Research seminar in sparsity

Coordinator: Francisco Gómez J PhD.

Research group: Complexus

Class time: Thursday 2:00 to 3:00 pm

email: fagomezj@gmail.com

Seminar description:

Signal acquisition and reconstruction is in the hearth of signal processing. Study of signal representation is a paramount important problem for this discipline. A sparse representation accounts for most information of a signal with an small combination of elementary signals called atoms. The concept of sparsity is the very base of the sucessful of Fourier Wavelet transforms and Singular Value Decomposition. The ideas of sparsity build the foundation of wavelets and have deep conections with the learniability of estimators in machine learning.

In this seminar we are going to study the basis of these representation. In particular, we are going to study seminal work about sparsity, dictionary learning and compressed sensing. We are going to cover also lastest advances in discriminative dictionary learning, co-sparsity and deep learning.

During the seminar we will also to provide some key issues about research: literature review, oral presentation and research work presentation.

Schedule:

Session

Topic

1

Introduction to sparsity and dictionary learning (Francisco Gómez PhD - U. Central)

2

Sparsity algorithms - Matching pursuit (Jorge Victorino MSc - U. Central)

3

Dictionary learning - KSVD algorithm (Jorge Victorino MSc - Francisco Gómez PhD - U. Central)

4

Regression with sparsity - LASSO Algorithm (Roger Guzman Eng., - U. Nacional)

5

Regression with sparsity II - LARS Algorithm (Roger Guzman Eng. - U. Nacional) 

6

Norm inducing sparsity (Javier Guaje Eng - U. Nacional )

7

Feature selection based on nested-leave-one-out cross validation and the Friedman test (Juan Molina - U. Central)

8

Compressed sensing (Jorge Rudas Eng - U. Nacional)

9

Co-sparsity (Hugo Franco PhD - U. Nacional)

 

Material

Dictionary learning: What is the right representation for my signal? Tosic, Ivana; Frossard, Pascal.  Published in: IEEE Signal Processing Magazine (ISSN: 1053-5888), vol. 28, num. 2, p. 27-38 Institute of Electrical and Electronics Engineers, 2011

M. Zibulevsky and M. Elad, L1-L2 Optimization in Signal and Image Processing, IEEE Signal Processing Magazine, Vol. 27 No. 3, Pages 78-88, May 2010.

Compressed Sensing, Sparsity, and Dimensionality in Neuronal Information Processing and Data Analysis Annual Review of Neuroscience. Vol. 35: 485-508 (Volume publication date July 2012) First published online as a Review in Advance on April 5, 2012 DOI: 10.1146/annurev-neuro-062111-150410

The K-SVD: An Algorithm for Designing of Overcomplete Dictionaries for Sparse Representation", M. Aharon, M. Elad, and A.M. Bruckstein, IEEE Trans. on Signal Processing, 2006

Regression Shrinkage and Selection via the Lasso. Robert Tibshirani. Journal of the Royal Statistical Society. Series B. 2003.

Efron Brad, et al. (2004) Least angle regression. Annals of Statistics, 32(2):407-499.

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