One-bit compressed sensing reconstruction for block sparse signals

Abstract

Data compression is crucial for resource-constrained signal acquisition and wireless transmission applications with limited data bandwidth. In such applications, wireless data transmission dominates the energy consumption, and the limited telemetry bandwidth could be overwhelmed by the large amount of data generated from multiple sensors. Conventional data compression techniques are computationally intensive, consume large silicon area and offset the energy benefits from reduced data transmission. Recently, compressed sensing (CS) has shown potential in achieving compression performance comparable to previous methods but it has simpler hardware. Especially, one-bit CS theory proves that the signs of compressed measurements contain sufficient information about signal reconstruction, gives that the signals are sparse or compressible in specific dictionaries, thus demonstrating its potential in energy-constrained signal recording and wireless transmission applications. However, the sparsity assumption is too restrictive in many actual scenarios, especially when it is difficult to seek sparse representation for signals. In this paper, a novel one-bit CS method is proposed to reconstruct the signals that are difficult to represent with traditional sparse models. It is capable of recovering signal with comparable compression ratio but avoiding the dictionary selection procedure.The proposed method consists of two parts. 1) The block sparse model is adopted to enforce the structured sparsity of the signals. It not only overcomes the drawbacks of conventional sparse models but also enhances the signal representation accuracy. 2) The probabilistic model of one-bit CS procedure is constructed. Because of the existence of logistic function in probabilistic model of one-bit CS, the Bayesian inference cannot be used to proceed, and the variational Bayesian inference algorithm is developed to reconstruct the original signals from one-bit measurements.Various experiments on different quantities of compressed measurements and iterations are carried out to evaluate the recovery performance of the proposed approach. The photoplethysmography (PPG) signals recorded from subject wrist (dorsal locations) by using PPG sensors built in a wristband are selected as the validation data because they are difficult to represent with traditional sparse dictionaries. The experimental results reveal that the proposed approach outperforms the state-of-the-art one-bit CS method in terms of both reconstruction accuracy and convergence rate.Compared with prior method on one-bit CS, the proposed method shows competitive or superior performance in three aspects. Firstly, by adopting the block sparse model, the proposed method improves the capability to compress signals that are difficult to represent with traditional sparse models, thus making it more practical for long term and real applications. Secondly, by embedding the statistical properties of the one-bit measurements into the recovery algorithm, the proposed method outperforms other one-bit CS methods in terms of both reconstruction performance and convergence speed. Finally, energy and computational efficiency of the proposed method make it an ideal candidate for resource-constrained, large scale, multiple channel signal acquisition and transmission applications.