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(a) A random sparse signal, (b) Reconstruction SNR versus measurement rate for the three proposed theorems and OMP-PKS.
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This paper proposes a new fast matching pursuit technique named Partially Known Least Support Orthogonal Matching Pursuit (PKLS-OMP) which utilizes partially known support as a prior knowledge to reconstruct sparse signals from a limited number of its linear projections. The PKLS-OMP algorithm chooses optimum least part of the support at each itera...
Contexts in source publication
Context 1
... the first experiment, we generate a random sparse signal having length N=1024 with K=200 nonzero entries (Figure 2 (a)). The location of the nonzero entries are selected randomly using standard Gaussian distribution, the RIC value for LS-OMP=0.495, ...
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... for PKLS-OMP =0.002, the prior support information T 0 =64. Figure 2 (b) compares the three proposed theorems and OMP-PKS for different number of measurements. Notice that inclusion of the prior information improves the reconstruction performance. ...
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... important notation according to Figure 11 T � : The known part of support Since the set T � � � T � is out of our working set as shown in Figure 2, then its value will be equal zero. Since T � � ∩ T � � T � � T � , then (c-32) ...
Context 4
... the first experiment, we generate a random sparse signal having length N=1024 with K=200 nonzero entries (Figure 2 (a)). The location of the nonze- ro entries are selected randomly using standard Gaussian distribution, the RIC value for LS-OMP=0.495, and for PKLS-OMP =0.002, the prior support in- formation T 0 =64. Figure 2 (b) compares the three proposed theorems and OMP-PKS for different number of measurements. Notice that inclusion of the prior information improves the reconstruction performance. That is the PKLS- OMP and the OMP-PKS perform better than the LS-OMP but it is obvious that the PKLS-OMP (Theorem 2 and 3) gives best result for all measurement ...
Context 5
... the first experiment, we generate a random sparse signal having length N=1024 with K=200 nonzero entries (Figure 2 (a)). The location of the nonze- ro entries are selected randomly using standard Gaussian distribution, the RIC value for LS-OMP=0.495, and for PKLS-OMP =0.002, the prior support in- formation T 0 =64. Figure 2 (b) compares the three proposed theorems and OMP-PKS for different number of measurements. Notice that inclusion of the prior information improves the reconstruction performance. That is the PKLS- OMP and the OMP-PKS perform better than the LS-OMP but it is obvious that the PKLS-OMP (Theorem 2 and 3) gives best result for all measurement ...
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Citations
... In this regime we would like to highlight the situation of a known support estimate for the original sparse signals discussed before, in which a variant of OM P was warm-started [7]. Variants of this approach -yet still following the same idea -are contained, for instance, in [40]. ...
Applications such as wireless communications require efficient sensing techniques of signals with the a priori knowledge of those being lattice-valued. In this paper, we study the impact of this prior information on compressed sensing methodologies, and introduce and analyze PROMP ("PReprojected Orthogonal Matching Pursuit'') as a novel algorithmic approach for sparse recovery of lattice-valued signals. More precisely, we first show that the straightforward approach to project the solution of Basis Pursuit onto a prespecified lattice does not improve the performance of Basis Pursuit in this situation. We then introduce PROMP as a novel sparse recovery algorithm for lattice-valued signals which has very low computational complexity, alongside a detailed mathematical analysis of its performance and stability under noise. Finally, we present numerical experiments which show that PROMP outperforms standard sparse recovery approaches in the lattice-valued signal regime.
Out of various cryptographic attacks, Chosen-Plaintext Attack (CPA) is one of the most powerful and widely used attack on encrypted images. In order to efficiently resist such a strong attack, a novel chaos and compressive sensing based image encryption algorithm is presented in this work. Firstly, the original plaintext image is compressed via Orthogonal Matching Pursuit with Partially Known Support (OMP-PKS) and then the compressed image is confused and diffused using TD-ERCS and Skew-tent chaotic maps, respectively. Correlation among the compressed pixels is break down via confusing the image pixels using Tangent Delay Ellipse Reflecting Cavity Map System (TD-ERCS). Skew-tent chaotic map is employed for the pixel diffusion process. To get the final ciphertext image, the confused pixels are further changed through bitwise XORed operation via random matrix. For the sake of higher security, the initial conditions of chaotic maps are made dependent on the plaintext image and the parameters are computed via SHA-512. Furthermore, to decrease the transmission bandwidth, the measurement matrix is generated via Beta chaotic map. Instead of sending the whole measurement matrix, the sender will just send the Beta chaotic map initial conditions and control parameters (key) values along with the compressed ciphertext. The reliability and robustness of the designed image compression and encryption scheme are verified via experimental analysis and simulation results. All the experimental and simulation results are in favor of the proposed scheme.
