Sparse Estimation Based on a New Random Regularized Matching Pursuit Generalized Approximate Message Passing Algorithm

Approximate Message Passing (AMP) and Generalized AMP (GAMP) algorithms usually suffer from serious convergence issues when the elements of the sensing matrix do not exactly match the zero-mean Gaussian assumption. To stabilize AMP/GAMP in these contexts, we have proposed a new sparse reconstruction algorithm, termed the Random regularized Matching pursuit GAMP (RrMpGAMP). It utilizes a random splitting support operation and some dropout/replacement support operations to make the matching pursuit steps regularized and uses a new GAMP-like algorithm to estimate the non-zero elements in a sparse vector. Moreover, our proposed algorithm can save much memory, be equipped with a comparable computational complexity as GAMP and support parallel computing in some steps. We have analyzed the convergence of this GAMP-like algorithm by the replica method and provided the convergence conditions of it. The analysis also gives an explanation about the broader variance range of the elements of the sensing matrix for this GAMP-like algorithm. Experiments using simulation data and real-world synthetic aperture radar tomography (TomoSAR) data show that our method provides the expected performance for scenarios where AMP/GAMP diverges