Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)

Maleki, Arian; Anitori, Laura; Yang, Zai; Baraniuk, Richard G.

doi:10.1109/tit.2013.2252232

Cited by 234 publications

(189 citation statements)

References 57 publications

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“…For least-favorite distribution: The complex AMP (CAMP) algorithm for least-favorite distribution has been analyzed in [21] providing a new Onsager term. The least-favorite distribution becomes p |x| = (1 − ǫ) ∆ |x|=0 + ǫ∆ |x|=+∞ with the assumption that the phase of x is isotropic and based on [21], the η function will be,…”

Section: Analysis In Complex Domainmentioning

confidence: 99%

“…The least-favorite distribution becomes p |x| = (1 − ǫ) ∆ |x|=0 + ǫ∆ |x|=+∞ with the assumption that the phase of x is isotropic and based on [21], the η function will be,…”

Section: Analysis In Complex Domainmentioning

confidence: 99%

“…The difference between them comes from the de-noising for the zero components of signal (second term). For the complete derivation of new Onsager term and calculation of η ′ (β t i , λ), please refer to [21].…”

Section: Analysis In Complex Domainmentioning

confidence: 99%

See 2 more Smart Citations

Optimal number of measurements for compressed sensing with quadratically decreasing SNR

Dai

Eldar

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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Abstract-In this paper, we consider a practical signal transmission application with fixed power budget such as radar/sonar. The system is modeled by a linear equation with the assumption that the signal energy per measurement decreases linearly and the noise energy per measurement increases approximately linearly with the increasing of the number of measurements. Thus the SNR decreases quadratically with the number of measurements. This model suggests an optimal operation point different from the common wisdom where more measurements always mean better performance. Our analysis shows that there is an optimal number of measurements, neither too few nor too many, to minimize the mean-squared error of the estimate. The analysis is based on a state evolution technique which is proposed for the approximate message passing algorithm. We consider the Gaussian, BernoulliGaussian and least-favorite distributions in both real and complex domains. Numerical results justify the correctness of our analysis.

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Section: Analysis In Complex Domainmentioning

confidence: 99%

“…The least-favorite distribution becomes p |x| = (1 − ǫ) ∆ |x|=0 + ǫ∆ |x|=+∞ with the assumption that the phase of x is isotropic and based on [21], the η function will be,…”

Section: Analysis In Complex Domainmentioning

confidence: 99%

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Optimal number of measurements for compressed sensing with quadratically decreasing SNR

Dai

Eldar

2017

2017 25th European Signal Processing Conference (EUSIPCO)

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“…To estimate the CIR h in (2), we first introduce the famous convex optimization model known as the Least Absolute Shrinkage and Selection Operator (LASSO) or Basis Pursuit De-Noising (BPDN) as follows [27]:…”

Section: Standard Homotopymentioning

confidence: 99%

Joint channel estimation algorithm via weighted Homotopy for massive MIMO OFDM system

Nan

Sun

Zhang

2016

Digital Signal Processing

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Massive (or large-scale) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) system is widely acknowledged as a key technology for future communication. One main challenge to implement this system in practice is the high dimensional channel estimation, where the large number of channel matrix entries requires prohibitively high computational complexity. To solve this problem efficiently, a channel estimation approach using few number of pilots is necessary. In this paper, we propose a weighted Homotopy based channel estimation approach which utilizes the sparse nature in MIMO channels to achieve a decent channel estimation performance with much less pilot overhead. Moreover, inspired by the fact that MIMO channels are observed to have approximately common support in a neighborhood, an information exchange strategy based on the proposed approach is developed to further improve the estimation accuracy and reduce the required number of pilots through joint channel estimation. Compared with the traditional sparse channel estimation methods, the proposed approach can achieve more than 2dB gain in terms of mean square error (MSE) with the same number of pilots, or * Corresponding author

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“…Both Z and R in (8) are complex valued matrices; thus, the solution of this optimization problem is not as straightforward as in real-valued lasso. Several methods have been proposed for complex lasso [15][16][17] ; however, they generally suffer from the computational intensity and/or lack of considering the physics of the problem. One such physical phenomena is that the poles of a physical system appear in complex conjugate pairs 11,12,14 .…”

Section: Sparse Generalized Pencil-of-functionmentioning

confidence: 99%

Sparse generalized pencil of function and its application to system identification and structural health monitoring

Mohammadi-Ghazi

Büyüköztürk

2016

SPIE Proceedings

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Singularity expansion method (SEM) is a system identification approach with applications in solving inverse scattering problems, electromagnetic interaction problems, remote sensing, and radars. In this approach, the response of a system is represented in terms of its complex poles; therefore, this method not only extracts the fundamental frequencies of the system from the signal, but also provides sufficient information about system's damping if its transient response is analyzed. There are various techniques in SEM among which the generalized pencil-of-function (GPOF) is the computationally most stable and the least sensitive one to noise. However, SEM methods, including GPOF, suffer from imposition of spurious poles on the expansion of signals due to the lack of apriori information about the number of true poles. In this study we address this problem by proposing sparse generalized pencil-of-function (SGPOF). The proposed method excludes the spurious poles through sparsity-based regularization with 1 -norm. This study is backed by numerical examples as well as an application example which employs the proposed technique for structural health monitoring (SHM) and compares the results with other signal processing methods.

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Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)

Cited by 234 publications

References 57 publications

Optimal number of measurements for compressed sensing with quadratically decreasing SNR

Optimal number of measurements for compressed sensing with quadratically decreasing SNR

Joint channel estimation algorithm via weighted Homotopy for massive MIMO OFDM system

Sparse generalized pencil of function and its application to system identification and structural health monitoring

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