimal first-order solver for the TV-$L_1$ optical flow problem
2010A (256x256) Pixel 76.7mW CMOS Imager/ Compressor Based on Real-Time In-Pixel Compressive Sensing
2010. IEEE International Symposium on Circuits and Systems (ISCAS), Paris, France, May 30 - June 2, 2010. p. 2956 - 2959. DOI : 10.1109/ISCAS.2010.5538021.Cascade of Descriptors to Detect and Track Objects Across Any Network of Cameras
Computer Vision and Image Understanding. 2010. DOI : 10.1016/j.cviu.2010.01.004.Tracking and Structure from Motion
2010Plenoptic based super-resolution for omnidirectional image sequences
2010. IEEE International Conference on Image Processing (ICIP), Hong Kong, September 26-29, 2010. p. 2829 - 2832. DOI : 10.1109/ICIP.2010.5652095.Stream Carving: an Adaptive Seam Carving Algorithm
2010. International conference on Image Processing, Honk hong, September 26-29, 2010. p. 901 - 904. DOI : 10.1109/ICIP.2010.5653984.Distributed Compressed Sensing of Hyperspectral Images via Blind Source Separation
2010. The Asilomar Conference on Signals, Systems, and Computers, PACIFIC GROVE, CA, USA, November 7-10, 2010. p. 196 - 198. DOI : 10.1109/ACSSC.2010.5757497.Multichannel Compressed Sensing via Source Separation for Hyperspectral Images
Spread spectrum for compressed sensing techniques in magnetic resonance imaging
2010. IEEE International Symp. on Biomedical Imaging: From Nano to macro (ISBI), Rotterdam, April 14-17, 2010. p. 756 - 759. DOI : 10.1109/ISBI.2010.5490066.Compressed sensing reconstruction of a string signal from interferometric observations of the cosmic microwave background
Monthly Notices of the Royal Astronomical Society. 2010. DOI : 10.1111/j.1365-2966.2009.16079.x.Nonnegative Matrix Factorization and Spatial Covariance Model for Under-Determined Reverberant Audio Source Separation
2010. 10th International Conference on Information Sciences, Signal Processing and their applications (ISSPA 2010), Kuala Lumpur , Malaysia, May 10-13, 2010.A union of incoherent spaces model for classification
2010. 35th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Dallas, March 14-19, 2010. p. 5490 - 5493. DOI : 10.1109/ICASSP.2010.5495208.Towards unifying diffusion and exemplar-based inpainting
2010. IEEE International Conference on Image Processing - ICIP 2010, Hong Kong, People's Republic of China, September 26-20, 2010. p. 417 - 420. DOI : 10.1109/ICIP.2010.5653412.Semi-supervised Extraction of Audio-Visual Sources
2010Method and system for automatic objects localization
US2014254875 ; US8749630 ; EP2386981 ; US2011279685 ; EP2386981 . 2010.Compressed sensing for radio interferometry: prior-enhanced Basis Pursuit imaging techniques
2009. SPARS'09, Saint-Malo, April 06-09, 2009.Wavelet domain Bayesian denoising of string signal in the cosmic microwave background
Monthly Notices of the Royal Astronomical Society. 2009. DOI : 10.1111/j.1365-2966.2009.14978.x.A Master-Slave Approach to Detect and Match Objects Across Several Uncalibrated Moving Cameras
2009Sparsity-driven People Localization Algorithm: Evaluation in Crowded Scenes Environments
2009. IEEE International Workshop on Performance Evaluation of Tracking and Surveillance, Snowbird, Utah, December 7-10, 2009. DOI : 10.1109/PETS-WINTER.2009.5399487.TV-Regularized Generation of Planar Images from Omnicams
2009. IEEE International Conference on Image Processing - ICIP 2009, Cairo, Egypt, November 7-11, 2009. DOI : 10.1109/ICIP.2009.5413712.Distributed Compressed Sensing for Sensor Networks Using Thresholding
2009. Wavelet XIII, SPIE, San Diego, CA, USA, August 2-6, 2009. p. 7446 - 50. DOI : 10.1117/12.827880.Cosmic string detection from interferometric data of the microwave background radiation
2009Geometric Video Approximation Using Weighted Matching Pursuit
IEEE Transactions on Image Processing. 2009. DOI : 10.1109/TIP.2009.2021315.CMOS Compressed Imaging by Random Convolution
2009. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Taipei, Taiwan, 19 -24 April 2009. p. 1113 - 1116. DOI : 10.1109/ICASSP.2009.4959783.Sport Players Detection and Tracking With a Mixed Network of Planar and Omnidirectional Cameras
2009. Third ACM/IEEE International Conference on Distributed Smart Cameras, Como, 30 August - 2 September, 2009. DOI : 10.1109/ICDSC.2009.5289406.Optical Flow and Depth from Motion for Omnidirectional Images using a TV-L1 Variational Framework on Graphs
2009. IEEE International Conference on Image Processing - ICIP 2009, Cairo, Egypt, November 7-11, 2009. p. 1469 - 1472. DOI : 10.1109/ICIP.2009.5414552.Compressed sensing for radio interferometry: spread spectrum imaging techniques
2009. WAVELET XIII, SPIE09, San Diego, August 02-06, 2009. DOI : 10.1117/12.824713.Spread spectrum for imaging techniques in radio interferometry
Monthly Notices of the Royal Astronomical Society. 2009. DOI : 10.1111/j.1365-2966.2009.15519.x.Sparsity & [and] dictionaries - algorithms & [and] design
Lausanne, EPFL, 2009. DOI : 10.5075/epfl-thesis-4349.Compressive Sampling of Pulse Trains : Spread the Spectrum !
2009. IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Taipei, Taiwan, 19 -24 April 2009. DOI : 10.1109/ICASSP.2009.4960224.A Sparsity Constrained Inverse Problem to Locate People in a Network of Cameras
2009. 16th International Conference on Digital Signal Processing, Aegean island of Santorini, Greece, July 5-7, 2009. DOI : 10.1109/ICDSP.2009.5201223.A low complexity orthogonal matching pursuit for sparse signal approximation with shift-invariant dictionaries
2009. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP09), Taipei, Taiwan, 2009. p. 3445 - 3448. DOI : 10.1109/ICASSP.2009.4960366.The Panoptic Camera - Plenoptic interpolation in an omnidirectional polydioptric camera
2009Compressed sensing imaging techniques for radio interferometry
Monthly Notices of the Royal Astronomical Society. 2009. DOI : 10.1111/j.1365-2966.2009.14665.x.CMOS Compressed Imaging by Random Convolution
IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Taipei, Taiwan, 19 -24 April 2009.A Variational Framework for Structure from Motion in Omnidirectional Image Sequences
2009Learning bimodal structure in audio-visual data
IEEE Transactions on Neural Networks. 2009. DOI : 10.1109/TNN.2009.2032182.Dictionary learning for the sparse modelling of atrial fibrillation in ECG signals
2009. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP09), Taipei, Taiwan, 2009. p. 465 - 468. DOI : 10.1109/ICASSP.2009.4959621.Method for spatially scalable video coding
US7616824 ; US2006120614 . 2009.Research
Topics
Data nowadays come in overwhelming volume. In order to cope with this deluge, we explore and use the benefits of geometry and symmetry in higher dimensional data. But volume is not the only problem: data models are also increasingly complex, mixing various components. We thus use sparse representations and dictionaries as dimensionality reduction tools to dig out information from complicated high-dimensional datasets and multichannel signals, or to model complex behaviours in more classical signals. Finally data can also be complex because they are collected on surfaces, or more generally manifolds, or because they are not scalar-valued. We thus explore extensions of Computational Harmonic Analysis in higher dimensions, in complex geometries, on graphs, networks or for non-scalar data.Teaching & PhD
Teaching
Electrical and Electronics Engineering
Microengineering
PhD Students
Boulougouri Maria, Guo Pengkang, Haget Anaïs Betsabeh, Hariri Ali, Nallapareddy Mohan Vamsi,Past EPFL PhD Students
Alahi Alexandre Massoud , Atzeni Mattia , Bagnato Luigi , Bayram Eda , Benzi Kirell Maël , Cerqueira Gonzalez Pena Rodrigo , Courtois Gilles André , D'Angelo Emmanuel , Defferrard Michaël , Dong Xiaowen , Golbabaee Mohammad , Grimaldi Vincent Pierre Olivier , Guicquéro William , Hosseini Kamal Mahdad , Jost Philippe , Kalofolias Vasilis , Karalias Nikolaos , Llagostera Casanovas Anna , Mamaghanian Hossein , Martin Lionel Jérémie , Matoba Kyle Michael , Mc Cann Anna Mary , Miz Volodymyr , Paratte Johann , Peic Tukuljac Helena , Perraudin Nathanaël , Pham Vu Thach , Pitas Konstantinos , Puy Gilles , Rivet Etienne Thierry Jean-Luc , Schnass Karin , Sergeev Stanislav , Shahid Nauman ,Courses
Matrix analysis
These lectures are intended as an applied linear algebra course, with a particular focus on providing intuition on the most standard tools. A particular emphasis is put on practice and digital notebooks help getting familiar with the most important concepts.
Signals and systems II (for MT)
This course is an introduction to the theory of discrete linear time invariant systems. Their properties and fundamental characteristics are discussed as well as the fundamental tools that are used to study and design them (Fourier transform, Z transform).
Signals and systems II (for SV)
This course is an introduction to the theory of discrete linear time invariant systems. Their properties and fundamental characteristics are discussed as well as the fundamental tools that are used to study and design them (Fourier transform, Z transform).