Image and signal processing of a digital camera; principles of image sensors; shot noise, read noise, dark current, and fixed pattern noise; statistical analysis of the noise; Gaussian and Poisson distributions; estimation techniques; maximum-likelihood estimation, maximum-a-posteriori estimation, minimum mean square estimation; formal definition of denoising; patch reoccurrence and nonlocal techniques; kernel regression, symmetric smoothing filters, and graph denoisers; total variation regularizations; fundamental limit of denoising; weak signals and the photon limit; variance stabilizing transforms; motion estimation under noise; noise estimation.
Week 1. Digital cameras in the 21st Century. CMOS and CCD image sensors
Week 2. Noise in image sensors: Read noise, shot noise, dark current, pixel response non-uniformity.
Week 3. Gaussian statistics: Single-variate and multivariate Gaussians. Central Limit Theorem.
Week 4. Poisson statistics: Poisson processes, and photon arrivals
Week 5. Principles of maximum-likelihood estimation
Week 6. Principles of maximum-a-posteriori estimation
Week 7. Principles of minimum mean square estimation
Week 8. Optimization techniques for solving estimation problems
Week 9. Patch reoccurrence and non-local techniques: Non-local means, BM3D, bilateral filter
Week 10. Variance stabilization for Poisson noise reduction
Week 11. How to estimate the noise level?
Week 12. Fundamental limit of noise removal
Week 13. Handling moving scenes
Week 14. Learning-based methods
Week 15. Generalization and beyond