LEARNING OUTCOMES
You will learn to identify an ill-posed inverse problem and to understand the restrictions its nature imposes on the solution process. You will familiarize yourself with several classical regularization methods for finding approximate solutions to linear ill-posed problems. You will learn to formulate an inverse problem as a Bayesian problem of statistical inference and to interpret the information contained in the resulting posterior probability distribution. You will learn to numerically implement the introduced solution techniques.
Credits: 5
Schedule: 28.02.2022 - 08.04.2022
Teacher in charge (valid for whole curriculum period):
Teacher in charge (applies in this implementation): Nuutti Hyvönen, Juha-Pekka Puska
Contact information for the course (applies in this implementation):
Lecturer: Nuutti Hyvönen (first.last@aalto.fi)
Assistant: Juha-Pekka Puska (first.last@aalto.fi)
CEFR level (valid for whole curriculum period):
Language of instruction and studies (applies in this implementation):
Teaching language: English. Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
valid for whole curriculum period:
The course s topic is computational methods for solving inverse problems arising from practical applications. The course consists of two parts: the first three weeks focus on classic regularization techniques, the latter three weeks discuss statistical methods.
applies in this implementation
Assessment Methods and Criteria
valid for whole curriculum period:
Teaching methods: lectures, exercises and home exam.
Assessment methods: exercises, a home exam.
applies in this implementation
The students are assumed to participate actively in the course by weekly returning their solutions to one home assignment (typically involving MATLAB computations). 25% of the overall grade is based on the home assignments and 75% on a home exam.
Workload
valid for whole curriculum period:
Contact hours 36h (no compulsory attendance)
Self-study ca 100h
applies in this implementation
Contact hours 24h (no compulsory attendance)
Lecture recordings 24h
Self-study ca 80h
DETAILS
Study Material
applies in this implementation
The lecture slides and recordings can be found at https://mycourses.aalto.fi/course/view.php?id=32070§ion=1
Recommended supplementary reading: J. Kaipio and E. Somersalo, Statistical and Computational Inverse Problems, Springer, 2005 (mainly Chapters 2 and 3), and D. Calvetti and E. Somersalo, Introduction to Bayesian Scientific Computing. Ten Lectures on Subjective Computing, Springer, 2007.
Substitutes for Courses
valid for whole curriculum period:
Prerequisites
valid for whole curriculum period:
FURTHER INFORMATION
Further Information
valid for whole curriculum period:
Teaching Language : English
Teaching Period : 2022-2023 Spring IV
2023-2024 Spring IVEnrollment :
Sisu (sisu.aalto.fi).
Details on the schedule
applies in this implementation
Week 1: Motivation and (truncated) singular value decomposition
Week 2: Morozov discrepancy principle and Tikhonov regularization
Week 3: Regularization by truncated iterative methods
Week 4: Motivation and preliminaries of Bayesian inversion, preliminaries of sampling
Week 5: Prior models, Gaussian densities, MCMC (Metropolis-Hastings algorithm)
Week 6: MCMC (Gibbs sampler), hypermodels