Due to non-homogeneous spread of sunlight, sensing nodes possess non-uniform energy budget in recharge- able Wireless Sensor Networks (WSNs). An energy-aware workload distribution strategy is therefore nec- essary to achieve good data accuracy subject to energy-neutral operation. Recently proposed signal approx- imation strategies assume uniform sampling and fail to ensure energy neutral operation in rechargeable wireless sensor networks. We propose EAST (Energy Aware Sparse approximation Technique), which ap- proximates a signal, by adapting sensor node sampling workload according to solar energy availability. To the best of our knowledge, we are the first to propose sparse approximation to model energy-aware workload distribution in rechargeable WSNs. Experimental results, using data from an outdoor WSN deployment suggest that EAST significantly improves the approximation accuracy offering approximately 50 higher sensor on-time. EAST requires the approximation error to be known beforehand to determine the number of measure- ments. However, it is not always possible to decide the accuracy a-priori. We improve EAST and propose EAST+, which, given only the energy budget of the nodes, computes the optimal number of measurements subject to the energy neutral operation.
Recently, we have extended the theory of compressive sensing showing that it can be used to support non-uniform sampling @cite_23 @cite_1 . However, in this paper we choose sparse random projections over compressive sensing, since the decoding process of compressive sensing is computationally expensive. The complexity of decoding a @math data point vector is @math . Whereas, decoding complexity of sparse random projections is as low as @math , where @math is the number of projections. In this paper the projects are generated locally without any coordination between basestation and nodes, and, the final signal recovery takes place at the resource enriched basestation. In our future study we seek to conduct the signal recovery at the resource limited sensor nodes. For that purpose a low complexity decoder will be very useful.
@cite_1 @cite_23
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Compressive Sensing theory details how a sparsely represented signal in a known basis can be reconstructed with an underdetermined linear measurement model. However, in reality there is a mismatch between the assumed and the actual bases due to factors such as discretization of the parameter space defining basis components, sampling jitter in A D conversion, and model errors. Due to this mismatch, a signal may not be sparse in the assumed basis, which causes significant performance degradation in sparse reconstruction algorithms. To eliminate the mismatch problem, this paper presents a novel perturbed orthogonal matching pursuit (POMP) algorithm that performs controlled perturbation of selected support vectors to decrease the orthogonal residual at each iteration. Based on detailed mathematical analysis, conditions for successful reconstruction are derived. Simulations show that robust results with much smaller reconstruction errors in the case of perturbed bases can be obtained as compared to standard sparse reconstruction techniques. The recently introduced theory of compressive sensing enables the recovery of sparse or compressible signals from a small set of nonadaptive, linear measurements. If properly chosen, the number of measurements can be much smaller than the number of Nyquist-rate samples. Interestingly, it has been shown that random projections are a near-optimal measurement scheme. This has inspired the design of hardware systems that directly implement random measurement protocols. However, despite the intense focus of the community on signal recovery, many (if not most) signal processing problems do not require full signal recovery. In this paper, we take some first steps in the direction of solving inference problems-such as detection, classification, or estimation-and filtering problems using only compressive measurements and without ever reconstructing the signals involved. We provide theoretical bounds along with experimental results. This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all standard models-e.g., Gaussian, frequency measurements-discussed in the literature, but also provides a framework for new measurement strategies as well. We prove that if the probability distribution F obeys a simple incoherence property and an isotropy property, one can faithfully recover approximately sparse signals from a minimal number of noisy measurements. The novelty is that our recovery results do not require the restricted isometry property (RIP) to hold near the sparsity level in question, nor a random model for the signal. As an example, the paper shows that a signal with s nonzero entries can be faithfully recovered from about s logn Fourier coefficients that are contaminated with noise. The theory of compressive sensing has shown that sparse signals can be reconstructed exactly from many fewer measurements than traditionally believed necessary. In [1], it was shown empirically that using lscrp minimization with p < 1 can do so with fewer measurements than with p = 1. In this paper we consider the use of iteratively reweighted algorithms for computing local minima of the nonconvex problem. In particular, a particular regularization strategy is found to greatly improve the ability of a reweighted least-squares algorithm to recover sparse signals, with exact recovery being observed for signals that are much less sparse than required by an unregularized version (such as FOCUSS, [2]). Improvements are also observed for the reweighted-lscr1 approach of [3].