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Instructor:
Prof.
Gene
Cheung
Lectures: T/R
8:30-10:00
Location:
VH
1020
Announcement
- 08/31/2023: Note location change to VH 1020!
- 08/27/2023: Course outline available on
eClass.
- 08/11/2023: Course homepage online.
Course
Summary
Fundamental 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.
Required
Textbook
- R. Gonzalez, R. Woods, Digital
Image Processing (4th Edition), Pearson
Education Limited, 2018.
Supplementary
Material
-
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,
Introduction
to Graph Signal Processing, Cambridge
University Press, 2022. (available in Amazon HERE)
- G. Cheung,
E. Magli, Graph
Spectral Image Processing,
Wiley-ISTE, 2021. (available in Amazon HERE)
- S. Boyd, L. Vandenberghe, Introduction
to Applied Linear Algebra: Vectors, Matrices,
and Least Squares, Cambridge
University Press, 2018.
Key
References
- 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.
-
M.
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.
-
E.
Candes,
X. Li, Y. Ma, J. Wright, "Robust
Principal Component Analysis?"
vol. 58, no. 3, article 11, Journal of
the ACM, May 2011.
-
S.
Boyd
et al., "Distributed Optimization and
Statistical Learning via the Alternating
Direction Method of Multipliers," Foundation
and Trends in Machine Learning, vol.
3, no. 1, January 2011, pp.1-122.
-
N.
Parikh
and S. Boyd, "Proximal Algorithms,"
Foundations and Trends in Optimization,
vol. 1, no. 3, 2013, pp. 127-239.
- J.
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.
- A.
Ortega
et al., "Graph
Signal Processing: Overview, Challenges,
and Applications," Proceedings
of the IEEE, vol. 106, no.5, May
2018, pp. 808-828.
- G.
Cheung
et al., "Graph
Spectral Image Processing," Proceedings of
the IEEE, vol. 106, no. 5, May
2018, pp. 907-930.
-
W.
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.
-
J.
Pang,
G. Cheung, "Graph Laplacian
Regularization for Image Denoising:
Analysis in the Continuous Domain,"
IEEE Transactions on Image Processing,
vol. 26, no.4, April, 2017, pp. 1770-1785.
(arXiv)
Evaluation
- Bi-weekly assignments (40%)
- Midterm (30%)
- Course project (30%)
Course
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 Signal Representations I
- Week 6: Reading Week
- Week 7: Sparse Signal Representations II
- Week 8: Low-Rank Representations
- Week 9: Image Compression
- Week 10: Image Denoising
- Week 11: Graph Spectral Image Compression
- Week 12: Graph Spectral Image Restoration
- Week 13: Graph-based 3D Point Cloud Processing
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last modified September 5, 2023
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