| TSBB06 |
Multidimensional Signal Analysis, 6 ECTS credits.
/Multidimensionell signalanalys/
For:
BME
D
I
Ii
IT
MED
MMAT
U
Y
|
| |
Prel. scheduled
hours: 68
Rec. self-study hours: 92
|
| |
Area of Education: Technology
Main field of studies: Electrical Engineering
|
| |
Advancement level
(G1, G2, A): A
|
|
Aim:
Passing the course means that the student is able to use concepts and methods in signal and image processing that are based on linear algebra. The student is then able to:
- Use homogeneous coordinates for the Euclidean geometry of two and three dimensions. This includes points and lines in two dimensions, points, planes, and lines in three dimensions, homographies and camera projections.
- Estimate geometric objects based on various types of least sqaures techniques.
- Use linear representations: bases, subspace bases, and frames for signals.
- Apply linear signal representations on practical problems, such as filter optimization, normalized convolution, over-sampling, PCA, wavelet-transform and filter banks.
|
|
Prerequisites: (valid for students admitted to programmes within which the course is offered)
Basic Linear Algebra: vector spaces, bases, scalar product, least squares problem, eigenvalue problems. Basic signal processing (corresponding to Linear Systems): sampling, convolution and Fourier transform of one-variable signals. Basic skills in Matlab is recommended.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
|
|
Supplementary courses:
Computer Vision, Image and Audio Coding, Medical Image Analysis, Neural Networks and Learning Systems, Image Sensors
|
|
Organisation:
The course has lectures that present basic concepts and theory, accompanied by lessons that exemplify some of the calculations. In a set of mandatory computer exercises, each participant must demonstrate the ability to carry out more complex calculation and answer related questions. The course runs over the entire autumn semester.
|
|
Course contents:
Signal spaces and signal bases, dual bases. Least squares problem, filteroptimering, normalized convolution. Eigenvalue and singular value analysis. Principal component analysis. Frames. Wavelet transform and filterbanks. Projective spaces, homogeneous coordinates, homographies, camera projections. Representation and estimation of various types of geometric objects.
|
|
Course literature:
The compendium Introduction to Representations and Estimation in Geometry, Klas Nordberg, covers the geometry part of the course. A supplementary compendium Prerequisites for studies at advanced level in Image Science at Linköping University describes prerequisites for the course. In addition to these, articles and exerpts from book and compendiums are used, in accordance with the course information at the start of the course.
|
|
Examination: |
|
Written examination
Laboratory work
Optional test
|
3 ECTS
3 ECTS
0 ECTS
|
| |
|
The written examination is divided into four parts that correspond to the four course objectives, and in order to pass the examination a certain level is required for each of the four parts. A failed examination can be completed if at least three of the parts are passed and if it is done as specified in the current course information.
The optional test covers the first half of the course and its result can be used in the first written examination after the course.
Some assignments of the laboratory work may include a small written exam that must be passed by the student before the rest of the assignment can be completed. |
Course language is Swedish/English.
Department offering the course: ISY.
Director of Studies: Klas Nordberg
Examiner: Klas Nordberg
Link to the course homepage at the department
Course Syllabus in Swedish
|