1-Explore the structure of images at "patch" level.

(Patches are small image extracts that are  processed in computational neural networks and in recent image processing.  The current dimension that  start being well  understood is about  8x8=64 to 60x60=3600)

2-Apply it to a fundamental problem requiring an understanding of this structure: image denoising

3-Compare image processing designed  by humans to image processing learned by deep neural  networks

This course addresses one  of the fundamental problems of  signal and image processing, the  separation  of noise and  signal.  This was  already the  key problem of  Shannon's foundational Mathematical  Theory of  Communication.  Ever since, this problem is recurring  and has uncountable applications for image formation,  image and video post-production,  and  feature detection.  Since the 70s, several denoising approaches have been identified and can be grouped in a handful of useful 'denoising principles' with notable progress.

Yet,  in 2016,  neural denoisers have started outperforming  (slightly) human made  denoising  algorithms. Their principles are quite different. Human  algorithms adopt mathematical principles to denoise and  stick  by them.  Neural algorithms are  fully pragmatic and learn jointly noise and  image structure from large collections of images. The inner workings of these learned denoising networks are not yet fully understood. 

This course organized by three image processing specialists and  deep learning  practitioners stands at this crucial crossroad.  We  will explain the  classical theories,  the neural devices and demonstrate what perspectives and  cross-fertilization  this comparison  yields.  Both theories process image patches.  The course  will be  designed to understand in depth patch structure and  the  structure  of  the  global ensemble  of  patches.

elementary probability, Fourier, differential calculus

Deep learning  will be  introduced from scratch