AIP (CS 754) by Prof. Ajit Rajwade

  • Lecture Notes

  • This course builds onto Digital Image Processing (CS 663). Modern advancements and recent work (2005-2020) in the field will be surveyed.

  • Relevant areas- ML, Statistics, Signal Processing

  • Processing of 2D images without referring to underlying 3D structure.

  • This course is not about Computer vision, graphics or animation, medical imaging, mathematics, machine learning (although there will be a section on deep neural networks).

  • This course is about Compressed sensing, tomography, learning image representations (dictionary learning, transform learning), statistics of natural images and textures.

  • Low rank Matrix analysis, principal component analysis, recent problems using convolutional neural networks for inverse problems, some analysis of neural networks.

  • Applications of inverse problems: image denoising, image deblurring, image category classification, reflection removal, forensics.

Statistics of Natural images

  • No. of all possible \(200 \times 200\) images is too large: \(256^{40000}\) which is more than the number of atoms in this universe. However only very small percentage are natural images. Knowing the statistics of natural images helps to reduce the feasible region by a huge amount.

  • What are the properties that distinguish natural images? The discrete cosine transform (DCT) has most coefficients close to zero. Similarly wavelet tranform has large magnitude of coefficients at neighbouring sites.

  • DCT is invertible. JPEG algorithm uses DCT.

\[y = \sum_{k=0}^{999} \Psi_k \theta_k\]

Resources