CS 754 - Advanced Image Processing

Course content
  • 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
  • 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
  • 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 onSignal Processing, and IEEE Transactions on Pattern Analysis and Machine Intelligence:
  • "Natural Image Statistics" by Aapo Hyvarinen, Jarmo Hurri and Patrick Hoyer,Springer Verlag 2009 (http://www.naturalimagestatistics.net/ - freely downloadable online)
  • "A Mathematical Introduction to Compressive Sensing" by Simon Foucart andHolger Rauhut, Birkhauser,2013 (http://www.springer.com/us/book/9780817649470)
  • Fung, Y. C.: Biomechanics: Mechanical Properties of Living Tissues. 2nd Ed., Springer.
  • R. Kamm and M. K. Mofrad. Cytoskeletal Mechanics: Models and Measurements. Cambridge University Press.
Pre-requisite : N/A
Total credits : 6 credits - Lecture
Type : Core Course
Duration : Full Semester
Name(s) of other Academic units to whom the course may be relevant : N/A