China
Africa
Explore chapters and articles related to this topic
Compressive Sensing Fundamentals
Published in Moeness Amin, Compressive Sensing for Urban Radar, 2017
The RIP is essentially a requirement that in the matrix A := ΦΨ any submatrix containing K columns will act as an approximate isometry (its K columns will be approximately orthonormal). While the definition of the RIP is itself a deterministic statement, the most efficient constructions of RIP matrices involve randomness. In fact, it has been shown that even checking whether the RIP holds for a given matrix with a specified isometry constant is NP-hard in general [164]. Fortunately, this property can be guaranteed to hold with very high probability under suitable conditions.
Compressive Sensing for Inverse Synthetic Aperture Radar Imaging
Published in C.H. Chen, Compressive Sensing of Earth Observations, 2017
Alessio Bacci, Elisa Giusti, Sonia Tomei, Davide Cataldo, Marco Martorella, Fabrizio Berizzi
However, recent results in signal processing have demonstrated the ability of compressive sensing (CS) to reconstruct a sparse or compressible signal from a limited number of measurements with a high probability by solving an optimization problem [13]. Such a technique has been successfully applied for data storage reduction in medical imaging [30] and radar imaging applications [3], among others. The successful application of CS relies on the sparsity of the signal, that is, the characteristic of the signal of being represented by few nonzero entries in a suitable orthonormal basis. Different basis can be identified which support different sparsity index such as that proposed in [18]. In the case of radar imaging, the applicability of CS has been justified by observing that at high frequencies a radar signal is sparse in the image domain, that is, when represented in the 2D Fourier basis, since it can be approximated by the superimposition of few prominent scatterer responses with respect to the pixels in the image in the radar image plane [20,22]. Another property which must be satisfied by the radar signal for the application of CS is the restricted isometry property (RIP). The RIP denotes the characteristic of the matrices which define the basis on which the signal is sparse of being orthonormal, at least when dealing with sparse vectors. It has been demonstrated that the Fourier matrices which define the domain in which the ISAR signal is sparse satisfy the RIP property [7,16], hence demonstrating the applicability of CS reconstruction to the ISAR imaging problem. CS reconstruction capabilities have been tested for a number of radar applications, such as synthetic aperture radar (SAR) imaging and ISAR [44], ground penetrating radars [25], multiple-input multiple-output (MIMO) radar [1,57] 3D ISAR imaging, [43] and interferometric ISAR (InISAR) [2]. Specifically, three different applications of CS to the ISAR imaging problem have been described in the literature [48]. First of all, CS can be applied for the reconstruction of ISAR images from data with random missing samples. For example, in [51] and [50], CS has been suggested as an effective ISAR image reconstruction tool in the case of data with missing samples in the slow-time and in the frequency domain, respectively. In addition, given the CS capability of reconstructing images from undersampled data, the sampling constraints related to Nyquist’s sampling theorem can be overcome, as demonstrated in [4]. CS for data storage reduction has been suggested also in [12,29,61]. In [24], CS has been suggested as an effective reconstruction tool to recover a signal from its principal component extracted via principal component analysis (PCA) to reduce the clutter effects and enhance the target return extraction. In this framework, the advantages of CS can be mainly associated with the capability of obtaining good quality images from a limited number of measurements, thus reducing the amount of data to be stored and processed.
Fault diagnosis, service restoration, and data loss mitigation through multi-agent system in a smart power distribution grid
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Ishan Srivastava, Sunil Bhat, Arvind R. Singh
where s is a (B x 1) matrix, it represents the original signal which is sampled at Nyquist rate, M is (A x B) matrix, and is called the measurement matrix. r matrix size is (A x 1), is known the measurement vector, which consists of CS samples, and the representation of s in the orthonormal basis Φ (G-sparse) is x. To perform proper reconstruction, sparsity of the signal is required in some domain and the measurement matrices satisfy coherence property or RIP (Candes and Wakin 2008).
Performance Comparison of Reconstruction Algorithms in Compressive Sensing Based Single Snapshot DOA Estimation
Published in IETE Journal of Research, 2022
Kankanala Srinivas, Saurav Ganguly, Puli Kishore Kumar
The next step is the compression or sampling process; by using an observation or sensing matrix Φ which senses the most useful information in the signal, the original signal is converted into a measurement vector y which is compressed and encrypted form. In order to promise a faithful reconstruction of the sparse signal, the sensing matrix is to be coherent and is to satisfy the Restricted Isometric Property (RIP).