Discrete least-square problems: minimum norm solution, singular value decomposition (SVD), truncated SVD (TSVD), pseudo-inverse, Golub-Kahan algorithm to compute the SVD, Landweber iteration. (24 h)

Ill-posed problems and regularization: filtering by TSVD, Tikhonov method, and SVD filtering. Strategies for estimating the regularization parameter: discrete Picard condition, discrepancy principle, L-curve, and GCV. Regularization iterative methods (Landweber method and conjugate gradients for normal equations). Convolution and discrete Fourier transform by fast Fourier transform. Compression, segmentation, and deconvolution of signals and images. (30 h)

Introduction to machine learning shows that the main idea of machine learning can be traced back to the regularization of an ill-posed inverse problem depending on the choice of the data fidelity measure and the predicting model. (10 h)

The numerical methods and some applications will be implemented and tested using MatLab.