TC-CSBP: Compressive sensing for time-correlated data based on belief propagation

Abstract

Existing compressive sensing techniques mostly consider the sparsity of signals in one dimension. However, a very important case that has rarely been studied is when the signal of interest is time varying and signal coefficients have correlation in time. Our proposed algorithm in this paper is a structureaware version of the compressive sensing reconstruction via belief propagation proposed by Baron et al. that exploits the time correlation between the signal components and provides the belief propagation algorithm with more accurate initial priors. Numerical simulations show that the belief propagation-based compressive sensing algorithm is able to utilize the side information about signal's time correlation and results in enhanced reconstruction performances.

Coalition Formation Based Compressive Sensing in Wireless Sensor Networks

“…The approaches used in the comparison are Bayesian compressive sensing (BCS) [12], clustered spatio-temporal Bayesian compressive sensing (STBCS) [13], Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 14 May 2018 doi:10.20944/preprints201805.0192.v1 temporal belief-propagation based compressive sensing (TBCS) [14], OMP based compressive sensing [15] and spatial Bayesian compressive sensing (SBCS) [16].…”

“…The study presented in [14] introduces a belief-propagation-based compressive sensing technique that considers the temporal correlation model of the signal as given information and employs it to reconstruct the signal. To model temporal correlation, one can decrease the number of required measurements and help to achieve better reconstruction accuracy with a specific spike-and-slab Markov model.…”

Less is more

“…Unlike classical compression techniques, compressive sensing simplifies the encoding procedure, while the decoding procedure remains complicated. This characteristic best suits wireless sensor network restrictions by employing simple encoding on the resource-restricted sensor nodes and a complex decoding procedure at the powerful base station [110,111,95]. Compressive sensing utilizes information rate instead of sampling rate to sample and recover the signal [95].…”

“…The study presented in [110] introduces a belief-propagation-based compressive sensing technique that considers the temporal correlation model of the signal as given information and employs it to reconstruct the signal. To model temporal correlation, one can decrease the number of required measurements and help to achieve better reconstruction accuracy with a specific spike-andslab Markov model.…”

“…Bayesian compressive sensing (BCS) [229] is another technique that uses statistical characterization of the signal to complement the conventional methods. It can provide better performance in terms of accurate data reconstruction, however, it is not widely used in the wireless sensor networks field [110]. TC-CSBP [110] is one of first researches which employs belief propagation (BP) technique to reconstruct the signal.…”