Harmonic Analysis for Signal Processing, Spring 2011 Harmonic Analysis and Signal Processing, Spring 2011, Resources

Harmonic Analysis and Signal Processing, Spring 2011, Resources


The following is a (partial) list of resources for the material in the course.


E. Prestini, The Evolution of Applied Harmonic Analysis, 2004. (amazon)

N. Young, An Introduction to Hilbert Space, 1988. (amazon)

  1. H.Feichtinger, T. Strohmer (eds.), Gabor Analysis and Algorithms, 1998 (amazon)

S. Mallat, A Wavelet Tour of Signal Processing, 3rd ed, 2008. (amazon)

I. Daubechies, Ten Lectures on Wavelets, 1992 (amazon)

C. S. Burrus, R. A. Gopinath, H. Guo, Introduction to Wavelets and Wavelet Transforms: A Primer, 1998. (amazon)

Papers, Manuscripts, and Notes

Bases and Frames

  1. J.Kovacevic and A. Chebira, “Life Beyond Bases: The Advent of Frames (Part I)”, 2007. (pdf)

J. Kovacevic and A. Chebira, “Life Beyond Bases: The Advent of Frames (Part II)”, 2007.

C. Heil, “A Basis Theory Primer,” 1988. (notes) (pdf)

I. Daubechies, A. Grossman, Y. Meyer, “Painless nonorthogonal expansions,” 1986. (pdf)

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis”, 1990                      (pdf)

J. R. Shewchuk, “An introduction to the conjugate gradient method without the agonizing pain,” 1994. (notes) (pdf)

H. Malvar, “The LOT: Transform Coding Without Blocking Effects,” 1989. (pdf)

Approximation Theory and Algorithms

R. DeVore, “Nonlinear Approximation,” 1998. (mathscinet)

R. DeVore, B. Jawerth, B. Lucier, “Image compression through wavelet transform coding,” 1992. (pdf)

R. Coifman, M. Wickerhauser, “Entropy-based algorithms for best basis selection, ” 1992. (pdf)

S. Chen, D. Donoho, M. Saunders, “Atomic decomposition by basis pursuit,” 1999. (pdf)

Statistical Estimation and Data Compression

D. Donoho, M. Vetterli, R. DeVore, I. Daubechies, “Data compression and harmonic analysis,” 1998. (pdf)

E. Candes, “Modern statistical estimation via oracle inequalities,” 2006. (pdf)

D. Donoho, “Unconditional bases are optimal bases for data compression and for statistical estimation,” 1993. (pdf)

I. Johnstone, “Function estimation and Gaussian sequence models,” 2002. (notes) (pdf)

Geometrical Representations for Images

E. Candes, D. Donoho, “New tight frames of curvelets and optimal representations of objects with piecewise C^2 singularities,” 2004. (pdf)

M. Do, M. Vetterli, “The contourlet transform: an efficient directional multiresolution image representation,” 2005. (pdf)

E. Le Pennec, S. Mallat, “Sparse geometric image representations with bandelets,” 2005. (pdf)

D. Donoho, “Wedgelets: nearly minimax estimation of edges,” 2001. (mathscinet)

M. Wakin, J. Romberg, H. Choi, R. Baraniuk, “Wavelet-domain approximation and compression of piecewise-smooth images,” 2006. (pdf)

  1. A.Cohen, N. Dyn, B. Matei, “Quasilinear subdivision schemes with applications to ENO interpolation,” 2003. (mathscinet)

Sparse Approximation and Compressive Sensing

  1. D.Donoho, P. Stark, “Uncertainty principles and signal recovery,” 1989. (pdf)

  1. D.Donoho, X. Huo, “Uncertainty principles and ideal atomic decomposition,” 2001. (pdf)

  1. M.Elad, A. Bruckstein, “A generalized uncertainty principles and sparse representations in pairs of R^N bases.” 2002. (pdf)

  1. R.Gribonval, M Nielson, “Sparse representations in unions of bases,” 2003. (pdf)

J. Tropp, “Just Relax: Convex programming methods for identifying sparse signals in noise,” 2006. (pdf)

E. Candes, J. Romberg, T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” 2006 (pdf).

E. Candes, J. Romberg, “Quantitative robust uncertainty principles and optimally sparse decompositions,” 2006 (pdf).

  1. E.Candes, T. Tao, “Near-optimal signal recovery from random projections: Universal encoding strategies?,” 2006 (pdf).

  1. D.Donoho, “Compressed Sensing,” 2006 (pdf).

  1. E.Candes, J. Romberg, T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” 2006 (pdf).

  1. J.Tropp, A. Gilbert, “Signal recovery from partial information via orthogonal matching pursuit,” 2007 (pdf).

  1. E.Candes, J. Romberg, “Sparsity and Incoherence in Compressive Sampling,” 2007 (pdf).

R. Baraniuk, M. Davenport, R. DeVore, and M. Wakin, “A simple proof of the restricted isometry property for random matrices,” 2008 (pdf).

M. Rudelson and R. Vershynin, “On sparse reconstruction from Fourier and Gaussian measurements,” 2008 (pdf).

  1. J.Romberg, “Compressive sensing by random convolution,” 2009 (pdf).

CS Theory Lecture Notes by E. Candes, 2007

CS Tutorial at ITA 2008 by Baraniuk, Romberg, and Wakin