Compressive Sensing, which offers exact reconstruction of sparse signal from a small number of measurements, has tremendous potential for trajectory compression. In order to optimize the compression, trajectory compression algorithms need to adapt compression ratio subject to the compressibility of the trajectory. Intuitively, the trajectory of an object moving in starlight road is more compressible compared to the trajectory of a object moving in winding roads, therefore, higher compression is achievable in the former case compared to the later. We propose an in-situ compression technique underpinning the support vector regression theory, which accurately predicts the compressibility of a trajectory given the mean speed of the object and then apply compressive sensing to adapt the compression to the compressibility of the trajectory. The conventional encoding and decoding process of compressive sensing uses predefined dictionary and measurement (or projection) matrix pairs. However, the selection of an optimal pair is nontrivial and exhaustive, and random selection of a pair does not guarantee the best compression performance. In this paper, we propose a deterministic and data driven construction for the projection matrix which is obtained by applying singular value decomposition to a sparsifying dictionary learned from the dataset. We analyze case studies of pedestrian and animal trajectory datasets including GPS trajectory data from 127 subjects. The experimental results suggest that the proposed adaptive compression algorithm, incorporating the deterministic construction of projection matrix, offers significantly better compression performance compared to the state-of-the-art alternatives.
Some other adaptive compression algorithms, although do not require lots of inter-node communication, however, require large number of on-node processing. For example, in @cite_29 authors propose an adaptive wavelet compression algorithm for wireless sensor networks. In the proposed method each receiving sensor computes the compression ratio, and calculates the total energy dissipation (using both computation and communication energy models) to make a decision about whether to increases wavelet transform level or to keep the present level. Then, the sensor, runs wavelet compression with next transform level to compute the new compression ratio, computes new value of total energy dissipation and compares it with the old value. The above steps will be repeated if the new energy estimate is smaller than old estimate and wavelet transform level is less than some maximum allowed value. After this operation, the nodes transmit data to the central nodes applying the computed wavelet transform level. This method will involve enormous computation given that for each trajectory segment it has to iterate multiple times to determine the optimal transform level for the best compression and energy trade-off.
@cite_29
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In this paper we proposed a novel Adaptive Distributed Wavelet Compression (ADWC) algorithm for reducing energy consumption in a wireless sensor network, where each of the sensors has limited power. This algorithm is characterized by a distributed lifting factorization, which matching well with the transmission strategy employed in wireless sensor networks., it also present an adaptive algorithm to selects the optimal wavelet compression parameters to minimize total energy dissipation. The simulation results showed that these approaches can achieve significant energy savings without sacrificing the quality of the data reconstruction.