- 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 |