Reordering for Better Compressibility

Compressed Sensing (CS) is a novel sampling paradigm that tries to take data-compression concepts down to the sampling layer of a sensory system. It states that discrete compressible signals are recoverable from sub-sampled data, when the data vector is acquired by a special linear transform of the original discrete signal vector. Distributed sampling problems especially in Wireless Sensor Networks (WSN) are good candidates to apply CS and increase sensing efficiency without sacrificing accuracy. In this paper, we discuss how to reorder the samples of a discrete spatial signal vector by defining an alternative permutation of the sensor nodes (SN). Accordingly, we propose a method to enhance CS in WSN through improving signal compressibility by finding a sub-optimal permutation of the SNs. Permutation doesn't involve physical relocation of the SNs. It is a reordering function computed at the sink to gain a more compressible view of the spatial signal. We show that sub-optimal reordering stably maintains a more compressible view of the signal until the state of the environment changes so that another up-to-date reordering has to be computed. Our method can increase signal reconstruction accuracy at the same spatial sampling rate, or recover the state of the operational environment with the same quality at lower spatial sampling rate. Subsampling takes place during the interval that our reordered version of the spatial signal remains more compressible than the original signal. Compressive Wireless Sensing; Spatial Sampling; Reordering; Permutation; Compressibility; Compressed Sensing;