- 12/20/2019: Course homepage online.
image processing theories and algorithms. Signal representation using
transforms, wavelets and frames is overviewed. Signal reconstruction
methods using total variation, sparse coding and low-rank prior, based
on convex optimization, are discussed. Applications include image
compression, restoration and enhancement. Prior background in digital
signal processing (EECS 4452 or equivalent) and numerical linear
algebra is strongly recommended.
- R. Gonzalez, R. Woods, Digital Image Processing (4th
Edition), Pearson Education Limited, 2018.
M. Vetterli, J. Kovacevic, V. Goyal, Foundations of Signal Processing,
Cambridge University Press, 2014. (also available online HERE)
- M. Elad, Sparse
and Redundant Representations, Springer, 2010.
- A. Ortega, Graph
Signal Processing: An Introduction, to be published by Cambridge
University Press, 2020.
- S. Boyd, L. Vandenberghe, Introduction to Applied Linear Algebra:
Vectors, Matrices, and Least Squares, Cambridge University
- A. Beck, M. Teboulle, "Fast Gradient-Based Algorithms for
Constrained Total Variation Image Denoising and Deblurring," IEEE Transactions on Image Processing,
vol. 18, no. 11, November 2009, pp. 2419-2434.
Aharon, M. Elad, A. Bruckstein, "K-SVD:
An Algorithm for designing
overcomplete sparse representation," IEEE Transactions on Signal
Processing, vol. 54, no. 11, Nov. 2006, pp. 4311-4322.
Candes, X. Li, Y. Ma, J.
Wright, "Robust Principal Component Analysis?"
vol. 58, no. 3, article 11, Journal of the ACM, May 2011.
Boyd et al., "Distributed
Optimization and Statistical Learning via the Alternating Direction
Multipliers," Foundation and Trends in Machine Learning,
3, no. 1, January 2011, pp.1-122.
Parikh and S. Boyd, "Proximal Algorithms," Foundations and
Trends in Optimization, vol. 1, no. 3, 2013, pp. 127-239.
Han, A. Saxena, V. Melkote, K. Rose, "Jointly
Optimized Spatial Prediction and Block Transform for Video and Image
Coding," IEEE Transactions on
Image Processing, vol.21, no.4, April 2012, pp. 1874--1884.
Ortega et al., "Graph Signal
Processing: Overview, Challenges, and Applications," Proceedings of the IEEE, vol. 106,
no.5, May 2018, pp. 808-828.
Cheung et al., "Graph Spectral Image
Processing," Proceedings of
the IEEE, vol. 106, no. 5, May 2018, pp. 907-930.
Hu, G. Cheung, A. Ortega,
O. Au, "Multiresolution Graph Fourier Transform for Compression of
Piecewise Smooth Images," IEEE Transactions on Image Processing,
vol.24, no.1, pp.419-433, January 2015.
Pang, G. Cheung, "Graph
Laplacian Regularization for Image Denoising: Analysis in the
IEEE Transactions on Image Processing,
vol. 26, no.4, April, 2017, pp.
- Bi-weekly assignments (40%)
- Midterm (30%)
- Course project (30%)
Outline (subject to change)
- Week 1: Linear Algebra Review
- Week 2: Inner-product, Hilbert Space
- Week 3: Image Analysis: Transforms
- Week 4: Image Analysis: Wavelets
- Week 5: Sparse / Low-Rank Signal Representations
- Week 6: Image / Video Compression
- Week 7: Image Restoration: Denoising and
- Week 8: Graph Spectral Image Compression
- Week 9: Graph Spectral Image Processing
- Week 10: Graph-based 3D Point Cloud Processing
- Week 11: Graph Neural Networks for Image
last modified March 5, 2020