The recovery of sparse generative models from few noisy measurements is an\nimportant and challenging problem. Many deterministic algorithms rely on some\nform of $\\ell_1$-$\\ell_2$ minimization to combine the computational convenience\nof the $\\ell_2$ penalty and the sparsity promotion of the $\\ell_1$. It was\nrecently shown within the Bayesian framework that sparsity promotion and\ncomputational efficiency can be attained with hierarchical models with\nconditionally Gaussian priors and gamma hyperpriors. The related Gibbs energy\nfunction is a convex functional and its minimizer, which is the MAP estimate of\nthe posterior, can be computed efficiently with the globally convergent\nIterated Alternating Sequential (IAS) algorithm \\cite{CSS}. Generalization of\nthe hyperpriors for these sparsity promoting hierarchical models to generalized\ngamma family yield either globally convex Gibbs energy functionals, or can\nexhibit local convexity for some choices for the hyperparameters. \\cite{CPrSS}.\nThe main problem in computing the MAP solution for greedy hyperpriors that\nstrongly promote sparsity is the presence of local minima. To overcome the\npremature stopping at a spurious local minimizer, we propose two hybrid\nalgorithms that first exploit the global convergence associated with gamma\nhyperpriors to arrive in a neighborhood of the unique minimizer, then adopt a\ngeneralized gamma hyperprior that promote sparsity more strongly. The\nperformance of the two algorithms is illustrated with computed examples.\n