A perturbation analysis of nonconvex block-sparse compressed sensing

Compressed sensing is well known for its superior compression performance, in existing schemes, in lossy compression. Conventional research aims to reach a larger compression ratio at the encoder, with acceptable quality reconstructed images at the decoder. This implies looking for compression performance with error-free transmission between the encoder and the decoder. Besides looking at compression performance, we applied block compressed sensing to digital images for robust transmission. For transmission over lossy channels, error propagation or data loss can be expected, and protection mechanisms for compressed sensing signals are required for guaranteed quality of the reconstructed images. We propose transmitting compressed sensing signals over multiple independent channels for robust transmission. By introducing correlations with multiple-description coding, which is an effective means for error resilient coding, errors induced in the lossy channels can effectively be alleviated. Simulation results presented the applicability and superiority of performance, depicting the effectiveness of protection of compressed sensing signals.

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“…By gathering all the elements together, C k1 and C k2 were formed from the compensated descriptions in Equation (12). Here we denote…”

Section: Proposed Algorithmmentioning

confidence: 99%

Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission

2019

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“…To investigate the theoretical analysis of the block-sparse compressed sensing with the BOMP algorithm for the completely perturbed model in (1.3) and (1.4), the restricted isometry property (RIP) forÂ (see [15]) is extended to the BRIP forÂ in Section 2 (see [29]).…”

Section: Introductionmentioning

confidence: 99%

A perturbation analysis based on group sparse representation with orthogonal matching pursuit

Liu

Zhang

Qiu

et al. 2020

Journal of Inverse and Ill-Posed Problems

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In this paper, by exploiting orthogonal projection matrix and block Schur complement, we extend the study to a complete perturbation model. Based on the block-restricted isometry property (BRIP), we establish some sufficient conditions for recovering the support of the block 𝐾-sparse signals via block orthogonal matching pursuit (BOMP) algorithm. Under some constraints on the minimum magnitude of the nonzero elements of the block 𝐾-sparse signals, we prove that the support of the block 𝐾-sparse signals can be exactly recovered by the BOMP algorithm in the case of \ell_{2} and \ell_{2}/\ell_{\infty} bounded total noise if 𝑨 satisfies the BRIP of order K+1 with\delta_{K+1}<\frac{1}{\sqrt{K+1}(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}+\frac{1}{(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1.In addition, we also show that this is a sharp condition for exactly recovering any block 𝐾-sparse signal with the BOMP algorithm. Moreover, we also give the reconstruction upper bound of the error between the recovered block-sparse signal and the original block-sparse signal. In the noiseless and perturbed case, we also prove that the BOMP algorithm can exactly recover the block 𝐾-sparse signal under some constraints on the block 𝐾-sparse signal and\delta_{K+1}<\frac{2+\sqrt{2}}{2(1+\epsilon_{\boldsymbol{A}}^{(K+1)})^{2}}-1.Finally, we compare the actual performance of perturbed OMP and perturbed BOMP algorithm in the numerical study. We also present some numerical experiments to verify the main theorem by using the completely perturbed BOMP algorithm.

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“…Chartrand [7] showed that fewer measurements are required for exact reconstruction if l 1 -norm is substituted with l p -norm. There exist many work regarding reconstructing x via the l p -minimization [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. In [7], numerical simulations demonstrated that fewer measurements are needed for exact reconstruction than when p = 1.…”

Section: Introductionmentioning

confidence: 99%

The perturbation analysis of nonconvex low-rank matrix robust recovery

Huang¹,

Wang²,

Zhang³

et al. 2020

Preprint

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In this paper, we bring forward a completely perturbed nonconvex Schatten p-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the investigation to a complete perturbation model thinking over not only noise but also perturbation, gives the restricted isometry property condition that guarantees the recovery of low-rank matrix and the corresponding reconstruction error bound. In particular, the analysis of the result reveals that in the case that p decreases 0 and a > 1 for the complete perturbation and low-rank matrix, the condition is the optimal sufficient condition δ 2r < 1 [21]. The numerical experiments are conducted to show better performance, and provides outperformance of the nonconvex Schatten p-minimization method comparing with the convex nuclear norm minimization approach in the completely perturbed scenario.

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A perturbation analysis of nonconvex block-sparse compressed sensing

Cited by 15 publications

References 21 publications

Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission

Error Resilience for Block Compressed Sensing with Multiple-Channel Transmission

A perturbation analysis based on group sparse representation with orthogonal matching pursuit

The perturbation analysis of nonconvex low-rank matrix robust recovery

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