Data acquisition by 2D compression and ID reconstruction techniques for WSN spatially correlated data

Compressed Sensing (CS) is an innovative approach allowing to represent signals through a small number of their projections. In this paper, we address the application of CS to the scenario of 2D readings recovery from a Wireless Sensors Network (WSN) with excellent accuracy, while collecting only a small fraction of them at a data gathering point. CS requires a suitable transformation that makes the signal sparse in some domain. In this work, the spatial correlation is exploited in order to generate the sparse representation of the considered signal. Although, this is not the first work on applying CS to the data compression exploiting their spatial correlation, it is the first to keep 2D reading of the 2D measurements rather than considering the ID concatenated data. In this way, a predefined transforms, such as wavelets and DCT methods, are investigated for data compression in WSN by simultaneously application on both directions. Also, a 2D Principal Component Analysis (2DPCA) based on spatial correlation, working on both rows and columns directions of the 2D readings data, is adapted to derive the 2D sparse representation. A small subset of the compressible data is then used at the sink for the whole measurements recovery. The whole data recovery at the sink is realized by ID Orthogonal Matching (OMP) reconstruction algorithm. A comparative study of the WSN data recovery performance is carried between one and two dimensional compression. It shows that the 2D scenario realizes a significant reconstruction performance enhancement with respect to ID compression.