| Overview: |
Hilbert space formulation of continuous-time and discrete-time signals. Sampling. Orthogonal and biorthogonal signal expansions. Uncertainty principles and the time-frequency plane. Two-channel filter banks, iterated filter banks, and discrete wavelet transforms. Multiresolution analysis. Wavelet bases, regularity, approximation properties, and nonlinear approximation. Basics of quantization and source coding. Compression, denoising, and other image processing using wavelets. Advanced topics from the current research literature. |
| Projects: |
Several term projects from the past two offerings of the course have been very successful. With additional work, they have led to papers and theses. These include (list still under construction):
- Generalized Regular Sampling of Trigonometric Polynomials and Optimal Sensor Arrangement
A. Deshpande, S. E. Sarma, and V. K. Goyal, IEEE Signal Processing Letters, vol. 14, no. 4, pp. 379-382, April 2010.
- Beyond Thresholding: Analysis and Improvements for Deterministic Parameter Estimation
B. I. Erkmen and V. K. Goyal, arXiv:0801.3490, 23 Jan 2008.
- Estimation of Channelized Features in Geological Media Using Sparsity Constraints
Behnam Jafarpour, S.M. thesis, February 2008.
- Reconstruction of Channelized Facies Using Sparsity Constraints
B. Jafarpour, V. K. Goyal, and W. T. Freeman, Proc. Soc. Exploration Geophysicists Annual Meeting (Las Vegas, NV), November 2008, pp. 1546-1550.
- Transform-Domain Sparsity Regularization for Inverse Problems in Geosciences
B. Jafarpour, V. K. Goyal, D. B. McLaughlin, and W. T. Freeman, Geophysics, vol. 74, no. 5, pp. R69-R83, September-October 2009.
- Generalizations of Permutation Source Codes
Ha Quy Nguyen, S.M. thesis, September 2009.
- Frame Permutation Quantization
H. Q. Nguyen, V. K. Goyal, and L. R. Varshney, Proc. Conf. Information Sciences & Systems (Princeton, NJ), March 2010.
- Frame Permutation Quantization
H. Q. Nguyen, V. K. Goyal, and L. R. Varshney, Applied and Computational Harmonic Analysis, to appear in vol. 30, 2011.
- Estimating Signals with Finite Rate of Innovation from Noisy Samples: A Stochastic Algorithm
V. F. Y. Tan and V. K. Goyal, IEEE Trans. on Signal Processing, vol. 56, no. 10, pp. 5135-5146, October 2008.
- On the Construction of Invertible Filter Banks on the 2-Sphere
B. T. T. Yeo, W. Ou and P. Golland, IEEE Trans. on Image Processing, vol. 17, no. 3, pp. 283-300, March 2008.
- Denoising Hyperspectral Imagery and Recovering Junk Bands using Wavelets and Sparse Approximation
A. C. Zelinski, V. K. Goyal, Proc. IEEE Int. Geoscience and Remote Sensing Symp. (IGARSS) (Denver, CO), August 2006, pp. 387-390.
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