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

Abstract

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.

A Two-Stage Method to Test the Robustness of the Generalized Approximate Message Passing Algorithm

“…drawn from N (0, 1). Set the range of γ to [0, 1, 1.8, 1.9, 1.95, 2,3,4,5,6,7,8,9,10,11,12]. Figure 1a shows that GAMP violently diverges at γ = 2, AMP fast diverges at γ = 5.…”

“…We propose a new GAMP-like algorithm, termed Bernoulli-Gaussian Pursuit GAMP (BGP-GAMP), to raise the robustness of standard GAMP algorithm. Our algorithm firstly utilizes the marginal posterior probability of x to sequentially find the support S, and then estimates the amplitudes on S by a tiny revised GAMP algorithm, termed Fixed Support GAMP (FS-GAMP) which has been proposed in our previous work [5]. A recent work has been proposed by Rodger [6], which is similar to our work, but gives another viewpoint from a neural network statistical model.…”

Sparsity Adaptive Matching Pursuit Detection Algorithm Based on Compressed Sensing for Radar Signals

“…The signal detection task could be implemented by directly using the sampled value of CS, since the structure and information of the original signal are well maintained in the sample value [3,13,14,15]. Then, the sampled value can be directly used for signal detection and estimation by the strictly theoretical derivation proved in [16].…”

“…For the target detection of a radar signal, the detection problem will become complicated and cause an unnecessary waste of resources if the target detection is performed after the original signal is reconstructed. The signal detection task could be implemented by directly using the sampled value of CS, since the structure and information of the original signal are well maintained in the sample value [ 3 , 13 , 14 , 15 ]. Then, the sampled value can be directly used for signal detection and estimation by the strictly theoretical derivation proved in [ 16 ].…”