The principal objective of this course is to expose the necessary mathematical and computational methods to design novel digital imaging systems, bridge the gap between optical 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, traditional display and acquisition systems, and image processing. We will then focus on modern approaches based on advanced numerical harmonic analysis and optimization methods to design image sensing technologies with applications in 3D geometry capture, inverse scattering, spectroscopy, sparse image recovery, medical imaging, imaging, computer vision and pattern recognition. The teaching will be based on a split between theory and practice, allowing the students to get hands 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
• Process and compute signals from/to cameras and display systems
• Process, reconstruct and restore digital images
• Design advanced and efficient imaging systems for a wide range of applications
• 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

The course consists of six parts:

1. Review of Fourier methods and wave physics for optical imaging
2. Image processing, display and acquisition technologies
3. Spectroscopy
4. Harmonic analysis methods for imaging
5. Sparse recovery, image reconstruction, inverse problems and compressive imaging
6. Statistical learning and deep learning for image analysis

We will start from reviewing Fourier analysis and wave imaging for optical imaging, and their underlying mathematical theories. Thereafter imaging methods based on coherence of waves, diffraction or polarization will be addressed.
We will then discuss image processing, with an emphasis on denoising and edge preservation, and describe the functional principles of display and sensing device like cameras and related sensors technologies (CMOS, CCD). In this part of the course, we will also tackle the problem of high dynamic range images, in both acquisition and display applications.
After the review of fundamental of imaging and Fourier methods, we will address spectroscopy in both its physical and imaging concepts.
The last part 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 this part, we will learn to recover data or physical properties from sparse measurements, reconstruct and restore images, design novel spectral imagers, and perform automated image analysis as facial recognition or AI aided medical diagnosis. 08. juli, 2020