1. Expectation-Maximization-Aided Hybrid Generalized Expectation Consistent for Sparse Signal Reconstruction
- Author
-
Hongwen Yang, Qiuyun Zou, and Haochuan Zhang
- Subjects
Signal Processing (eess.SP) ,FOS: Computer and information sciences ,Ground truth ,Signal reconstruction ,Computer science ,Information Theory (cs.IT) ,Computer Science - Information Theory ,Applied Mathematics ,Message passing ,Stability (learning theory) ,Approximation algorithm ,020206 networking & telecommunications ,02 engineering and technology ,Transformation matrix ,Signal Processing ,Expectation–maximization algorithm ,FOS: Electrical engineering, electronic engineering, information engineering ,0202 electrical engineering, electronic engineering, information engineering ,Electrical Engineering and Systems Science - Signal Processing ,Electrical and Electronic Engineering ,Unavailability ,Algorithm - Abstract
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., 15 pages, 4 figures. This paper has been submitted to IEEE Signal Processing Letters
- Published
- 2021
- Full Text
- View/download PDF