A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit

Li, Haifeng; Wen, Jinming

doi:10.1109/lsp.2018.2885919

Cited by 39 publications

(22 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, we give a lower bound on the left-hand side of (20) and an upper bound of the right-hand side of (20) (see (21)) . On the other hand, we have (see (22)) .…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

RIP based condition for support recovery with A* OMP in the presence of noise

Chen

2020

IET signal process.

Self Cite

View full text Add to dashboard Cite

A* orthogonal matching pursuit (A* OMP) aims at combination of best-first tree search with the OMP algorithm for the compressed sensing problem. In this study, the authors present a new analysis for the A* OMP algorithm using the restricted isometry property (RIP). The results show that if the sampling matrix A satisfies the RIP with δ K ⋆ < B/(K + B) (K ⋆ = max {2K, K + B}), then under some constraints on SNR, A* OMP accurately recovers the support of any K-sparse signal x from the samples y = Ax + e, where B is the number of child paths for each candidate in the algorithm. In addition, the proposed condition is an optimal condition that guarantees the success of A* OMP in the noise-free case.

show abstract

“…Now, we give a lower bound on the left-hand side of (20) and an upper bound of the right-hand side of (20) (see (21)) . On the other hand, we have (see (22)) .…”

Section: Resultsmentioning

confidence: 99%

“…On the other hand, we have (see (22)) . Thus, according to (21) and (22), to prove (20), it needs to show that…”

Section: Resultsmentioning

confidence: 99%

RIP based condition for support recovery with A* OMP in the presence of noise

Chen

2020

IET signal process.

Self Cite

View full text Add to dashboard Cite

show abstract

“…us, they can improve the reconstruction accuracy. Besides, block orthogonal matching pursuit algorithm (BOMP) is also proposed for block sparse signal [15,16], and sharp sufficient conditions for stable recovery are also given [17]. In this paper, we mainly consider the normal sparse signal.…”

Section: Introductionmentioning

confidence: 99%

Improved Generalized Sparsity Adaptive Matching Pursuit Algorithm Based on Compressive Sensing

Zhao

Jia

2020

Journal of Electrical and Computer Engineering

View full text Add to dashboard Cite

The modified adaptive orthogonal matching pursuit algorithm has a lower convergence speed. To overcome this problem, an improved method with faster convergence speed is proposed. In respect of atomic selection, the proposed method computes the correlation between the measurement matrix and residual and then selects the atoms most related to residual to construct the candidate atomic set. The number of selected atoms is the integral multiple of initial step size. In respect of sparsity estimation, the proposed method introduces the exponential function to sparsity estimation. It uses a larger step size to estimate sparsity at the beginning of iteration to accelerate the algorithm convergence speed and a smaller step size to improve the reconstruction accuracy. Simulations show that the proposed method has better performance in terms of convergence speed and reconstruction accuracy for one-dimension signal and two-dimension signal.

show abstract

“…The iteration process of these general reconstruction methods lead to complexity computational time, so they are not suitable for largescale datasets. Besides, in the noisy case, there are some reconstruction methods proposed, like block OMP [28] and composite robust ADMM [29]. In this paper, the CS-based reconstruction are applied to image patches [30], [31].…”

Section: Introductionmentioning

confidence: 99%

Tensor-Based Light Field Compressed Sensing and Epipolar Plane Images Reconstruction via Deep Learning

2020

View full text Add to dashboard Cite

Light field (LF) can capture the spatial and angular information of the light in one single exposure. And the LF images are widely used in various fields, especially in immersive media. The rich imaging information in the LF poses great challenges for transmission. However, LF images are sparse and redundant to some extent, which makes LF compression possible. Besides, the compressed sensing (CS) theory shows that images can be recovered from a small number of measurements when they are sparse. In this paper, we propose a Tensor-based Compressed Sensing method to compress images and Epipolar Plane Images for reconstruction (TCSEPI). This method divides the viewpoints of LF images into several regions and stacks the images in each region into a 4D tensor, which conduct CS together and yields measurements with common characteristics. Subsequently, the epipolar plane images are used to reconstruct the LF images and restore the geometric consistency information. To achieve better reconstruction results, we design two cascaded convolutional neural networks to implement the measurement matrix optimization and LF images reconstruction sequentially. Experimental results show the superior performance of TCSEPI, which achieves at least 3dB gain in PSNR and outperforms state-of-the-art in the reconstruction quality. INDEX TERMS Light field, compressed sensing, epipolar plane images, convolutional neural network, image reconstruction

show abstract

A New Analysis for Support Recovery With Block Orthogonal Matching Pursuit

Cited by 39 publications

References 16 publications

RIP based condition for support recovery with A* OMP in the presence of noise

RIP based condition for support recovery with A* OMP in the presence of noise

Improved Generalized Sparsity Adaptive Matching Pursuit Algorithm Based on Compressive Sensing

Tensor-Based Light Field Compressed Sensing and Epipolar Plane Images Reconstruction via Deep Learning

Contact Info

Product

Resources

About