Multi-Block Convex Optimization Methods And Its Application In Pattern Recognition

Many problems in imaging science and machine learning can be formulated as a multi-block convex optimization problem, specially when the image could be reconstructed by sparse representation. In this thesis, we are interested in the block coordinate descent methods(BCD) for regularized multiconvex optimization with application to multiple cells recognition problem. By adding the matrix norm to the three different type methods, we apply the primal-dual ?xed point algorithms to solve the subproblem and demonstrate the convergence of the BCD method. Finally, we illustrate the e?ciency of algorithms through dictionary based multi-cells localization with the regularization of L1 norm and TV norm.