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Register a new userCompressed Sensing with Prior Information via Maximizing Correlation
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Added by
Yulong Liu
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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Compressed sensing (CS) with prior information concerns the problem of reconstructing a sparse signal with the aid of a similar signal which is known beforehand. We consider a new approach to integrate the prior information into CS via maximizing the correlation between the prior knowledge and the desired signal. We then present a geometric analysis for the proposed method under sub-Gaussian measurements. Our results reveal that if the prior information is good enough, then the proposed approach can improve the performance of the standard CS. Simulations are provided to verify our results.
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This paper considers the problem of recovering a structured signal from a relatively small number of noisy measurements with the aid of a similar signal which is known beforehand. We propose a new approach to integrate prior information into the standard recovery procedure by maximizing the correlation between the prior knowledge and the desired signal. We then establish performance guarantees (in terms of the number of measurements) for the proposed method under sub-Gaussian measurements. Specific structured signals including sparse vectors, block-sparse vectors, and low-rank matrices are also analyzed. Furthermore, we present an interesting geometrical interpretation for the proposed procedure. Our results demonstrate that if prior information is good enough, then the proposed approach can (remarkably) outperform the standard recovery procedure. Simulations are provided to verify our results.
In this paper, we consider the problem of compressive sensing (CS) recovery with a prior support and the prior support quality information available. Different from classical works which exploit prior support blindly, we shall propose novel CS recovery algorithms to exploit the prior support adaptively based on the quality information. We analyze the distortion bound of the recovered signal from the proposed algorithm and we show that a better quality prior support can lead to better CS recovery performance. We also show that the proposed algorithm would converge in $mathcal{O}left(logmbox{SNR}right)$ steps. To tolerate possible model mismatch, we further propose some robustness designs to combat incorrect prior support quality information. Finally, we apply the proposed framework to sparse channel estimation in massive MIMO systems with temporal correlation to further reduce the required pilot training overhead.
In this paper, we study a support set reconstruction problem in which the signals of interest are jointly sparse with a common support set, and sampled by joint sparsity model-2 (JSM-2) in the presence of noise. Using mathematical tools, we develop upper and lower bounds on the failure probability of support set reconstruction in terms of the sparsity, the ambient dimension, the minimum signal to noise ratio, the number of measurement vectors and the number of measurements. These bounds can be used to provide a guideline to determine the system parameters in various applications of compressed sensing with noisy JSM-2. Based on the bounds, we develop necessary and sufficient conditions for reliable support set reconstruction. We interpret these conditions to give theoretical explanations about the benefits enabled by joint sparsity structure in noisy JSM-2. We compare our sufficient condition with the existing result of noisy multiple measurement vectors model (MMV). As a result, we show that noisy JSM-2 may require less number of measurements than noisy MMV for reliable support set reconstruction.
This paper presents an approach for visible light communication-based indoor positioning using compressed sensing. We consider a large number of light emitting diodes (LEDs) simultaneously transmitting their positional information and a user device equipped with a photo-diode. By casting the LED signal separation problem into an equivalent compressed sensing framework, the user device is able to detect the set of nearby LEDs using sparse signal recovery algorithms. From this set, and using proximity method, position estimation is proposed based on the concept that if signal separation is possible, then overlapping light beam regions lead to decrease in positioning error due to increase in the number of reference points. The proposed method is evaluated in a LED-illuminated large-scale indoor open-plan office space scenario. The positioning accuracy is compared against the positioning error lower bound of the proximity method, for various system parameters.
The orthogonal matching pursuit (OMP) algorithm is a commonly used algorithm for recovering $K$-sparse signals $xin mathbb{R}^{n}$ from linear model $y=Ax$, where $Ain mathbb{R}^{mtimes n}$ is a sensing matrix. A fundamental question in the performance analysis of OMP is the characterization of the probability that it can exactly recover $x$ for random matrix $A$. Although in many practical applications, in addition to the sparsity, $x$ usually also has some additional property (for example, the nonzero entries of $x$ independently and identically follow the Gaussian distribution), none of existing analysis uses these properties to answer the above question. In this paper, we first show that the prior distribution information of $x$ can be used to provide an upper bound on $|x|_1^2/|x|_2^2$, and then explore the bound to develop a better lower bound on the probability of exact recovery with OMP in $K$ iterations. Simulation tests are presented to illustrate the superiority of the new bound.
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