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.
 Sparse signal representation, analysis, and sensing have received a lot of attention in recent years from the signal processing, optimization, and learning communities. On one hand, learning overcomplete dictionaries that facilitate a sparse representation of the data as a liner combination of a few atoms from such dictionary leads to state-of-the-art results in image and video restoration and classification. On the other hand, the framework of compressed sensing (CS) has shown that sparse signals can be recovered from far less samples than those required by the classical Shannon-Nyquist Theorem. The samples used in CS correspond to linear projections obtained by a sensing projection matrix. It has been shown that, for example, a nonadaptive random sampling matrix satisfies the fundamental theoretical requirements of CS, enjoying the additional benefit of universality. On the other hand, a projection sensing matrix that is optimally designed for a certain class of signals can further improve the reconstruction accuracy or further reduce the necessary number of samples. In this paper, we introduce a framework for the joint design and optimization, from a set of training images, of the nonparametric dictionary and the sensing matrix. We show that this joint optimization outperforms both the use of random sensing matrices and those matrices that are optimized independently of the learning of the dictionary. Particular cases of the proposed framework include the optimization of the sensing matrix for a given dictionary as well as the optimization of the dictionary for a predefined sensing environment. The presentation of the framework and its efficient numerical optimization is complemented with numerous examples on classical image datasets. Compressed sensing (CS) offers a joint compression and sensing processes, based on the existence of a sparse representation of the treated signal and a set of projected measurements. Work on CS thus far typically assumes that the projections are drawn at random. In this paper, we consider the optimization of these projections. Since such a direct optimization is prohibitive, we target an average measure of the mutual coherence of the effective dictionary, and demonstrate that this leads to better CS reconstruction performance. Both the basis pursuit (BP) and the orthogonal matching pursuit (OMP) are shown to benefit from the newly designed projections, with a reduction of the error rate by a factor of 10 and beyond.