λ J(x) (Pλ(y)) Trade-oﬀ between data ﬁdelity and prior regularization • Data ﬁdelity: 2 loss, logistic, etc. F(y, x) = 1 2 ||y − Φx||2 2 • Parameter: By hand or automatic like SURE. • Regularization: ?
sparse representations in arbitrary redundant bases. • Tropp, J. A. (2006). Just relax: Convex programming methods for identifying sparse signals in noise. • Grasmair, M. and al. (2008). Sparse regularization with q penalty term. • Bach, F. R. (2008). Consistency of the group lasso and multiple kernel learning & Consistency of trace norm minimization. • V. and al. (2011). Robust sparse analysis regularization. • Grasmair, M. and al. (2011). Necessary and suﬃcient conditions for linear convergence of 1-regularization. • Grasmair, M. (2011). Linear convergence rates for Tikhonov regularization with positively homogeneous functionals. (and more !)