Sparse Signal Reconstruction with Statistical Prior Information: A Data-Driven Method

Weighted $\ell _{1}$ minimization (WL1M) is a general and powerful framework for reconstructing sparse signals from underdetermined measurements. The performance improvement of WL1M owes to the incorporation of additional structural priors of signals by means of its weights. However, the selection of weights relies on hand-crafted designs in existing works, so that high-order structural priors of signals are hard to be captured. This paper proposes a data-driven method, namely RBM-WL1M, to alleviate this situation. In the RBM-WL1M, restricted Boltzmann machines (RBMs) are employed to learn the prior distribution of the signals from training data; furthermore, utilizing the RBM, high frequency support set and non-zero probabilities for each of the entries in signals can be estimated effectively, which are used to appropriately select the weights. In our experiments, the proposed framework demonstrates superior performance over several state-of-the-art CS methods on the Physikalisch-Technische Bundesanstalt(PTB) Diagnostic ECG Data set.