The literature on compressed sensing has focused almost entirely on settings where the signal is noiseless and the measurements are contaminated by noise. In practice, however, the signal itself is often subject to random noise prior to measurement. We briefly study this setting and show that, for the vast majority of measurement schemes employed in compressed sensing, the two models are equivalent with the important difference that the signal-to-noise ratio is divided by a factor proportional to p/n, where p is the dimension of the signal and n is the number of observations. Since p/n is often large, this leads to noise folding which can have a severe impact on the SNR.
Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes of encoders are considered, namely optimal nonlinear, optimal linear and random linear encoders. Focusing on optimal decoders, we investigate the fundamental tradeoff between measurement rate and reconstruction fidelity gauged by error probability and noise sensitivity in the absence and presence of measurement noise, respectively. The optimal phase transit…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance since they cannot be implemented on real acquisition systems. In this paper, we study a new random sampling approach that consists in projecting the signal over blocks of sensing vectors. A typical example is the case of blocks made of horizontal lines in the 2D Fourier plane. We provide theoretical results on the number of blocks that are required for exact s…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon basis pursuit for exact recovery in compressed sensing. We exhibit a condition that links the accuracy of the weights to the RIP and incoherency constants, which ensures exact recovery. In a second part, we introduce a new algorithm for matrix completion, based on the idea of iterative reweighting. Since a weighted nuclear "norm" is typically non-convex, it c…
We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via latent group LASSO regularizations. We achieve smoothness in the signal via fusion. We develop low-complexity solvers for our proposed formulations through the alternating direction method of multipliers.
We examine the use of a structured thresholding algorithm for sparse underwater channel estimation using compressed sensing. This method shows some improvements over standard algorithms for sparse channel estimation such as matching pursuit, iterative detection and least squares.
This paper proposes a simple adaptive sensing and group testing algorithm for sparse signal recovery. The algorithm, termed Compressive Adaptive Sense and Search (CASS), is shown to be near-optimal in that it succeeds at the lowest possible signal-to-noise-ratio (SNR) levels, improving on previous work in adaptive compressed sensing. Like traditional compressed sensing based on random non-adaptive design matrices, the CASS algorithm requires only k log n measurements to recover a k-sparse signal of dimension n. However, CASS succeeds at SNR levels that are a factor log n less than required by …
This letter proposes a low-computational Bayesian algorithm for noisy sparse recovery in the context of one bit compressed sensing with sensing matrix perturbation. The proposed algorithm which is called BHT-MLE comprises a sparse support detector and an amplitude estimator. The support detector utilizes Bayesian hypothesis test, while the amplitude estimator uses an ML estimator which is obtained by solving a convex optimization problem. Simulation results show that BHT-MLE algorithm offers more reconstruction accuracy than that of an ML estimator (MLE) at a low computational cost.
As a lossy compression framework, compressed sensing has drawn much attention in wireless telemonitoring of biosignals due to its ability to reduce energy consumption and make possible the design of low-power devices. However, the non-sparseness of biosignals presents a major challenge to compressed sensing. This study proposes and evaluates a spatio-temporal sparse Bayesian learning algorithm, which has the desired ability to recover such non-sparse biosignals. It exploits both temporal correlation in each individual biosignal and inter-channel correlation among biosignals from different chan…
This letter proposes a dictionary learning algorithm for blind one bit compressed sensing. In the blind one bit compressed sensing framework, the original signal to be reconstructed from one bit linear random measurements is sparse in an unknown domain. In this context, the multiplication of measurement matrix $\Ab$ and sparse domain matrix $Φ$, \ie $\Db=\AbΦ$, should be learned. Hence, we use dictionary learning to train this matrix. Towards that end, an appropriate continuous convex cost function is suggested for one bit compressed sensing and a simple steepest-descent method is exploited to…
Goal: This paper deals with the problems that some EEG signals have no good sparse representation and single channel processing is not computationally efficient in compressed sensing of multi-channel EEG signals. Methods: An optimization model with L0 norm and Schatten-0 norm is proposed to enforce cosparsity and low rank structures in the reconstructed multi-channel EEG signals. Both convex relaxation and global consensus optimization with alternating direction method of multipliers are used to compute the optimization model. Results: The performance of multi-channel EEG signal reconstruction…
Qom University of Technology（库姆理工大学）；Swinburne University of Technology（斯威本科技大学）；Sharif University of Technology（谢里夫理工大学）
This letter proposes a sparse diffusion steepest-descent algorithm for one bit compressed sensing in wireless sensor networks. The approach exploits the diffusion strategy from distributed learning in the one bit compressed sensing framework. To estimate a common sparse vector cooperatively from only the sign of measurements, steepest-descent is used to minimize the suitable global and local convex cost functions. A diffusion strategy is suggested for distributive learning of the sparse vector. Simulation results show the effectiveness of the proposed distributed algorithm compared to the stat…
We consider a linear stochastic bandit problem where the dimension $K$ of the unknown parameter $θ$ is larger than the sampling budget $n$. In such cases, it is in general impossible to derive sub-linear regret bounds since usual linear bandit algorithms have a regret in $O(K\sqrt{n})$. In this paper we assume that $θ$ is $S-$sparse, i.e. has at most $S-$non-zero components, and that the space of arms is the unit ball for the $||.||_2$ norm. We combine ideas from Compressed Sensing and Bandit Theory and derive algorithms with regret bounds in $O(S\sqrt{n})$.
We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has independent Gaussian entries, then one can recover a sparse signal x exactly by tractable \ell1 minimimization even if a positive fraction of the measurements are arbitrarily corrupted, provided the number of nonzero entries in x is O(m/(log(n/m) + 1)). 2) In the very general sensing model introduced in "A probabilistic and RIPless theory of compressed sensing…
Testing covariance structure is of significant interest in many areas of statistical analysis and construction of compressed sensing matrices is an important problem in signal processing. Motivated by these applications, we study in this paper the limiting laws of the coherence of an $n\times p$ random matrix in the high-dimensional setting where $p$ can be much larger than $n$. Both the law of large numbers and the limiting distribution are derived. We then consider testing the bandedness of the covariance matrix of a high dimensional Gaussian distribution which includes testing for independe…
Compressed sensing (sparse signal recovery) has been a popular and important research topic in recent years. By observing that natural signals are often nonnegative, we propose a new framework for nonnegative signal recovery using Compressed Counting (CC). CC is a technique built on maximally-skewed p-stable random projections originally developed for data stream computations. Our recovery procedure is computationally very efficient in that it requires only one linear scan of the coordinates. Our analysis demonstrates that, when 0<p<=0.5, it suffices to use M= O(C/eps^p log N) measurements so …
University College London（伦敦大学学院）；FU-Berlin（柏林自由大学）
We give a new, very general, formulation of the compressed sensing problem in terms of coordinate projections of an analytic variety, and derive sufficient sampling rates for signal reconstruction. Our bounds are linear in the coherence of the signal space, a geometric parameter independent of the specific signal and measurement, and logarithmic in the ambient dimension where the signal is presented. We exemplify our approach by deriving sufficient sampling densities for low-rank matrix completion and distance matrix completion which are independent of the true matrix.
Compressed sensing in MRI enables high subsampling factors while maintaining diagnostic image quality. This technique enables shortened scan durations and/or improved image resolution. Further, compressed sensing can increase the diagnostic information and value from each scan performed. Overall, compressed sensing has significant clinical impact in improving the diagnostic quality and patient experience for imaging exams. However, a number of challenges exist when moving compressed sensing from research to the clinic. These challenges include hand-crafted image priors, sensitive tuning parame…
University of Electronic Science and Technology of China（电子科技大学）；Stevens Institute of Technology（斯蒂文斯理工学院）
We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed sensing. The basic idea of the proposed method is to identify and remove the outliers from sparse signal recovery. To automatically identify the outliers, we employ a set of binary indicator hyperparameters to indicate which observations are outliers. These indicator hyperparameters are treated as random variables and assigned a beta process prior such that…
Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the parameterization of the Lorenz-96 model with two time-scales that mimics mid-latitude atmospheric dynamics with microscopic convective processes. Compressed sensing is used to build models (vector fields) to emulate the behavior of the fine-scale process, so that explicit simulations become an online benchmark for parameterization. We apply compressed sensin…
We adopt data structure in the form of cover trees and iteratively apply approximate nearest neighbour (ANN) searches for fast compressed sensing reconstruction of signals living on discrete smooth manifolds. Levering on the recent stability results for the inexact Iterative Projected Gradient (IPG) algorithm and by using the cover tree's ANN searches, we decrease the projection cost of the IPG algorithm to be logarithmically growing with data population for low dimensional smooth manifolds. We apply our results to quantitative MRI compressed sensing and in particular within the Magnetic Reson…
Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS theory is based on random Gaussian projection matrices, which satisfy recovery guarantees with high probability; however, sparse ternary {0, -1, +1} projections are more suitable for hardware implementation. In this paper, we present a deep learning approach to obtain very sparse ternary projections for compressed sensing. Our deep learning architecture jointly …
Iowa State University（爱荷华州立大学）；New York University（纽约大学）
Deep generative models have emerged as a powerful class of priors for signals in various inverse problems such as compressed sensing, phase retrieval and super-resolution. Here, we assume an unknown signal to lie in the range of some pre-trained generative model. A popular approach for signal recovery is via gradient descent in the low-dimensional latent space. While gradient descent has achieved good empirical performance, its theoretical behavior is not well understood. In this paper, we introduce the use of stochastic gradient Langevin dynamics (SGLD) for compressed sensing with a generativ…
This paper first present a new general completely perturbed compressed sensing (CS) model y=(A+E)(x+u)+e,called \emph{noise folding based on general completely perturbed CS system},~where $y\in R^m,~u \in R^m,~u\neq 0,~e\in R^m$, $A\in R^{m\times n},~m\ll n$,~$E\in R^{m\times n}$ with incorporating general nonzero perturbation E to sensing matrix A and noise u into signal x simultaneously based on the standard CS model y=Ax+e.~Our constructions mainly will whiten the new proposed CS model and explore into RIP,~coherence for A+E of the new CS model after being whitened.
We discuss the applicability of compressed sensing theory. We take a genuine look at both experimental results and theoretical works. We answer the following questions: 1) What can compressed sensing really do? 2) More importantly, why?
In this paper the authors describe the problem of acquisition of interfered signals and formulate a filtering problem. A frequency-selective compressed sensing technique is proposed as a solution to this problem. Signal acquisition is critical in facilitating frequency-selective compressed sensing. The authors propose a filtering compressed sensing parameter, which allows to assess if a given acquisition process makes frequency-selective compressed sensing possible for a given filtering problem. A numerical experiment which shows how the described method works in practice is conducted.
The restricted isometry property (RIP) has become well-known in the compressed sensing community. Recently, a weaken version of RIP was proposed for exact sparse recovery under weak moment assumptions. In this note, we prove that the weaken RIP is also sufficient for \textsl{stable and robust} sparse recovery by linking it with a recently introduced robust width property in compressed sensing. Moreover, we show that it can be widely apply to other compressed sensing instances as well.
In this letter, we propose a turbo compressed sensing algorithm with partial discrete Fourier transform (DFT) sensing matrices. Interestingly, the state evolution of the proposed algorithm is shown to be consistent with that derived using the replica method. Numerical results demonstrate that the proposed algorithm outperforms the well-known approximate message passing (AMP) algorithm when a partial DFT sensing matrix is involved.
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive character sequences. The Weil bound is then used to show that the matrix has asymptotically optimal coherence for $N=K^2$, and to present a sufficient condition on the sparsity level for unique sparse recovery. Also, the restricted isometry property (RIP) is statistically studied for the deterministic matrix. Using additive character sequences with small alp…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and compressed sensing has emerging applications in medical imaging, big data, and statistics. Finding practical matrix constructions and computationally efficient recovery algorithms for compressed sensing is an area of intense research interest. Many probabilistic matrix constructions have been proposed, and it is now well known that matrices with entries drawn …
Wireless tomography is a technique for inferring a physical environment within a monitored region by analyzing RF signals traversed across the region. In this paper, we consider wireless tomography in a two and higher dimensionally structured monitored region, and propose a multi-dimensional wireless tomography scheme based on compressed sensing to estimate a spatial distribution of shadowing loss in the monitored region. In order to estimate the spatial distribution, we consider two compressed sensing frameworks: vector-based compressed sensing and tensor-based compressed sensing. When the sh…
Compressed sensing is now established as an effective method for dimension reduction when the underlying signals are sparse or compressible with respect to some suitable basis or frame. One important, yet under-addressed problem regarding the compressive acquisition of analog signals is how to perform quantization. This is directly related to the important issues of how "compressed" compressed sensing is (in terms of the total number of bits one ends up using after acquiring the signal) and ultimately whether compressed sensing can be used to obtain compressed representations of suitable signa…
In this paper, we analyze the information theoretic lower bound on the necessary number of samples needed for recovering a sparse signal under different compressed sensing settings. We focus on the weighted graph model, a model-based framework proposed by Hegde et al. (2015), for standard compressed sensing as well as for one-bit compressed sensing. We study both the noisy and noiseless regimes. Our analysis is general in the sense that it applies to any algorithm used to recover the signal. We carefully construct restricted ensembles for different settings and then apply Fano's inequality to …
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in…
A new reconstruction method for Wigner function is reported for quantum tomography based on compressed sensing. By analogy with computed tomography, Wigner functions for some quantum states can be reconstructed with less measurements utilizing this compressed sensing based method.
In the present note we develop some theoretical results in the theory of anisotropic compressed sensing that allow to take structured sparsity and variable density structured sampling into account. We expect that the obtained results will be useful to derive explicit expressions for optimal sampling strategies in the non-Cartesian (radial, spiral, etc.) setting in MRI.
Although largely different concepts, echo state networks and compressed sensing models both rely on collections of random weights; as the reservoir dynamics for echo state networks, and the sensing coefficients in compressed sensing. Several methods for generating the random matrices and metrics to indicate desirable performance are well-studied in compressed sensing, but less so for echo state networks. This work explores any overlap in these compressed sensing methods and metrics for application to echo state networks. Several methods for generating the random reservoir weights are considere…
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…
This chapter gives an overview over recovery guarantees for total variation minimization in compressed sensing for different measurement scenarios. In addition to summarizing the results in the area, we illustrate why an approach that is common for synthesis sparse signals fails and different techniques are necessary. Lastly, we discuss a generalizations of recent results for Gaussian measurements to the subgaussian case.
In this paper, we provide a new approach to estimating the error of reconstruction from $ΣΔ$ quantized compressed sensing measurements. Our method is based on the restricted isometry property (RIP) of a certain projection of the measurement matrix. Our result yields simple proofs and a slight generalization of the best-known reconstruction error bounds for Gaussian and subgaussian measurement matrices.
This paper surveys recent work in applying ideas from graphical models and message passing algorithms to solve large scale regularized regression problems. In particular, the focus is on compressed sensing reconstruction via ell_1 penalized least-squares (known as LASSO or BPDN). We discuss how to derive fast approximate message passing algorithms to solve this problem. Surprisingly, the analysis of such algorithms allows to prove exact high-dimensional limit results for the LASSO risk. This paper will appear as a chapter in a book on `Compressed Sensing' edited by Yonina Eldar and Gitta Kutyn…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even smaller number of samples is sufficient when there exists prior knowledge about the distribution of the unknown vector, or when only partial recovery is needed. An information-theoretic lower bound with connections to free probability theory and an upper bound corresponding to a computationally simple thresholding estimator are derived. It is shown that…
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable to natural non-Gaussian distributions without further assumptions, as can be demonstrated by simple counter-examples. We show that approximately sparse signals that are not extremely sparse can be accurately reconstructed from single-bit measurements sampled according to a sub-gaussian distribution, and the reconstruction comes as the solution to a convex pr…
The weak-$\ell^p$ norm can be used to define a measure $s$ of sparsity. When we compute $s$ for the discrete cosine transform coefficients of a signal, the value of $s$ is related to the information content of said signal. We use this value of $s$ to define a reference-free index $\mathcal{E}$, called the sparsity index, that we can use to predict with high accuracy the quality of signal reconstruction in the setting of compressed sensing imaging. That way, when compressed sensing is framed in the context of sampling theory, we can use $\mathcal{E}$ to decide when to further partition the samp…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to machine-type communications. Coded compressed sensing uses a divide-and-conquer approach to break the sparse recovery task into sub-components whose dimensions are amenable to conventional compressed sensing solvers. The recovered fragments are then stitched together using a low complexity decoder. This article introduces an enhanced decoding algorithm for coded compre…
This paper addresses the topic of robust Bayesian compressed sensing over finite fields. For stationary and ergodic sources, it provides asymptotic (with the size of the vector to estimate) necessary and sufficient conditions on the number of required measurements to achieve vanishing reconstruction error, in presence of sensing and communication noise. In all considered cases, the necessary and sufficient conditions asymptotically coincide. Conditions on the sparsity of the sensing matrix are established in presence of communication noise. Several previously published results are generalized …
This paper describes performance bounds for compressed sensing in the presence of Poisson noise when the underlying signal, a vector of Poisson intensities, is sparse or compressible (admits a sparse approximation). The signal-independent and bounded noise models used in the literature to analyze the performance of compressed sensing do not accurately model the effects of Poisson noise. However, Poisson noise is an appropriate noise model for a variety of applications, including low-light imaging, where sensing hardware is large or expensive, and limiting the number of measurements collected i…
Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with orthogonal matching pursuit (OMP). The main part of STrMP is as concise as OMP and hence STrMP is simple to implement. In contrast to previous greedy algorithms for one-bit compressed sensing, STrMP only need to solve a convex and unconstraint subproblem at each iteration. Numerical experiments show that STrMP is fast and accurate for one-bit compressed sensing c…
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications, such as signal detection, motion detection and radar. Moreover, in these applications it is often not necessary to know the support of the signal exactly, but instead small errors in the support and signal are tolerable. Despite the abundance of work utilizing incoherent sensing matrices, for this type of tolerant recovery we suggest that coherence is actually…
The analysis sparsity model is a very effective approach in modern Compressed Sensing applications. Specifically, redundant analysis operators can lead to fewer measurements needed for reconstruction when employing the analysis $l_1$-minimization in Compressed Sensing. In this paper, we pick an eigenvector of the Zauner unitary matrix and -- under certain assumptions on the ambient dimension -- we build a spark deficient Gabor frame. The analysis operator associated with such a spark deficient Gabor frame, is a new (highly) redundant Gabor transform, which we use as a sparsifying transform in …
In this letter, a binary sparse Bayesian learning (BSBL) algorithm is proposed to slove the one-bit compressed sensing (CS) problem in both single measurement vector (SMV) and multiple measurement vectors (MMVs). By utilising the Bussgang-like decomposition, the one-bit CS problem can be approximated as a standard linear model. Consequently, the standard SBL algorithm can be naturally incorporated. Numerical results demonstrate the effectiveness of the BSBL algorithm.
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative character sequences. Precisely, a constant multiple of a cyclic shift of an $M$-ary power residue or Sidelnikov sequence is arranged as a column vector of the matrix, through modulating a primitive $M$-th root of unity. The Weil bound is then used to show that the matrix has asymptotically optimal coherence for large $K$ and $M$, and to present a sufficient con…
A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions on the number of measurements. However, in the context of image reconstruction, it has been extensively documented that sampling strategies based on Fourier measurements outperform this purportedly optimal approach. Motivated by this seeming paradox, we investigate the problem of optimal sampling for compressed sensing. Rigorously combining the theories of wavelet approximation and infinite-dimensional compressed sensing, our analysis leads to…
Data compression capability of "Compressed sensing (sampling)" in signal discretization is numerically evaluated and found to be far from the theoretical upper bound defined by signal sparsity. It is shown that, for the cases when ordinary sampling with subsequent data compression is prohibitive, there is at least one more efficient, in terms of data compression capability, and more simple and intuitive alternative to Compressed sensing: random sparse sampling and restoration of image band-limited approximations based on energy compaction capability of transforms. It is also shown that asserti…
In many compressed sensing applications, linear programming (LP) has been used to reconstruct a sparse signal. When observation is noisy, the LP formulation is extended to allow an inequality constraint and the solution is dependent on a parameter $δ$, related to the observation noise level. Recently, some researchers also considered quadratic programming (QP) for compressed sensing signal reconstruction and the solution in this case is dependent on a Lagrange multiplier $β$. In this work, we investigated the relation between $δ$ and $β$ and derived an upper and a lower bound on $β$ in terms o…
Data saving capability of "Compressed sensing (sampling)" in signal discretization is disputed and found to be far below the theoretical upper bound defined by the signal sparsity. On a simple and intuitive example, it is demonstrated that, in a realistic scenario for signals that are believed to be sparse, one can achieve a substantially larger saving than compressing sensing can. It is also shown that frequent assertions in the literature that "Compressed sensing" can beat the Nyquist sampling approach are misleading substitution of terms and are rooted in misinterpretation of the sampling t…
In 'An asymptotic result on compressed sensing matrices', a new construction for compressed sensing matrices using combinatorial design theory was introduced. In this paper, we use deterministic and probabilistic methods to analyse the performance of matrices obtained from this construction. We provide new theoretical results and detailed simulations. These simulations indicate that the construction is competitive with Gaussian random matrices, and that recovery is tolerant to noise. A new recovery algorithm tailored to the construction is also given.
An intriguing phenomenon in many instances of compressed sensing is that the reconstruction quality is governed not just by the overall sparsity of the signal, but also on its structure. This paper is about understanding this phenomenon, and demonstrating how it can be fruitfully exploited by the design of suitable sampling strategies in order to outperform more standard compressed sensing techniques based on random matrices.
