Mixed norms are used to introduce in an easy way, both structures and sparsity in the framework of sparse regression problems, and then introduce implicitly couplings between regression coefficients. Corresponding algorithms are described and analyzed. Besides the classical sparse regression problem, at the same time the multi-layered expansion of signals are considered, using union of dictionaries. These sparse structured expansions are done subject to equality constraint, using a modified FOCUSS algorithm. When the mixed norms are used in the framework of regularized inverse problem, a thresholded Landweber iteration is used to minimize the corresponding variational problem.