MATA2510 Introduction to Computational Inverse Problems (4 cr)

Matlab programming, discerete convolution and deconvolution, Hadamard's conditions of well-posedness, minimum norm solutions, singular value decomposition (SVD) and condition number, Moore-Penrose pseudoinverse, truncated SVD, Tikhonov regularization

• Understands discrete convolution as a matrix model
• Learns least-squares solution technique and see that it can be numerically unstable
• Shows how to use SVD to detect ill-posedness in a matrix-based inverse problem
• Understands why deconvolution needs special regularised methods
• Knows how to write robust Matlab algorithms for signal deconvolution and image deblurring

Linear Algebra and Geometry 2, Vector calculus 1, basic programming skill is helpful but not mandatory

1. The open MOOC-course of the University of Helsinki: Introduction to Computational Inverse Problems (mooc.helsinki.fi).
2. Jennifer Mueller, Samuli Siltanen: Linear and Nonlinear Inverse Problems with Practical Applications, 2012. (A supporting textbook, but not mandatory.)