We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce an accurate estimate $\hat{\bf x}$ even in the presence of additive noise. Low density frames are sparse matrices and have small storage requirements. Our decoding algorithms for these frames have $O(M)$ complexity. Simulation results are provided, demonstrating that our approach significantly outperforms state-of-the-art recovery algorithms for numerous cases of interest. In particular, for Gaussian sparse signals and Gaussian noise, we are within 2 dB range of the theoretical lower bound in most cases.
Is compressive sensing overrated? Or can it live up to our expectations? What will come after compressive sensing and sparsity? And what has Galileo Galilei got to do with it? Compressive sensing has taken the signal processing community by storm. A large corpus of research devoted to the theory and numerics of compressive sensing has been published in the last few years. Moreover, compressive sensing has inspired and initiated intriguing new research directions, such as matrix completion. Potential new applications emerge at a dazzling rate. Yet some important theoretical questions remain ope…
We consider the total variation (TV) minimization problem used for compressive sensing and solve it using the generalized alternating projection (GAP) algorithm. Extensive results demonstrate the high performance of proposed algorithm on compressive sensing, including two dimensional images, hyperspectral images and videos. We further derive the Alternating Direction Method of Multipliers (ADMM) framework with TV minimization for video and hyperspectral image compressive sensing under the CACTI and CASSI framework, respectively. Connections between GAP and ADMM are also provided.
Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, we show how to recover the support of sparse high-dimensional vectors in the one-bit compressive sensing framework with an asymptotically near-optimal number of measurements. We also improve the bounds on the number of measurements for approximately recovering vectors from one-bit compressive sensing measurements. Our results are universal, namely the same measurement scheme works …
In most compressive sensing problems l1 norm is used during the signal reconstruction process. In this article the use of entropy functional is proposed to approximate the l1 norm. A modified version of the entropy functional is continuous, differentiable and convex. Therefore, it is possible to construct globally convergent iterative algorithms using Bregman's row action D-projection method for compressive sensing applications. Simulation examples are presented.
In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide an explicit trade-off between the rate and the decoding complexity. The key difference of compressive sensing and traditional information theoretic approaches is at their decoding side. Although optimal decoders to recover the original signal, compressed by source coding have high complexity, the compressive sensing decoder is a linear or convex optimizatio…
We propose a joint source-channel-network coding scheme, based on compressive sensing principles, for wireless networks with AWGN channels (that may include multiple access and broadcast), with sources exhibiting temporal and spatial dependencies. Our goal is to provide a reconstruction of sources within an allowed distortion level at each receiver. We perform joint source-channel coding at each source by randomly projecting source values to a lower dimensional space. We consider sources that satisfy the restricted eigenvalue (RE) condition as well as more general sources for which the randomn…
Sequential Compressive Sensing, which may be widely used in sensing devices, is a popular topic of recent research. This paper proposes an online recovery algorithm for sparse approximation of sequential compressive sensing. Several techniques including warm start, fast iteration, and variable step size are adopted in the proposed algorithm to improve its online performance. Finally, numerical simulations demonstrate its better performance than the relative art.
This paper introduces a new framework of fast and efficient sensing matrices for practical compressive sensing, called Structurally Random Matrix (SRM). In the proposed framework, we pre-randomize a sensing signal by scrambling its samples or flipping its sample signs and then fast-transform the randomized samples and finally, subsample the transform coefficients as the final sensing measurements. SRM is highly relevant for large-scale, real-time compressive sensing applications as it has fast computation and supports block-based processing. In addition, we can show that SRM has theoretical se…
We study the average distortion introduced by scalar, vector, and entropy coded quantization of compressive sensing (CS) measurements. The asymptotic behavior of the underlying quantization schemes is either quantified exactly or characterized via bounds. We adapt two benchmark CS reconstruction algorithms to accommodate quantization errors, and empirically demonstrate that these methods significantly reduce the reconstruction distortion when compared to standard CS techniques.
Compressive sensing (CS) is a sampling technique designed for reducing the complexity of sparse data acquisition. One of the major obstacles for practical deployment of CS techniques is the signal reconstruction time and the high storage cost of random sensing matrices. We propose a new structured compressive sensing scheme, based on codes of graphs, that allows for a joint design of structured sensing matrices and logarithmic-complexity reconstruction algorithms. The compressive sensing matrices can be shown to offer asymptotically optimal performance when used in combination with Orthogonal …
We consider compressive sensing as a source coding method for signal transmission. We concatenate a convolutional coding system with 1-bit compressive sensing to obtain a serial concatenated system model for sparse signal transmission over an AWGN channel. The proposed source/channel decoder, which we refer to as turbo CS, is robust against channel noise and its signal reconstruction performance at the receiver increases considerably through iterations. We show 12 dB improvement with six turbo CS iterations compared to a non-iterative concatenated source/channel decoder.
In this paper, data-aided sensing as a cross-layer approach in Internet-of-Things (IoT) applications is studied, where multiple IoT nodes collect measurements and transmit them to an Access Point (AP). It is assumed that measurements have a sparse representation (due to spatial correlation) and the notion of Compressive Sensing (CS) can be exploited for efficient data collection. For data-aided sensing, a node selection criterion is proposed to efficiently reconstruct a target signal through iterations with a small number of measurements from selected nodes. Together with Compressive Random Ac…
Wideband spectrum sensing is a critical component of a functioning cognitive radio system. Its major challenge is the too high sampling rate requirement. Compressive sensing (CS) promises to be able to deal with it. Nearly all the current CS based compressive wideband spectrum sensing methods exploit only the frequency sparsity to perform. Motivated by the achievement of a fast and robust detection of the wideband spectrum change, total variation mnimization is incorporated to exploit the temporal and frequency structure information to enhance the sparse level. As a sparser vector is obtained,…
Instituto de Telecomunicações（电信研究所）；Instituto Superior Técnico, Technical University of Lisbon（里斯本技术大学高等技术学院）
We propose a new method, {\it binary fused compressive sensing} (BFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed algorithm is a modification of the previous {\it binary iterative hard thresholding} (BIHT) algorithm, where, in addition to the sparsity constraint, the total-variation of the recovered signal is upper constrained. As in BIHT, the data term of the objective function is an one-sided $\ell_1$ (or $\ell_2$) norm. Experiments on the recovery of sparse piece-wise smooth signals show that the proposed algorithm is able to take advantag…
Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensiv…
In this paper, the theoretical analysis of compressive sensing via random filter, firstly outlined by J. Romberg [compressive sensing by random convolution, submitted to SIAM Journal on Imaging Science on July 9, 2008], has been refined or generalized to the design of general random filter used for compressive sensing. This universal CS measurement consists of two parts: one is from the convolution of unknown signal with a random waveform followed by random time-domain subsampling; the other is from the directly time-domain subsampling of the unknown signal. It has been shown that the proposed…
Existing approaches to compressive sensing of frequency-sparse signals focuses on signal recovery rather than spectral estimation. Furthermore, the recovery performance is limited by the coherence of the required sparsity dictionaries and by the discretization of the frequency parameter space. In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most exis…
We study the recovery conditions of weighted $\ell_1$ minimization for real-valued signal reconstruction from phaseless compressive sensing measurements when partial support information is available. A strong restricted isometry property condition is provided to ensure the stable recovery. Moreover, we present the weighted null space property as the sufficient and necessary condition for the success of $k$-sparse phaseless recovery via weighted $\ell_1$ minimization. Numerical experiments are conducted to illustrate our results.
This paper presents a novel, model-based compressive antenna design method for high sensing capacity imaging applications. Given a set of design constraints, the method maximizes the sensing capacity of the compressive antenna by varying the constitutive properties of scatterers distributed along the antenna. Preliminary 2D design results demonstrate the new method's ability to produce antenna configurations with enhanced imaging capabilities.
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary samples---only the sign of each linear measurement is maintained. Existing results in one-bit compressive sensing rely on the assumption that the signals of interest are sparse in some fixed orthonormal basis. However, in most practical applications, signals are sparse with respect to an overcomplete dictionary, rather than a basis. There has already been a surge of act…
Compressive sensing is the newly emerging method in information technology that could impact array beamforming and the associated engineering applications. However, practical measurements are inevitably polluted by noise from external interference and internal acquisition process. Then, compressive sensing based beamforming was studied in this work for those noisy measurements with a signal-to-noise ratio. In this article, we firstly introduced the fundamentals of compressive sensing theory. After that, we implemented two algorithms (CSB-I and CSB-II). Both algorithms are proposed for those pr…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is established when the reconstruction is also required to be sparse. The result holds in general when the distortion constraint is on the expected $p$-norm of error between the source and the reconstruction. A new restricted isometry like property is introduced for this purpose and the existence of matrices that satisfy this property is shown.
This letter proposes a novel distributed compressed estimation scheme for sparse signals and systems based on compressive sensing techniques. The proposed scheme consists of compression and decompression modules inspired by compressive sensing to perform distributed compressed estimation. A design procedure is also presented and an algorithm is developed to optimize measurement matrices, which can further improve the performance of the proposed distributed compressed estimation scheme. Simulations for a wireless sensor network illustrate the advantages of the proposed scheme and algorithm in t…
We propose to reduce the original well-posed problem of compressive sensing to weighted-MAX-SAT. Compressive sensing is a novel randomized data acquisition approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate. The original problem of compressive sensing in sparse recovery is NP-hard; therefore, in addition to restrictions for the uniqueness of the sparse solution, the coding matrix has also to satisfy additional stringent constraints -usually the restricted isometry property (RIP)- so we can handle it by its convex or nonconvex re…
We introduce q-ary compressive sensing, an extension of 1-bit compressive sensing. We propose a novel sensing mechanism and a corresponding recovery procedure. The recovery properties of the proposed approach are analyzed both theoretically and empirically. Results in 1-bit compressive sensing are recovered as a special case. Our theoretical results suggest a tradeoff between the quantization parameter q, and the number of measurements m in the control of the error of the resulting recovery algorithm, as well its robustness to noise.
The physics of compressive sensing (CS) and the gradient-based recovery algorithms are presented. First, the different forms for CS are summarized. Second, the physical meanings of coherence and measurement are given. Third, the gradient-based recovery algorithms and their geometry explanations are provided. Finally, we conclude the report and give some suggestion for future work.
We study the recovery results of $\ell_p$-constrained compressive sensing (CS) with $p\geq 1$ via robust width property and determine conditions on the number of measurements for standard Gaussian matrices under which the property holds with high probability. Our paper extends the existing results in Cahill and Mixon (2014) from $\ell_2$-constrained CS to $\ell_p$-constrained case with $p\geq 1$ and complements the recovery analysis for robust CS with $\ell_p$ loss function.
Nonlinear sparse sensing (NSS) techniques have been adopted for realizing compressive sensing in many applications such as Radar imaging. Unlike the NSS, in this paper, we propose an adaptive sparse sensing (ASS) approach using reweighted zero-attracting normalized least mean fourth (RZA-NLMF) algorithm which depends on several given parameters, i.e., reweighted factor, regularization parameter and initial step-size. First, based on the independent assumption, Cramer Rao lower bound (CRLB) is derived as for the trademark of performance comparisons. In addition, reweighted factor selection meth…
Compressive sensing is a novel approach that linearly samples sparse or compressible signals at a rate much below the Nyquist-Shannon sampling rate and outperforms traditional signal processing techniques in acquiring and reconstructing such signals. Compressive sensing with matrix uncertainty is an extension of the standard compressive sensing problem that appears in various applications including but not limited to cognitive radio sensing, calibration of the antenna, and deconvolution. The original problem of compressive sensing is NP-hard so the traditional techniques, such as convex and no…
In this paper, we endeavor for predicting the performance of quantized compressive sensing under the use of sparse reconstruction estimators. We assume that a high rate vector quantizer is used to encode the noisy compressive sensing measurement vector. Exploiting a block sparse source model, we use Gaussian mixture density for modeling the distribution of the source. This allows us to formulate an optimal rate allocation problem for the vector quantizer. Considering noisy CS quantized measurements, we analyze upper- and lower-bounds on reconstruction error performance guarantee of two estimat…
We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover such a signal if the sensing matrix is a complex Gaussian random matrix and the number of measurements is large compared to the signal sparsity. Our approach consists in recasting the (non-linear) PO-CS scheme as a linear compressive sensing model. We built it from a signal normalization constraint and a phase-consistency constraint. Practically, we achieve…
The performance of existing approaches to the recovery of frequency-sparse signals from compressed measurements is limited by the coherence of required sparsity dictionaries and the discretization of frequency parameter space. In this paper, we adopt a parametric joint recovery-estimation method based on model selection in spectral compressive sensing. Numerical experiments show that our approach outperforms most state-of-the-art spectral CS recovery approaches in fidelity, tolerance to noise and computation efficiency.
For wideband spectrum sensing, compressive sensing has been proposed as a solution to speed up the high dimensional signals sensing and reduce the computational complexity. Compressive sensing consists of acquiring the essential information from a sparse signal and recovering it at the receiver based on an efficient sampling matrix and a reconstruction technique. In order to deal with the uncertainty, improve the signal acquisition performance, and reduce the randomness during the sensing and reconstruction processes, compressive sensing requires a robust sampling matrix and an efficient recon…
In this paper, we propose \textit{coded compressive sensing} that recovers an $n$-dimensional integer sparse signal vector from a noisy and quantized measurement vector whose dimension $m$ is far-fewer than $n$. The core idea of coded compressive sensing is to construct a linear sensing matrix whose columns consist of lattice codes. We present a two-stage decoding method named \textit{compute-and-recover} to detect the sparse signal from the noisy and quantized measurements. In the first stage, we transform such measurements into noiseless finite-field measurements using the linearity of latti…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises of processing the random projections directly, without first reconstructing the signal. In this paper, we show that circulant sensing matrices allow to perform a variety of classical signal processing tasks such as filtering, interpolation, registration, transforms, and so forth, directly in the compressed domain and in an exact fashion, \emph{i.e.}, without…
Cost-efficient compressive sensing of big media data with fast reconstructed high-quality results is very challenging. In this paper, we propose a new large-scale image compressive sensing method, composed of operator-based strategy in the context of fixed point continuation method and weighted LASSO with tree structure sparsity pattern. The main characteristic of our method is free from any assumptions and restrictions. The feasibility of our method is verified via simulations and comparisons with state-of-the-art algorithms.
In this paper, the design of universal compressive sensing filter based on normal filters including the lowpass, highpass, bandpass, and bandstop filters with different cutoff frequencies (or bandwidth) has been developed to enable signal acquisition with sub-Nyquist sampling. Moreover, to control flexibly the size and the coherence of the compressive sensing filter, as an example, the microstrip filter based on defected ground structure (DGS) has been employed to realize the compressive sensing filter. Of course, the compressive sensing filter also can be constructed along the identical idea …
In this paper we propose a novel form of clipping mitigation in OFDM using compressive sensing that completely avoids tone reservation and hence rate loss for this purpose. The method builds on selecting the most reliable perturbations from the constellation lattice upon decoding at the receiver, and performs compressive sensing over these observations in order to completely recover the temporally sparse nonlinear distortion. As such, the method provides a unique practical solution to the problem of initial erroneous decoding decisions in iterative ML methods, offering both the ability to augm…
Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, a…
We propose a new method, {\it robust binary fused compressive sensing} (RoBFCS), to recover sparse piece-wise smooth signals from 1-bit compressive measurements. The proposed method is a modification of our previous {\it binary fused compressive sensing} (BFCS) algorithm, which is based on the {\it binary iterative hard thresholding} (BIHT) algorithm. As in BIHT, the data term of the objective function is a one-sided $\ell_1$ (or $\ell_2$) norm. Experiments show that the proposed algorithm is able to take advantage of the piece-wise smoothness of the original signal and detect sign flips and c…
We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired by message passing algorithms on bipartite graphs. Its asymptotic error performance can be accurately predicted and tracked through the state evolution formalism. We utilize these results to design mean-square optimal scalar quantizers for relaxed BP signal reconstruction and empirically demonstrate the superior error performance of the resulting quantizers.
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can perfectly recover such a signal with high probability and up to global unknown amplitude if the sensing matrix is a complex Gaussian random matrix and if the number of measurements is large compared to the complexity level of the signal space. Our approach proceeds by recasting the (non-linear) PO-CS scheme as a linear compressive sensing model built from a…
An analysis of the influence of missing samples in signals exhibiting sparsity in the Hermite transform domain is provided. Based on the statistical properties derived for the Hermite coefficients of randomly undersampled signal, the probability of success in detection of signal components support is determined. Based on the probabilistic analysis, a threshold for the detection of signal components is provided. It is a crucial step in the definition of a simple non-iterative algorithm for compressive sensing signal reconstruction. The derived theoretical concepts are proved on several examples…
In a sensor network with remote sensor devices, it is important to have a method that can accurately localize a sound event with a small amount of data transmitted from the sensors. In this paper, we propose a novel method for localization of a sound source using compressive sensing. Instead of sampling a large amount of data at the Nyquist sampling rate in time domain, the acoustic sensors take compressive measurements integrated in time. The compressive measurements can be used to accurately compute the location of a sound source.
Simultaneous sparse approximation is a generalization of the standard sparse approximation, for simultaneously representing a set of signals using a common sparsity model. Generalizing the compressive sensing concept to the simultaneous sparse approximation yields distributed compressive sensing (DCS). DCS finds the sparse representation of multiple correlated signals using the common + innovation signal model. However, DCS is not efficient for joint recovery of a large number of signals since it requires large memory and computational time. In this paper, we propose a new hierarchical algorit…
In this paper we deal with the linear frequency modulated signals and radar signals that are affected by disturbance which is the inevitable phenomenon in everyday communications. The considered cases represent the cases when the signals of interest overlap with other signals or with noise. In order to successfully separate these signals we propose the compressive sensing method, which states that the useful signal part can be separated successfully from a small amount of measurements as long as the acquired signal can be presented as sparse in a certain transformation domain. The effectivenes…
In the Cognitive Compressive Sensing (CCS) problem, a Cognitive Receiver (CR) seeks to optimize the reward obtained by sensing an underlying $N$ dimensional random vector, by collecting at most $K$ arbitrary projections of it. The $N$ components of the latent vector represent sub-channels states, that change dynamically from "busy" to "idle" and vice versa, as a Markov chain that is biased towards producing sparse vectors. To identify the optimal strategy we formulate the Multi-Armed Bandit Compressive Sensing (MAB-CS) problem, generalizing the popular Cognitive Spectrum Sensing model, in whic…
In this paper, a cooperative spectrum sensing scheme based on compressive sensing is proposed. In this scheme, secondary users (SUs) are organized in clusters. In each cluster, SUs forward their compressed signals to the cluster head. Then, the cluster heads report the local sensing data to the fusion center to make the final decision. Analog to information converter is adopted to acquire the received SUs signals. The proposed scheme is evaluated using several metrics, including probability of detection, compression ratio, probability of error, and processing time. The simulation results are c…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm generalises and extends previous iterative hard thresholding algorithms and we give sufficient conditions for successful reconstruction of the original data signal. In addition we show that by underestimating the sparsity of the data signal we can increase the success rate of the algorithm. We also present a number of modifications to this algorithm: the incorporation…
In this paper, we consider a cognitive radio network in which energy constrained secondary users (SUs) can harvest energy from the randomly deployed power beacons (PBs). A new frame structure is proposed for the considered network. A wireless power transfer (WPT) model and a compressive spectrum sensing model are introduced. In the WPT model, a new WPT scheme is proposed, and the closed-form expressions for the power outage probability are derived. In compressive spectrum sensing model, two scenarios are considered: 1) Single SU, and 2) Multiple SUs. In the single SU scenario, in order to redu…
It is well established in the compressive sensing (CS) literature that sensing matrices whose elements are drawn from independent random distributions exhibit enhanced reconstruction capabilities. In many CS applications, such as electromagnetic imaging, practical limitations on the measurement system prevent one from generating sensing matrices in this fashion. Although one can usually randomized the measurements to some degree, these sensing matrices do not achieve the same reconstruction performance as the truly randomized sensing matrices. In this paper, we present a novel method, based up…
The fundamental problem considered in this paper is "What is the \textit{energy} consumed for the implementation of a \emph{compressive sensing} decoding algorithm on a circuit?". Using the "information-friction" framework, we examine the smallest amount of \textit{bit-meters} as a measure for the energy consumed by a circuit. We derive a fundamental lower bound for the implementation of compressive sensing decoding algorithms on a circuit. In the setting where the number of measurements scales linearly with the sparsity and the sparsity is sub-linear with the length of the signal, we show tha…
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 restricte…
Compressive sensing (CS) is a data acquisition technique that measures sparse or compressible signals at a sampling rate lower than their Nyquist rate. Results show that sparse signals can be reconstructed using greedy algorithms, often requiring prior knowledge such as the signal sparsity or the noise level. As a substitute to prior knowledge, cross validation (CV), a statistical method that examines whether a model overfits its data, has been proposed to determine the stopping condition of greedy algorithms. This paper first analyzes cross validation in a general compressive sensing framewor…
This paper considers the problem of compressive sensing over a finite alphabet, where the finite alphabet may be inherent to the nature of the data or a result of quantization. There are multiple examples of finite alphabet based static as well as time-series data with inherent sparse structure; and quantizing real values is an essential step while handling real data in practice. We show that there are significant benefits to analyzing the problem while incorporating its finite alphabet nature, versus ignoring it and employing a conventional real alphabet based toolbox. Specifically, when the …
Compressive sensing (CS) is a promising technology for realizing energy-efficient wireless sensors for long-term health monitoring. In this paper, we propose a data-driven CS framework that learns signal characteristics and individual variability from patients' data to significantly enhance CS performance and noise resilience. This is accomplished by a co-training approach that optimizes both the sensing matrix and dictionary towards improved restricted isometry property (RIP) and signal sparsity, respectively. Experimental results upon ECG signals show that our framework is able to achieve be…
Many communication systems involve high bandwidth, while sparse, radio frequency (RF) signals. Working with high frequency signals requires appropriate system-level components such as high-speed analog-to-digital converters (ADC). In particular, an analog signal should be sampled at rates that meet the Nyquist requirements to avoid aliasing. However, implementing high-speed ADC devices can be a limiting factor as well as expensive. To mitigate the caveats with high-speed ADC, the solution space can be explored in several dimensions such as utilizing the compressive sensing (CS) framework in or…
Energy and direction are tow basic properties of a vector. A discrete signal is a vector in nature. RIP of compressive sensing can not show the direction information of a signal but show the energy information of a signal. Hence, RIP is not complete. Orthogonal matrices can preserve angles and lengths. Preservation of length can show energies of signals like RIP do; and preservation of angle can show directions of signals. Therefore, Restricted Conformal Property (RCP) is proposed according to preservation of angle. RCP can show the direction of a signal just as RIP shows the energy of a signa…
In this work we address the problem of blindly reconstructing compressively sensed signals by exploiting the co-sparse analysis model. In the analysis model it is assumed that a signal multiplied by an analysis operator results in a sparse vector. We propose an algorithm that learns the operator adaptively during the reconstruction process. The arising optimization problem is tackled via a geometric conjugate gradient approach. Different types of sampling noise are handled by simply exchanging the data fidelity term. Numerical experiments are performed for measurements corrupted with Gaussian …
