Number Of Compressive Sensing Measurements Research Articles

Collaborative and Compressed Mobile Sensing for Data Collection in Distributed Robotic Networks

In this paper, we exploit an integration between the mobility of robots and the collaboration between them to sample sensing areas that need to be observed. A collaborative and compressed mobile sensing algorithm is proposed for distributed robotic networks to build scalar field maps. In order to move in the sensing field and to avoid collision with obstacles and with each other, a control law is embedded into the robots. At a sampling time, each robot senses and adds data within its sensing range and collaborates to the others by exchanging data with its neighbors. A compressed sensing (CS) measurement created is a sum of scalar values collecting by a connected group of robots. A certain number of CS measurements is required at each robot to reconstruct all sensory readings from points of interest visited by the group of robots. The method reduces significantly data traffic among robots. We further analyze and formulate power consumption for the robots, and suggest some optimal cases for the robot to consume the least power.

Spread spectrum image watermark detection on degraded compressed sensing measurements with distortion minimization

In the age of digital world, the wide dissemination of images need bandwidth (BW) efficient transmission as well as ownership protection during transmission over radio mobile channel. Compressed sensing (CS) nowadays finds a potential application for BW efficient transmission over wireless network while digital watermarking, more specifically, spread spectrum (SS) watermarking is found to be efficient for copyright protection. To this aim, an SS watermarking scheme on CS images is proposed in presence of both multiplicative and additive impairments that support a general framework of radio mobile channel. First a mathematical form of watermark detection threshold in log-likelihood ratio model is derived followed by an optimization framework to minimize the visual distortion that includes CS reconstruction and watermark embedding distortion while satisfying some certain detection reliability constraints. An approximate closed form solution to the optimization problem in terms of embedding strength and a set of appropriate host samples selection for a given number of CS measurements is derived. A large set of simulation results on Rayleigh distribution as multiplicative degradation and Gaussian distribution as additive noise are reported. Performance comparison with the existing works validate the efficacy of the proposed method in terms of imperceptibility and improved detection reliability against a large set of diverse signal processing operations.

Spread Spectrum Watermark Detection on Degraded Compressed Sensing

This letter proposes a robust spread spectrum image watermark detection on compressed sensing (CS) measurements degraded by both multiplicative and additive noise. Watermark detection threshold is calculated first using log-likelihood ratio model. Distortion minimization problem is then formulated in terms of watermark embedding strength and the number of CS measurements under the constraint of detector reliability. A large set of simulation results show high detection probability with low false rate at low watermark power.

Compressive Sensing-Based ISAR Imaging via the Combination of the Sparsity and Nonlocal Total Variation

The sparsity of targets intrinsically paves a new way to apply compressive sensing (CS) to inverse SAR (ISAR) imaging. However, in the CS-based ISAR imaging system, the ISAR image is considered as a vector composed of random and independent scattering points, and the dependence between pixels is ignored, which always results in the degradation of the shape and geometry of targets, especially when the number of CS measurements and the signal-to-noise ratio are small. In this letter, a novel ISAR imaging framework is proposed via a combination of local sparsity constraint and nonlocal total variation (NLTV). The sparsity is a form prior that the number of strong scattering points is smaller than that of pixels in the image plane. It plays the role of classification of the strong scattering point from the clutter background. NLTV aims to suppress the noise and to remove some false strong scattering centers or clutter and simultaneously preserves the shape and geometry of target regions. Experiments on real data confirm the proposed method's validity.

Compressed Sensing: How Sharp Is the Restricted Isometry Property?

Compressed sensing (CS) seeks to recover an unknown vector with $N$ entries by making far fewer than $N$ measurements; it posits that the number of CS measurements should be comparable to the information content of the vector, not simply $N$. CS combines directly the important task of compression with the measurement task. Since its introduction in 2004 there have been hundreds of papers on CS, a large fraction of which develop algorithms to recover a signal from its compressed measurements. Because of the paradoxical nature of CS—exact reconstruction from seemingly undersampled measurements—it is crucial for acceptance of an algorithm that rigorous analyses verify the degree of undersampling the algorithm permits. The restricted isometry property (RIP) has become the dominant tool used for the analysis in such cases. We present here an asymmetric form of RIP that gives tighter bounds than the usual symmetric one. We give the best known bounds on the RIP constants for matrices from the Gaussian ensemble. Our derivations illustrate the way in which the combinatorial nature of CS is controlled. Our quantitative bounds on the RIP allow precise statements as to how aggressively a signal can be undersampled, the essential question for practitioners. We also document the extent to which RIP gives precise information about the true performance limits of CS, by comparison with approaches from high-dimensional geometry.