A Framework of Generalized Distributed Compressive Sensing

다국어 초록 (Multilingual Abstract)

In distributed sensor network, compression of the transmitted signal is a important issue since a power limitation of each sensor is very low. However, since to get a whole signal correlation structure at each sensor demands huge overhead, the compression technique requiring the correlation of the whole signal structure cannot be used. Compressive sensing (CS), which does not demand any signal correlation structure for compression, is emerging to adequate technique for compression of sensor network. Baron et al., proposed a new framework of signal encoding and decoding in [2] that is applicable to sensor network, named
“Distributed Compressive Sensing(DCS)”. Unlike previous work, DCS takes advantages
to capitalize on both intra- and inter- signal correlation structure during decoding procedure.
However, in [2], there are assumptions that are not general or not practical. At first, it is assumed that there is only inter signal correlation which affects whole signals measured in the field, although it is more general and natural assumption that there exist both full inter signal correlation, which affects whole signals as in [2], and additionally, partial inter signal correlations which affect only parts of the signals. Furthermore, as a joint decoding method, weighted l1 minimization is used in [2]. This algorithm requires proper weights for providing performance advantages, however, the numerical optimization to obtain the proper weights
needs the sparsity information of the signals which are not allowed practically before the decoding is done. In this paper, we show that a elaborated signal structure considering partial inter signal correlation can reduce the required number of measurements. To this end, we introduce a new concept of partial common information which is shared by some parts of sensors, however not by every sensor. The theoretical bound of the number of measurements is obtained using the proposed signal model. In addition to this, we introduce a new decoding algorithm that enables to provide performance advantages without sparsity information of the signals. Numerical results show that with the proposed model, improved signal recovery performance can be achieved even when a priori sparsity information
is not given. Finally, we propose a new mehod to obtain a gain of a joint decoding without a priori information of inter- signal correlation structure.