Nonconvex compressed sensing with partially known signal support

İnce, Taner; Nacaroğlu, Arif; Watsuji, Nurdal

doi:10.1016/j.sigpro.2012.07.011

Cited by 41 publications

(18 citation statements)

References 20 publications

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“…It can be incoherent to most of the basis Ψ and satisfy the property of RIP. In detail, the RIP explanation can be seen in detail as in the following Definition 3.Definition Matrix Φ is called to satisfy the RIP of order m if there is a constant δ satisfying Equation for any m sparse signal x .

(1 - δ) ∥ x ∥_{2}^{2} \leq ∥ normalΦx ∥_{2}^{2} \leq (1 + δ) ∥ x ∥_{2}^{2}

…”

Section: Framework Of Compressed Sensingmentioning

confidence: 99%

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Compression and encryption for remote sensing image using chaotic system

Huang

Chai

et al. 2015

Security Comm Networks

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In this paper, because of the acquisition principle and big data of remote sensing image, we suggest an encryption scheme using chaotic system to build up the compressed sensing framework. A two‐dimensional generalized Arnold map is adopted here to generate the entries of the Toeplitz matrix used as measurement matrix. Then, the selecting row of the Toeplitz matrix is also decided by the chaotic sequence generated randomly by the Arnold map. With a further function of permutation operation, we can also encrypt remote sensing image after compression. The key space is constructed by the initial conditions in chaotic system. Experiment results show that the proposed method can be suitable to compressed sensing when the random measurement matrix is generated using chaotic system. Additionally, although the permutation operation is adopted, it is mainly used to enhance the security of cipher‐image. The reconstruction result is only dependent on the standard recovery algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

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(1 - δ) ∥ x ∥_{2}^{2} \leq ∥ normalΦx ∥_{2}^{2} \leq (1 + δ) ∥ x ∥_{2}^{2}

…”

Section: Framework Of Compressed Sensingmentioning

confidence: 99%

“…Reference analyzed that color channels are highly correlated, then gave us a reconstruction method using group sparse optimization and applied it to color image. Many other applications can be seen in literatures .…”

Section: Introductionmentioning

confidence: 99%

Compression and encryption for remote sensing image using chaotic system

Huang

Chai

et al. 2015

Security Comm Networks

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“…Proof Since the objective function in Equation (12) is convex, we can get that M * i is an optimal solution to Equation (12) if and only if…”

Section: An Apg Algorithm For Low N-rank Tensor Recoverymentioning

confidence: 99%

“…By Lemma 3.2, we know that the matrix shrinkage operator applied to ((τ/N)G (i) + (1/λ)X (i) )/ (τ/N + 1/λ) gives an optimal solution to Equation (12).…”

Section: An Apg Algorithm For Low N-rank Tensor Recoverymentioning

confidence: 99%

“…In recent years, compressed sensing has attracted more and more attention for both its scientific challenges and its wide applications, through which certain signals and images are able to be accurately recovered from far fewer measurements or samples with high probability [5,7,12,23]. The mathematical model of this problem is to find the sparsest vector satisfying some linear constraints [7]:…”

Section: Introductionmentioning

confidence: 99%

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An inexact continuation accelerated proximal gradient algorithm for lown-rank tensor recovery

Liu

Song

2014

International Journal of Computer Mathematics

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The low n-rank tensor recovery problem is an interesting extension of the compressed sensing. This problem consists of finding a tensor of minimum n-rank subject to linear equality constraints and has been proposed in many areas such as data mining, machine learning and computer vision. In this paper, operator splitting technique and convex relaxation technique are adapted to transform the low n-rank tensor recovery problem into a convex, unconstrained optimization problem, in which the objective function is the sum of a convex smooth function with Lipschitz continuous gradient and a convex function on a set of matrices. Furthermore, in order to solve the unconstrained nonsmooth convex optimization problem, an accelerated proximal gradient algorithm is proposed. Then, some computational techniques are used to improve the algorithm. At the end of this paper, some preliminary numerical results demonstrate the potential value and application of the tensor as well as the efficiency of the proposed algorithm.

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