The lectures for ``Beyond Wavelets'' were given May 22-26 at University of Missouri, St. Louis, and again June 13-17 at Royal Institute of Technology, Stockholm

The development and presentation of these lectures was sponsored by the National Science Foundation CBMS Lecture Series program.

The lectures are available as Acrobat Files (.pdf)

Lecture 1: Finding Hidden Components By Data Analysis

Lecture 2: Finding Hidden Components by Mathematical Analysis

Lecture 3: Ridgelets-I: Ridgelets and Ridge Functions

Lecture 4: Ridgelets-II: Ridgelets and Linear Singularities

Lecture 5: Ridgelets-III: Algorithms and Generalizations

Lecture 6: Curvelets-I: Curvelets and Curvilinear Singularities

Lecture 7: Curvelets-II: Curvelets and Curvilinear Integrals

Lecture 8: Curvelets-III: Curvelets and Linear Inverse Problems

Lecture 9: Beamlets

Lecture 10: Multiple Bases

Reading List

Overall Resources:

• A Wavelet Tour of Signal Processing. Stephane Mallat. 1998. Academic Press.
• Wavelets: Algorithms and Applications. Y. Meyer. 1993. SIAM.
• About Wavelab. DLD and Ofer Levi.
• Adapted Wavelet Analysis: Theory and Algorithms. Wickerhauser M. V. 1993. A.K. Peters.
• B. Wandell:

Lecture 1: Hidden Components By Data Analysis

• Nature vs. Math: Interpreting Independent Components Analysis in lightof Computational Harmonic Analysis. DLD.
• Sparse Coding with an Overcomplete Basis Set: A Strategy Employed by V1? Olshausen B.A., Field D.J. 1998. Vision Research. 37. 3311-3325.
• Independent Component Analysis of Natural Image Sequences Yields Spatiotemproal Filters Similar to Simple Cells in Primary Visual Cortex. Van Hateren J.H., Ruderman D.L. 1998. Proceedings Royal Society of London. 265.
• Independent Component Filters of Natural Images Compared with simple Cells in the Primary Visual Cortex. Van Hateren J. H., Van der Scharf A. 1998. Proceedings Royal Society of London. 265. 359-366.
• Could Information Theory Provide an Ecological Theory of Sensory Processing? Atick J.J. 1992. Network, 213-251.
• The Statistics of Natural Images. Ruderman D.L. 1993. Network, 4, 517-548.
• Independent Component Analysis by Minimization of Mutual Information. Hyvarinen A. 1997. Hensinki University of Technology. Report A46.

Lecture 2: Hidden Components by Mathematical Analysis

• Data Compression and Harmonic Analysis DLD, Vetterli M., DeVore R.A., and Daubechies I. 1998. IEEE Trans. Information Theory. 6, 2435-2476.
• Sparse Components Analysis and Optimal Atomic Decomposition. DLD.
• Unconditional Bases are Optimal Bases for Data Compression and Statistical Estimation. DLD
• Counting Bits with Kolmogorov and Shannon. DLD

Lecture 3: Ridgelets-I: Ridgelets and Ridge Functions

• Optimal Reconstruction of a Function from its Projections. Logan B.F., and Shepp L.A. 1975. Duke Mathematical Journal. 42. no. 4, 645-659.
• Projection Pursuit Regression. Friedman J., and Stuetzle W. 1981. Journal of the American Statistical Association. 76. 817-823.
• Ridgelets: Theory and Applications. Candes E. 1998. PhD. Thesis, Department of Statistics, Stanford University.
• Ridgelets: Key to Intermittency in Higher Dimensions? Candes E., DLD 1999. Proceedings Royal Society of London.
• Orthonormal Ridgelets and Linear Singularities. DLD 1998.
• Ridge Functions and Orthonormal Ridgelets. DLD 1998.

Lecture 4: Ridgelets-II: Ridgelets and Linear Singularities

• Orthonormal Ridgelets and Linear Singularities. DLD 1998.
• Ridge Functions and Orthonormal Ridgelets. DLD 1998.

Lecture 5: Ridgelets-III: Algorithms and Generalizations

• Fast Ridgelet Transform Via Rectopolar Coordinate . DLD
• Ridgelet Packets. Averbuch A., DLD, Hel Or, H, and Hel Or Y.
• Polar FFT, Rectopolar FFT, and Applications. Averbuch A., Coifman R., DLD, Israeli, and Walden.
• Tight Frames of k-plane Ridgelets and the Problem of Representing Singularities of Dimension $d$ in R^n. DLD 1998.

Lecture 6: Curvelets-I: Curvelets and Curvilinear Singularities

• Curvelets: A Surprisingly Effective Nonadaptive Representation of Objects with Edges. Candès E, and DLD.
• Curvelets and Curvilinear Integrals. Candès E., and DLD.
• Digital Curvelet Transform. DLD, and Duncan M. 1999.

Lecture 7: Curvelets-II: Curvelets and Curvilinear Integrals

• Edge-Preserving Reconstruction in Ill-posed Inverse Problems: Optimality of Curvelet Frames. Candes E.,and DLD.

Lecture 8: Curvelets-III: Curvelets and Linear Inverse Problems

• Edge-Preserving Reconstruction in Ill-posed Inverse Problems: Optimality of Curvelet Frames. Candes E.,and DLD.

Lecture 9: Beamlets-I

• Wedgelets: Nearly-Minimax Estimation of Edges. DLD.

Lecture 10: Multiple Bases

• Atomic Decomposition by Basis Pursuit. Chen S, DLD, and Saunders.
• Uncertainty Principles and Ideal Atomic Decomposition. DLD and Huo X.
• Matching Pursuits in a Time-Frequency Dictionary. Mallat S. and Zhang S. Dec. 1993. IEEE Transactions on Signal Processing

Updated Aug 9 2000 by dld