A Blind Recovery Algorithm for Multicoset Sampling via Graph Spectral Support Identification

A predominant limitation of current graph sampling approaches is their inability to reliably process multiband graph signals with unknown spectral support. In this paper, we present a minimal graph sampling rate for multiband graph signals, which standardizes the minimum number of required samples for both scenarios: known graph spectral support and unknown graph spectral support. Moreover, we propose a multicoset graph sampling method to achieve sub-Nyquist sampling rates. This multicoset graph sampling is essentially a type of periodic non-uniform sampling method. Furthermore, based on the graph continuous-to-finite block (GCFB), we propose two multicoset blind recovery (MCBR) algorithms. One is entitled the MCBR1 algorithm and uses a single instance of the GCFB. When the sampling rate is sufficiently high, the MCBR1 algorithm guarantees favorable reconstruction performance. The other is referred to as the MCBR2 algorithm and involves a bi-section procedure and several uses of the GCFB. The MCBR2 algorithm operates at the minimum sampling rate and can accurately identify the graph spectral support. Finally, by comparing the mean squared error (MSE), signal-to-noise ratio (SNR) and success rate of different methods, the experiments show that our MCBR2 algorithm has the smallest reconstruction error and best noise resistance. Practical validation on the real-world Intel Berkeley wireless sensor network dataset further verifies the practicability and scalability of the proposed sampling and recovery framework.