Enhancing compressed sensing recovery with Bayesian and generalized orthogonal matching pursuit: a progressive approach to signal reconstruction

The problem of accurate reconstruction of undersampled signals is always the core problem in the compressed sensing (CS) field. Type-II Laplacian prior-based orthogonal matching pursuit is a recovery model that applies Bayesian estimation to matching pursuit. By combining the greedy method with Bayes idea, it can not only take advantage of recovery accuracy brought by Bayes maximum posterior reconstruction but also achieve the feature of fast matching with a few iterations without processing the vector inner product many times. However, when decoding the CS undersampling problem, there are still some problems, such as single searching mode, relying on signal sparsity prior and initializing modeling parameters from empirical values. We propose a joint reconstruction of Bayesian and generalized orthogonal matching pursuit, which has a more reasonable search pattern, stronger adaptive ability, and higher solving accuracy. First, the Bayes hyperparameters updating method is coupled with generalized orthogonal matching pursuit to enhance the reconstruction accuracy and solution stability of the traditional method. Second, to deal with the problem that this method relies on prior knowledge such as correct signal sparsity, a positive feedback sparsity adaptive estimation strategy is proposed. Finally, a parameter initialization strategy based on pseudo inverse information of the sensor matrix is proposed to reduce the number of iterations effectively and improve the reconstruction performance. The results of random one- and two-dimensional signal simulation show that the combined reconstruction scheme proposed in this paper has better reconstruction performance than other similar methods under different conditions.