Text Reference |
We will extensively refer to the following textbooks, besides a number of research papers
from journals such as IEEE Transactions on Image Processing, IEEE Transactions on
Signal Processing, and IEEE Transactions on Pattern Analysis and Machine Intelligence:
1. "Natural Image Statistics" by Aapo Hyvarinen, Jarmo Hurri and Patrick Hoyer,
Springer Verlag 2009 (h ttp://www.naturalimagestatistics.net/ - freely
downloadable online)
2. "A Mathematical Introduction to Compressive Sensing" by Simon Foucart and
Holger Rauhut, Birkhauser,2013 ( http://www.springer.com/us/book/9780817649470) |
Description |
(1) Image transforms and statistics of natural images
● survey of statistical properties of image transform coefficients
● implications of these statistics for important image processing applications such as
denoising, compression, source separation, deblurring and image forensics
● non-local self-similarity in images
(2) Dictionary learning and sparse representations in image processing
● Overview of Principal Components Analysis (PCA), Singular Value Decomposition
(SVD) and Independent Components Analysis (ICA); PCA, SVD and ICA in the context of
image processing
● Sparse PCA
● Concept of overcomplete dictionaries
● Greedy pursuit algorithms: matching pursuit (MP), orthogonal matching pursuit (OMP)
and basis pursuit (BP)
● Popular dictionary learning techniques: Method of Optimal Directions (MOD), Unions of
Orthonormal Bases, K-SVD, Non-negative sparse coding – along with applications in
image compression, denoising, inpainting and deblurring
● Sparsity-seeking algorithms: iterative shrinkage and thresholding (ISTA)
(3) Compressed Sensing (CS)
● Concept and need for CS
● Theoretical treatment: concept of coherence, null-space property and restricted
isometry property, proof of a key theorem in CS
● Algorithms for CS (covered in part 2) and some key properties of these algorithms
● Applications of CS: Rice Single Pixel Camera and its variants, Video compressed
sensing, Color and Hyperspectral CS, Applications in Magnetic Resonance Imaging (MRI),
Implications for Computed Tomography
● CS under Forward Model Perturbations: a few key results and their proofs as well as
applications
● Designing Forward Models for CS
● Low-rank matrix estimation and Robust Principal Components Analysis: concept and
application scenarios in image processing, statement of some key theorems, and proof of
one important theorem |