Efficient Compressive Sampling of Spatially Sparse Fields in Wireless Sensor Networks

Wireless sensor networks (WSN), i.e. networks of autonomous, wireless sensing nodes spatially deployed over a geographical area, are often faced with acquisition of spatially sparse fields. In this paper, we present a novel bandwidth/energy efficient CS scheme for acquisition of spatially sparse fields in a WSN. The paper contribution is twofold. Firstly, we introduce a sparse, structured CS matrix and we analytically show that it allows accurate reconstruction of bidimensional spatially sparse signals, such as those occurring in several surveillance application. Secondly, we analytically evaluate the energy and bandwidth consumption of our CS scheme when it is applied to data acquisition in a WSN. Numerical results demonstrate that our CS scheme achieves significant energy and bandwidth savings wrt state-of-the-art approaches when employed for sensing a spatially sparse field by means of a WSN.Comment: Submitted to EURASIP Journal on Advances in Signal Processin

Stable image reconstruction using total variation minimization

This article presents near-optimal guarantees for accurate and robust image recovery from under-sampled noisy measurements using total variation minimization. In particular, we show that from O(slog(N)) nonadaptive linear measurements, an image can be reconstructed to within the best s-term approximation of its gradient up to a logarithmic factor, and this factor can be removed by taking slightly more measurements. Along the way, we prove a strengthened Sobolev inequality for functions lying in the null space of suitably incoherent matrices.Comment: 25 page

Sparse Recovery from Combined Fusion Frame Measurements

Sparse representations have emerged as a powerful tool in signal and information processing, culminated by the success of new acquisition and processing techniques such as Compressed Sensing (CS). Fusion frames are very rich new signal representation methods that use collections of subspaces instead of vectors to represent signals. This work combines these exciting fields to introduce a new sparsity model for fusion frames. Signals that are sparse under the new model can be compressively sampled and uniquely reconstructed in ways similar to sparse signals using standard CS. The combination provides a promising new set of mathematical tools and signal models useful in a variety of applications. With the new model, a sparse signal has energy in very few of the subspaces of the fusion frame, although it does not need to be sparse within each of the subspaces it occupies. This sparsity model is captured using a mixed l1/l2 norm for fusion frames. A signal sparse in a fusion frame can be sampled using very few random projections and exactly reconstructed using a convex optimization that minimizes this mixed l1/l2 norm. The provided sampling conditions generalize coherence and RIP conditions used in standard CS theory. It is demonstrated that they are sufficient to guarantee sparse recovery of any signal sparse in our model. Moreover, a probabilistic analysis is provided using a stochastic model on the sparse signal that shows that under very mild conditions the probability of recovery failure decays exponentially with increasing dimension of the subspaces