Academia.edu no longer supports Internet Explorer.
To browse Academia.edu and the wider internet faster and more securely, please take a few seconds to upgrade your browser.
2013, IEEE Transactions on Signal Processing
AI
This paper introduces a novel algorithm called Perturbed Orthogonal Matching Pursuit (POMP) to address the mismatch between assumed and actual bases in compressive sensing. The algorithm applies controlled perturbation of selected support vectors to minimize the orthogonal residual during signal reconstruction. Through mathematical analysis and simulation results, POMP demonstrates significantly improved reconstruction accuracy compared to traditional sparse reconstruction methods, particularly in scenarios where the basis is perturbed.
IEEE Access
Compressive sensing allows the reconstruction of original signals from a much smaller number of samples as compared to the Nyquist sampling rate. The effectiveness of compressive sensing motivated the researchers for its deployment in a variety of application areas. The use of an efficient sampling matrix for high-performance recovery algorithms improves the performance of the compressive sensing framework significantly. This paper presents the underlying concepts of compressive sensing as well as previous work done in targeted domains in accordance with the various application areas. To develop prospects within the available functional blocks of compressive sensing frameworks, a diverse range of application areas are investigated. The three fundamental elements of a compressive sensing framework (signal sparsity, subsampling, and reconstruction) are thoroughly reviewed in this work by becoming acquainted with the key research gaps previously identified by the research community. Similarly, the basic mathematical formulation is used to outline some primary performance evaluation metrics for 1D and 2D compressive sensing. INDEX TERMS Compressed sensing, compressive sampling, reconstruction algorithms, sensing matrix. IRFAN AHMED received the B.Sc. and M.Sc. degrees in electrical engineering and the Ph.D. degree in computer systems engineering from the University of Engineering & Technology Peshawar. He is currently employed as a full-time Lecturer with the
Compressive sensing is a novel scenario in which a sparse signal in a known transform domain is acquired with much fewer samples than is required by the dimensions of the domain. The only condition is that the sampling process is incoherent with the transform that achieves the sparse representation and by sparse we mean that most of the weighting coefficients of the signal representation in the transform domain are zero. By incoherent it is meant that the distances between sparse signals are approximately conserved as distances between their respective measurements generated by the sampling process.
Journal of emerging technologies and innovative research, 2015
This paper gives the conventional approach of reconstructing signals or images from calculated data by following the well-known Shannon sampling theorem. This principle underlies the majority devices of current technology, such as analogto-digital conversion, medical imaging, or audio and video electronics. The primary objective of this paper is to establish the need of compressive sensing in the field of signal processing and image processing. Compressive sensing (CS) is a novel kind of sampling theory, which predicts that sparse signals and images can be reconstructed from what was in the past thought to be partial information. CS has two distinct major approaches to sparse recovery that each present different benefits and shortcomings. The first, l1-minimization methods such as Basis Pursuit use a linear optimization problem to recover the signal. This method provides strong guarantees and stability, but relies on Linear Programming, whose methods do not yet have strong polynomia...
In recent years, compressed sensing (CS) has attracted considerable attention in areas of applied mathematics, computer science, and electrical engineering by suggesting that it may be possible to surpass the traditional limits of sampling theory. CS builds upon the fundamental fact that we can represent many signals using only a few non-zero coefficients in a suitable basis or dictionary. Nonlinear optimization can then enable recovery of such signals from very few measurements. In this chapter, we provide an up-to-date review of the basic theory underlying CS. After a brief historical overview, we begin with a discussion of sparsity and other low-dimensional signal models. We then treat the central question of how to accurately recover a high-dimensional signal from a small set of measurements and provide performance guarantees for a variety of sparse recovery algorithms. We conclude with a discussion of some extensions of the sparse recovery framework. In subsequent chapters of the book, we will see how the fundamentals presented in this chapter are extended in many exciting directions, including new models for describing structure in both analog and discrete-time signals, new sensing design techniques, more advanced recovery results, and emerging applications.
Compressive sensing (CS) is a novel sampling paradigm that samples signals in a much more efficient way than the established Nyquist Sampling Theorem. CS has recently gained a lot of attention due to its exploitation of signal sparsity. Sparsity, an inherent characteristic of many natural signals, enables the signal to be stored in few samples and subsequently be recovered accurately, courtesy of compressive sensing. This article gives a brief background on the origins of this idea, reviews the basic mathematical foundation of the theory and then goes on to highlight different areas of its application with a major emphasis on communications and network domain. Finally, the survey concludes by identifying new areas of research where CS could be beneficial.
IEEE Transactions on Signal Processing, 2015
Greed is good. However, the tighter you squeeze, the less you have. In this paper, a less greedy algorithm for sparse signal reconstruction in compressive sensing, named orthogonal matching pursuit with thresholding is studied. Using the global 2-coherence , which provides a "bridge" between the well known mutual coherence and the restricted isometry constant, the performance of orthogonal matching pursuit with thresholding is analyzed and more general results for sparse signal reconstruction are obtained. It is also shown that given the same assumption on the coherence index and the restricted isometry constant as required for orthogonal matching pursuit, the thresholding variation gives exactly the same reconstruction performance with significantly less complexity.
2017
In this paper, at first, compressive sensing theory involves introducing measurement matrices to dedicate the signal dimension and so sensing cost reduction, and sparse domain to examine the conditions for the possibility of signal recovering, are explained. In addition, three well known recovery algorithms called Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), and L1-Norm are briefly introduced. Then, the performance of three mentioned recovery algorithms are compared with respect to the mean square error (MSE) and the result images quality. For this purpose, Gaussian and Bernoulli as the measurement matrices are used, where Haar and Fourier as sparse domains are applied.
Reconstruction of sparse signals acquired in reduced dimensions requires the solution with minimum 0 norm. As solving the 0 minimization directly is unpractical, a number of algorithms have appeared for finding an indirect solution. A semi-greedy approach, A* Orthogonal Matching Pursuit (A*OMP), is proposed in [1] where the solution is searched on several paths of a search tree. Paths of the tree are evaluated and extended according to some cost function, for which novel dynamic auxiliary cost functions are suggested. This paper describes the A*OMP algorithm and the proposed cost functions briefly. The novel dynamic auxiliary cost functions are shown to provide improved results as compared to a conventional choice. Reconstruction performance is illustrated on both synthetically generated data and real images, which show that the proposed scheme outperforms well-known CS reconstruction methods.
IEEE Transactions on Signal Processing, 2000
Compressed-Sensing (CS) offers a joint compression-and sensing-processes, based on the existence of a sparse representation of the treated signal and a set of projected measurements. Work on CS thus far typically assumes that the projections are drawn at random. In this paper we consider the optimization of these projections. As a direct such optimization is prohibitive, we target an average measure of the mutualcoherence of the effective dictionary, and demonstrate that this leads to better CS reconstruction performance. Both the Basis-Pursuit and the Orthogonal-Matching-Pursuit are shown to benefit from the newly designed projections, with a reduction of the error-rate by a factor of 10 and beyond.
Compressed sensing was introduced some ten years ago as an effective way of acquiring signals, which possess a sparse or nearly sparse representation in a suitable basis or dictionary. Dueto its solid mathematical backgrounds, it quickly attracted the attention of mathematicians from several different areas, so that the most important aspects of the theory are nowadays very well understood. In recent years, its applications started to spread out through applied mathematics, signal processing, and electrical engineering. The aim of this chapter is to provide an introduction into the basic concepts of compressed sensing. In the first part of this chapter, we present the basic mathematical concepts of compressed sensing, including the Null Space Property, Restricted Isometry Property, their connection to basis pursuit and sparse recovery, and construction of matrices with small restricted isometry constants. This presentation is easily accessible, largely self-contained, and includes p...
Proceedings Elmar 2011, 2011
Compressive sensing is a new approach of sampling theory, which assumes that signal can be exactly recovered from incomplete information. It relies on properties such as incoherence, signal sparsity and compressibility, and does not follow traditional acquisition process based on transform coding. Sensing procedure is very simple, nonadaptive method that employs linear projections of signal onto test functions. Set of test functions is arranged in the measurement matrix that allows acquiring random samples of original signal. Signal reconstruction is achieved from small amount of data by an optimization process which has the aim to find the sparsest vector with transform coefficients among all possible solutions. This paper gives an overview of compressive sensing theory, background, measurement and reconstruction processes. Reconstruction process was presented on a few types of signals at the end of this paper. Experimental results show that accurate reconstruction is possible for various type of signals.
Compressed sensing is a novel research area, which was introduced in 2006, and since then has already become a key concept in various areas of applied mathematics, computer science, and electrical engineering. It surprisingly predicts that high-dimensional signals, which allow a sparse representation by a suitable basis or, more generally, a frame, can be recovered from what was previously considered highly incomplete linear measurements by using efficient algorithms. This article shall serve as an introduction to and a survey about compressed sensing.
This paper represents the reconstruction of sampled signal in CS by using OMP algorithm. We have used the concept of compressive sensing for sub Nyquist sampling of sparse signal. Compressive sensing reconstruction methods have complex algorithms of l1 optimisation to reconstruct a signal sampled at sub nyquist rate. But out of those algorithm OMP algorithm is fast and computationally efficient. To prove the concept of CS implementation, we have simulated OMP algorithm for recovery of sparse signal of length 256 with sparsity 8.
Compressed sensing or compressive sensing or CS is a new data acquisition protocol that has been an active research area for nearly a decade. It samples the signal of interest at a rate much below the Shannon nyquist rate and has led to better results in many cases as compared to the traditional Shannon – nyquist sampling theory. This paper surveys the theory of Compressive sensing and its applications in various fields of interest.
2010
Compressive sensing investigates the recovery of a signal that can be sparsely represented in an orthonormal basis or overcomplete dictionary given a small number of linear combinations of the signal. We present a novel matching pursuit algorithm that uses the measurements to probabilistically select a subset of bases that is likely to contain the true bases constituting the signal. The algorithm is successful in recovering the original signal in cases where deterministic matching pursuit algorithms fail. We also show that exact recovery is possible when the number of nonzero coefficients is upto one less than the number of measurements. This overturns a previously held assumption in compressive sensing research.
ArXiv, 2017
A signal is sparse in one of its representation domain if the number of nonzero coefficients in that domain is much smaller than the total number of coefficients. Sparse signals can be reconstructed from a very reduced set of measurements/observations. The topic of this paper are conditions for the unique reconstruction of sparse signals from a reduced set of observations. After the basic definitions are introduced, the unique reconstruction conditions are reviewed using the spark, restricted isometry, and coherence of the measurement matrix. Uniqueness of the reconstruction of signals sparse in the discrete Fourier domain (DFT), as the most important signal transformation domain, is considered as well.
International Journal of Communications, Network and System Sciences, 2015
In digital signal processing (DSP), Nyquist-rate sampling completely describes a signal by exploiting its bandlimitedness. Compressed Sensing (CS), also known as compressive sampling, is a DSP technique efficiently acquiring and reconstructing a signal completely from reduced number of measurements, by exploiting its compressibility. The measurements are not point samples but more general linear functions of the signal. CS can capture and represent sparse signals at a rate significantly lower than ordinarily used in the Shannon's sampling theorem. It is interesting to notice that most signals in reality are sparse; especially when they are represented in some domain (such as the wavelet domain) where many coefficients are close to or equal to zero. A signal is called K-sparse, if it can be exactly represented by a basis, { } 1 ψ N i i = , and a set of coefficients k x , where only K coefficients are nonzero. A signal is called approximately K-sparse, if it can be represented up to a certain accuracy using K non-zero coefficients. As an example, a K-sparse signal is the class of signals that are the sum of K sinusoids chosen from the N harmonics of the observed time interval. Taking the DFT of any such signal would render only K non-zero values k x. An example of approximately sparse signals is when the coefficients k x , sorted by magnitude, decrease following a power law. In this case the sparse approximation constructed by choosing the K largest coefficients is guaranteed to have an approximation error that decreases with the same power law as the coefficients. The main limitation of CS-based systems is that they are employing iterative algorithms to recover the signal. The sealgorithms are slow and the hardware solution has become crucial for higher performance and speed. This technique enables fewer data samples than traditionally required when capturing a signal with relatively high bandwidth, but a low information rate. As a main feature of CS, efficient algorithms such as 1 -minimization can be used for recovery. This paper gives a survey of both theoretical and numerical aspects of compressive sensing technique and its applications. The theory of CS has many potential applications in signal processing, wireless communication, cognitive radio and medical imaging.
Applications of Digital Signal Processing, 2011
2011 National Conference on Communications (NCC), 2011
Compressed Sensing (CS) provides a set of mathematical results showing that sparse signals can be exactly reconstructed from a relatively small number of random linear measurements. A particularly appealing greedy-approach to signal reconstruction from CS measurements is the so called Orthogonal Matching Pursuit (OMP). We propose two modifications to the basic OMP algorithm, which can be handy in different situations.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.