The principal objective of this course is to expose the necessary mathematical and computational methods to bridge the gap between optics and image processing, and perform image analysis in the context of computer vision. The course will first cover the fundamental of optical imaging, harmonic analysis, image acquisition systems, and image processing. We will then focus on modern approaches based on advanced numerical harmonic analysis and optimization methods to design image processing systems with applications in 3D geometry capture, inverse scattering, spectroscopy, sparse image recovery, medical imaging, imaging, computer vision and pattern recognition. The teaching will split between theory and exercises, allowing the students to get hands on experience on the taught methods. En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:

• Apply the concepts of Fourier analysis and its relations to optical imaging
• Design efficient computer vision systems and algorithms
• Analyze and process signals from cameras and optical sensors
• Process, reconstruct and restore digital images
• Apply recovery and inverse problems methods in imaging
• Relate the theory of advanced harmonic analysis methods and Compressive Sensing to real world problems
• Use advanced computational and mathematical models to solved imaging based problems
• Recover, analyze and process spectrally resolved data from optical sensors or images
• Retrieve photometric and reflectance quantities from optical sensors or images
• Apply the concepts of artificial intelligence to imaging science and optics

The course consists of five parts:

1. Image processing, image acquisition technologies
2. Spectroscopy and scene analysis
3. Wavelets transform and redundant dictionaries
4. Sparse recovery, image reconstruction, inverse problems and compressive imaging
5. Introduction to Statistical learning and deep learning for image analysis

We will start with image processing basics, with an emphasis on denoising and filtering, and describe the functional principles of sensing devices like cameras and related sensors technologies and hyperspectral imaging.
After the review of fundamental of image processing, we will address imaging spectroscopy with applications in scene analysis.
The second half of the course will be fully dedicated to advanced and novel concepts, grounded in harmonic analysis mathematical optimization, and statistical learning, leveraging limitation of traditional imaging methods that the first part of the course addresses. In a first step, the theory of harmonic analysis, applied to imaging, will be introduced. Then the theoretical foundation of Compressive sensing, sparse and inverse methods, as well as an introduction to artificial intelligence (AI) methods in the context of imaging, will be presented, allowing us to design advanced imaging systems with applications in diverse fields from medical imaging to spectroscopy.
In practice, we will learn to recover data or physical properties from sparse measurements, reconstruct and restore images, and perform automated image analysis as facial recognition or AI aided medical diagnosis. 27. april, 2021