Aula 1B1, Venerdì 23 Gennaio 2015, ore 12:00
Prof. Ivan Selesnick, New York University
“Linear Inverse Problems, Sparse Regularization, and Convex Optimization”
Abstract: Several fundamental problems in signal processing can be formulated as ill-conditioned linear inverse problems (for example: noise reduction, deblurring, missing data restoration, and nonlinear signal decomposition). In these problems the regularizer has an important role. It should be chosen based on properties the underlying signal is known to have. We compare two forms of regularization: quadratic and sparse. It will be seen that sparse regularization provides advantages over quadratic regularization in several cases. We discuss the use of convex optimization to solve the large-scale non-smooth optimization problems arising from the use of sparse regularization. We describe enhancements of pure sparse regularization: structured sparsity, compound regularization, and new non-convex regularizers that ensure the convexity of the objective function. We show several applications, including: detection of EEG sleep spindles, noise reduction for speech and electrocardiograms, restoration of clipped speech, and baseline removal for chromatography.