Dictionary Learning for Blind One Bit Compressed Sensing

Abstract

This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix $\Ab$ and sparse domain matrix $\Phi$, \ie $\Db=\AbΦ$, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to learn the rows of the matrix $\Db$. Experimental results show the effectiveness of the proposed algorithm against the case of no dictionary learning, specially with increasing the number of training signals and the number of sign measurements.

5 pages, 3 figures

Cited by in corpus (8)

• On the Performance of One-Bit DoA Estimation via Sparse Linear Arrays
• Localization with One-Bit Passive Radars in Narrowband Internet-of-Things using Multivariate Polynomial Optimization
• Multi-modal dictionary learning for image separation with application in art investigation
• Sparse Recovery and Dictionary Learning from Nonlinear Compressive Measurements
• One-Bit Compressive Sensing: Can We Go Deep and Blind?
• DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds
• Convex Quantization Preserves Logconcavity
• Generalization analysis of an unfolding network for analysis-based Compressed Sensing