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Recently, distributed algorithms have been proposed for the recovery of sparse signals in networked systems, e.g. wireless sensor networks. Such algorithms allow large networks to operate autonomously without the need of a fusion center, and are very appealing for smart sensing problems employing low-power devices. They exploit local communications, where each node of the network updates its estimates...
In this paper we studied effectiveness in using Compressive Sensing (CS) algorithm in order to reduce measuring in IEEE 802.15.4 Standard Wireless Sensor Network (WSN). As well known, in common WSN work system, Base Station (BS) gather some information from available nodes, which the process itself consumes a lot of energy from each node. We also use an existing CS algorithm, the Basis Pursuit. Furthermore,...
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Compressed sensing enables the acquisition of sparse signals at a rate that is much lower than the Nyquist rate. Various greedy recovery algorithms have been proposed to achieve a lower computational complexity compared to the optimal ℓ1 minimization, while maintaining a good reconstruction accuracy. We propose a new greedy recovery algorithm for compressed sensing, called the Adaptive Reduced-set...
In this paper we consider the problem of nonlocal image completion from random measurements and using an ensemble of dictionaries. Utilizing recent advances in the field of compressed sensing, we derive conditions under which one can uniquely recover an incomplete image with overwhelming probability. The theoretical results are complemented by numerical simulations using various ensembles of analytical...
In compressed sensing (CS) framework, a signal is sampled below Nyquist rate, and the acquired samples are generally random in nature. Thus, for efficient estimation of the actual signal, the sensing matrix must preserve the relative distances among the underlying sparse vectors. Provided this condition is fulfilled, we show that CS samples will also preserve the envelope of the actual signal. Exploiting...
Compressed Sensing (CS) is an emerging field in communications and mathematics that is used to measure few measurements of long sparse vectors with the ability of lossless reconstruction. In this paper we use results from channel coding to design a recovery algorithm for CS with a deterministic measurement matrix by exploiting error correction schemes. In particular, we show that a generalized Reed...
The LASSO is a variable subset selection procedure in statistical linear regression based on sparsity promoting `1 penalization of the least-squares operator. In many applications, the design matrix has strongly correlated columns which are smoothly evolving with the column index. For such applications, the standard LASSO does not provide satisfactory solutions in practice because some incoherence...
Compressive sensing (CS) is a new framework for simulations sensing and compressive. How to reconstruct a sparse signal from limited measurements is the key problem in CS. For solving the reconstruction problem of a sparse signal, we proposed a self-adaptive proximal point algorithm (PPA). This algorithm can handle the sparse signal reconstruction by solving a substituted problem — ℓ1 problem. At...
The design of measurement matrices is one of the key contents of the compressed sensing (CS) theory. This paper constructs a new dual-structured measurement matrix-unit array + random matrix, by combining the advantages of the random measurement matrices with high recovery probability and the structured measurement matrices of low storage. The experiments show that the reconstruction errors can be...
In this paper, we propose a novel compressed sensing based joint detection and tracking algorithm, named CS-JDT algorithm, to track multiple targets for STAP radar system. A novel general similar sensing matrix pursuit (GSSMP) algorithm is proposed to reconstruct the whole radar scenario (DOA-Doppler plane) for each range gate at consecutive scans. The proposed GSSMP algorithm addresses several problems...
Based on the fact that the spectrum in cognitive radio system is typically sparse, a novel wideband spectrum sensing algorithm is proposed taking advantage of Bayesian compressed sensing. Under our proposed scheme, the signal of interest can be sampled at sub-Nyquist rate so relaxing the sampling tension of front-end hardware. Furthermore, the block structure of the spectrum molded by a set of double-level...
The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor measurements using compressed sensing. In the first half of the paper, we present both uniform and nonuniform recovery guarantees for the conventional sparse signal...
Compressed sensing has found several applications in hyperspectral imaging because it helps in reducing the size of data to be captured or to be transmitted to ground stations. This work is based on the reconstruction of a hyperspectral image from compressive measurements. There are various hardware models proposed in the literature for compressed sensing of hyperspectral images. This work considers...
To elongate the battery life of sensors worn in wireless body area networks, recent studies have advocated compressing the acquired biological signals before transmitting them. The signals are compressed using compressive sensing (CS), by projecting them onto a lower dimension. The original signals are then recovered using CS recovery techniques at the base station, where the computational power is...
In this paper, we propose an efficient technique for dimensionality reduction of Mass Spectrometry (MS) data by employing Compressive Sensing (CS). Not only can CS significantly reduce MS data dimensionality, but it also will allow for full reconstruction of original data. The framework developed in this work is based on forming Sparse Difference (SD) to sparsify MS signals and implementing the Block...
The technology of the distributed compressed sensing is thought as an extension of compressed sensing and it makes applying multiple signals into compressed sensing possible. A vital issue in distributed compressed sensing is to minimize the difference between the original signal and the recovery signal. In this paper, we improve the distributed compressed sensing for smooth signals in wireless sensor...
This paper addresses distributed finite-rate quantized compressed sensing (QCS) acquisition of correlated sparse sources in wireless sensor networks. We propose a distributed variable-rate QCS compression method with complexity-constrained encoding to minimize a weighted sum of the mean square error distortion of the signal reconstruction and the average encoding rate. The variable-rate coding is...
The goal of many electromagnetic imaging applications is to recover the complex permittivity of an object of interest. In many instances, it is possible to recover the permittivity from a small number of measurements using compressive sensing techniques. This paper presents a novel physicality constrained compressive sensing optimization program, which enforces the fundamental constraints placed on...
The projection matrix in compressive light field acquisition has specific structural features that can be utilized for more efficient compressive sensing. In this paper, we propose a new mask design scheme for projection optimization in light field compressing with a novel circulant matrix structure. A learning circulant kernel algorithm is developed and applied to compute the projection matrix optimization...
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