Sensitivity to Basis Mismatch in Compressed Sensing

Chi, Yuejie; Scharf, Louis L.; Pezeshki, Ali; Calderbank, A.R.

doi:10.1109/tsp.2011.2112650

Cited by 815 publications

(532 citation statements)

References 37 publications

Supporting

Mentioning

526

Contrasting

Order By: Relevance

“…However, there are some important problems where it can lead to significant problems, since the underlying problem is continuous/analogue. Discretization of the problem in order to produce a finite-dimensional, vector-space model can lead to substantial errors [3,7,22,76], due to the phenomenon of model mismatch.…”

Section: Main Theorems Ii: the Infinite-dimensional Casementioning

confidence: 99%

“…Conversely, the standard CS is based on a finite-dimensional model. Such a mismatch between the computational and the physical model can lead to critical errors when CS techniques are applied to real data arising from continuous models, or inverse crimes when the data is inappropriately simulated [22,46]. To overcome this issue, a theory of CS in infinite dimensions was recently introduced in [3].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Adcock

Hansen

Poon³

et al. 2017

Forum of Mathematics, Sigma

262

461

View full text Add to dashboard Cite

This paper presents a framework for compressed sensing that bridges a gap between existing theory and the current use of compressed sensing in many real-world applications. In doing so, it also introduces a new sampling method that yields substantially improved recovery over existing techniques. In many applications of compressed sensing, including medical imaging, the standard principles of incoherence and sparsity are lacking. Whilst compressed sensing is often used successfully in such applications, it is done largely without mathematical explanation. The framework introduced in this paper provides such a justification. It does so by replacing these standard principles with three more general concepts: asymptotic sparsity, asymptotic incoherence and multilevel random subsampling. Moreover, not only does this work provide such a theoretical justification, it explains several key phenomena witnessed in practice. In particular, and unlike the standard theory, this work demonstrates the dependence of optimal sampling strategies on both the incoherence structure of the sampling operator and on the structure of the signal to be recovered. Another key consequence of this framework is the introduction of a new structured sampling method that exploits these phenomena to achieve significant improvements over current state-of-the-art techniques.2010 Mathematics Subject Classification: 94A20, 94A08 (primary); 42C40, 65R32, 92C55 (secondary)

show abstract

Section: Main Theorems Ii: the Infinite-dimensional Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Adcock

Hansen

Poon³

et al. 2017

Forum of Mathematics, Sigma

262

461

View full text Add to dashboard Cite

show abstract

“…This assumes both that the imaging scene consists of 2-D predefined grids and that all the scatterers are located exactly on these grids. Otherwise, those off-grid scatterers would severely affect the imaging performance [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…However, CS-based reconstruction still belongs to the scope of discrete parameter estimation. Thus, it cannot avoid the off-grid phenomenon, and would lead to the well-known basis mismatch problem [10,11]. Besides, conventional methods for continuous parameter estimation [14,15], such as the estimating signal parameters via rotational invariance techniques (ESPRIT), and the matrix pencil (MP) method, which are free of grid dependence, would become less effective if the number of given samples is small by under-sampling.…”

Section: Introductionmentioning

confidence: 99%

High-Resolution Grid-Independent Imaging for Terahertz 2-D Synthetic Aperture Radar With Spatial Under-Sampling

Ding¹,

Ding²,

Ye³

et al. 2017

PIER

View full text Add to dashboard Cite

Abstract-For the purpose of two-dimensional (2-D) imaging in the Terahertz (THz) near field through 2-D synthetic aperture radar technology, Fourier transform (FT) is one of the most popular imaging ways. However, FT-based algorithms would encounter performance loss either when spatial sampling is under Nyquist frequency or there are off-grid scatterers in the scene of interest. Therefore, by exploiting the theory of matrix enhancement and continuous parameter estimation, we propose to use matrix enhancement and matrix pencil (MEMP) method and matched filter to deal with arbitrarily located scatterers when spatial under-sampling is adopted. Through constructing a specifically expanded matrix, the information of the scatterers involved in the small data set can be enhanced. Then, highresolution grid-independence 2-D imaging can be achieved by the combination of MP and matched filter. Simulation results verify the effectiveness of the proposed algorithm.

show abstract

“…Some new ways have been presented in the past few years. Compressed sensing (CS) theory [8][9][10] shows that if a signal is compressible or sparse in a certain transform domain, we can reconstruct the signal from the received signal with a high probability by introducing a signal independent observation matrix and an optimal solution algorithm. Typical CS receivers which could be used in ESM include the CS receiver using random demodulation [11] and the one with random filters for compressive sampling and reconstruction [12].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation of LFM Signal Intercepted by Synchronous Nyquist Folding Receiver

Zeng¹,

Cheng²,

Zhu³

et al. 2011

PIER C

View full text Add to dashboard Cite

Abstract-Nyquist folding receiver (NYFR) is a new kind of interception architecture, which can simultaneously intercept wideband signals in multi-Nyquist zones with one or two analog-to-digital converters (ADCs). A parameter estimation algorithm of the linear frequency modulated (LFM) signal intercepted by an improved NYFR is presented. Firstly, the NYFR is improved by introducing a synchronous mechanism, and we denote this structure as a synchronous NYFR (SNYFR). Secondly, taking LFM as an example, the input and output noise distributions of an SNYFR are discussed. Then, a fast parameter estimation algorithm is derived from the frequency spectrum of the output signal, and an advice for the design of local oscillator signal is given. Simulations show that the parameter estimation accuracy is close to the maximum likelihood when the signal to noise ratio (SNR) is above −3 dB.

show abstract

Sensitivity to Basis Mismatch in Compressed Sensing

Cited by 815 publications

References 37 publications

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

Breaking the Coherence Barrier: A New Theory for Compressed Sensing

High-Resolution Grid-Independent Imaging for Terahertz 2-D Synthetic Aperture Radar With Spatial Under-Sampling

Parameter Estimation of LFM Signal Intercepted by Synchronous Nyquist Folding Receiver

Contact Info

Product

Resources

About