Graph Signal Reconstruction from Low-Resolution Multi-Bit Observations

Low hardware cost and power consumption in information transmission, processing and storage is an urgent demand for many big data problems, in which the high-dimensional data often be modelled as graph signals. This paper considers the problem of recovering a smooth graph signal by using its low-resolution multi-bit quantized observations. The underlying problem is formulated as a regularized maximum-likelihood optimization and is solved via an expectation maximization scheme. With this scheme, the multi-bit graph signal recovery (MB-GSR) is efficiently implemented by using the quantized observations collected from random subsets of graph nodes. The simulation results show that increasing the sampling resolution to 2 or 3 bits per sample leads to a considerable performance improvement, while the energy consumption and implementation costs remain much lower compared to the implementation of high resolution sampling.