  The reconstruction of sparse signal is an active area of research. Different
from a typical i.i.d. assumption, this paper considers a non-independent prior
of group structure. For this more practical setup, we propose EM-aided HyGEC, a
new algorithm to address the stability issue and the hyper-parameter issue
facing the other algorithms. The instability problem results from the ill
condition of the transform matrix, while the unavailability of the
hyper-parameters is a ground truth that their values are not known beforehand.
The proposed algorithm is built on the paradigm of HyGAMP (proposed by Rangan
et al.) but we replace its inner engine, the GAMP, by a matrix-insensitive
alternative, the GEC, so that the first issue is solved. For the second issue,
we take expectation-maximization as an outer loop, and together with the inner
engine HyGEC, we learn the value of the hyper-parameters. Effectiveness of the
proposed algorithm is also verified by means of numerical simulations.
