__Hyperspectral____ Image Processing__

Hyperspectral
images are now available for a wide range of applications: monitoring, mapping
or helping with disaster management. A major challenge lies in the interpretation
of these images, a task which is referred to in computer science as the
classification of images. For each pixel, we are provided with a set of
intensities, one for each bandwidth. These intensities are somehow related to
the surface reflectance and hence to the type of land cover or of land use. And
instead of being able to model precisely this extremely complex relationship
between intensities and interpretation, the scientific literature provides an
abundance of techniques to capture information from the data themselves with
the help of the ground truth. These lectures aim at describing some of these
techniques: what are their objectives, what kind of information they use, how
reliable are their predictions? To study these techniques, we will consider toy
examples, sometimes get involved in the mathematical technicalities and
sometimes consider simple algorithms. Some ideas developed in these lectures
come from textbooks for university students, many others stem from research
papers and related questions. I would expect these lectures to help getting
more familiar with how proposed techniques are described in research papers.
Throughout these lectures we will consider in the context of binary
classification of hyperspectral images the following
issues: learning regarded as an optimization problem, can we be positive about
machine learning predictions, why is there a need for some strange concepts? If
we have enough time, we will consider spatial issues, how we may take advantage
of knowing which pixel is near which or deal with subpixel
issues.

Notebook (only started) with in appendix, all
exercises and all Octave/Matlab
code to yield the displayed figures in the slides

Slides used during
the lecture

__First lecture (27th of April 2023)__

Link to video HIP_lesson_1.mp4

__Second lecture (4 ^{th} of May 2023)__

__Third lecture (5 ^{th} of May 2023)__

__Fourth lecture (8 ^{th} of May 2023)__

Regarding triangular decompositions,
in the literature there seems to be three different ideas: A=LU where L is a
lower triangular matrix and U is an upper. This is obtained with the Gauss
algorithm with the objective of solving linear systems. A=LL’ with L a lower
matrix for A symmetric and positive, it aims at quickly solving linear systems
and has applications for some matrix equations but it cannot be derived or used
to yield the eigenvalue decomposition problem. Last,
there is the QR decomposition where Q is a orthogonal
matrix and R is triangular matrix. It also aims at solving quickly linear
systems. It can be used to get the SVD decomposition. However there are many
variations with specificities regarding the numerical complexity, the stability
of the computations, the kind of matrices to which it applies and different kinds
of applications. For research applications, I have used the last one not the
two first ones.

This is my mail Gabriel.dauphin@univ-paris13.fr
(please mention HIP in the subject of emails).

GABRIEL
DAUPHIN