A fast tree-based algorithm for Compressed Sensing with sparse-tree prior

Bui, Huy; La, C.N.H.; Minh, N.

doi:10.1016/j.sigpro.2014.10.026

Cited by 13 publications

(11 citation statements)

References 29 publications

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“…Compressed Sensing based approaches for recovering a function from a limited collection of measurements or evaluations of a function were considered in [3], [6], [9], [23], [29], [34], [24] among others. Many of these works use the underlying assumption that the OoI can be well approximated by an expansion like (1) were only a few coefficients are large.…”

Section: A Related Resultsmentioning

confidence: 99%

“…Here we plot: in Figure (2a) the values of all wavelet coefficients where the coefficients recovered by unweighted and weighted 1 -minimization are shifted so that their differences are more readily seen; and in Figure (2b) the coefficients whose magnitudes are larger than 0.01. two kinds of greedy algorithms. Another example where the structure of the wavelet trees is utilized is [6], where a novel, Gram-Schmidt process inspired implementation of an orthogonal matching pursuit algorithm is developed. The practicality of using sparse tree structures for real world signals has also been shown.…”

Section: A Related Resultsmentioning

confidence: 99%

“…Our proposed weighted 1 -minimization problem can be related to an iterative weighted soft-thresholding approach, where our choice of weights encourages the recovered wavelet coefficients to exhibit structure similar to the original signal. According to (6), the deeper a wavelet coefficient lies in the tree, the larger the weight associated with it is, resulting in more aggressive thresholding.…”

Section: B Recovery Of Ooi From Noisy Measurementsmentioning

confidence: 99%

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A Weighted $\ell_1$-Minimization Approach For Wavelet Reconstruction of Signals and Images

Daws¹,

Petrosyan²,

Tran³

et al. 2019

Preprint

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In this effort we propose a convex optimization approach based on weighted 1-regularization for reconstructing objects of interest, such as signals or images, that are sparse or compressible in a wavelet basis. We recover the wavelet coefficients associated to the functional representation of the object of interest by solving our proposed optimization problem. We give a specific choice of weights and show numerically that the chosen weights admit efficient recovery of objects of interest from either a set of sub-samples or a noisy version. Our method not only exploits sparsity but also helps promote a particular kind of structured sparsity often exhibited by many signals and images. Furthermore, we illustrate the effectiveness of the proposed convex optimization problem by providing numerical examples using both orthonormal wavelets and a frame of wavelets. We also provide an adaptive choice of weights which is a modification of the iteratively reweighted 1-minimization method introduced in [8].

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Section: A Related Resultsmentioning

confidence: 99%

Section: A Related Resultsmentioning

confidence: 99%

Section: B Recovery Of Ooi From Noisy Measurementsmentioning

confidence: 99%

See 1 more Smart Citation

A Weighted $\ell_1$-Minimization Approach For Wavelet Reconstruction of Signals and Images

Daws¹,

Petrosyan²,

Tran³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Also, the sparse-tree structure has been exploited in the wavelet transform of piecewise smooth signals [12]. In [13], the same structure was exploited in the tree-based OMP algorithm, which was introduced to recover signals with a sparse-tree prior. Further, Kwon.…”

Section: Introductionmentioning

confidence: 99%

An Accelerated MMP With a Pruning Tree Strategy

Chen

Xiang

et al. 2019

IEEE Access

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Multipath matching pursuit (MMP) has been developed to solve the sparse signal recovery problems in compressed sensing, which can generate recovery error less than the traditional orthogonal matching pursuit type algorithms in terms of mean square error. However, the computational burden of MMP is seriously heavy, and limits itself in applications, finding the need to be improved urgently. To lighten the burden, in this paper, an accelerated version of the MMP is proposed based on pruning tree strategy for sparse signal recovery, that attempts to reduce some of the paths in subsequent searching. By this strategy, an accelerated MMP is established in the scenarios where the MMP works. It retains the desirable performance as MMP and can shorten the running time. We demonstrate the acceleration ability of the proposed algorithm with almost the same accuracy of the original MMP, for the reconstruction of both synthetic data and images. INDEX TERMS Compressed sensing, multipath matching pursuit, sparse recovery, pruning tree strategy, restricted isometry constant.

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“…Other algorithms exploit the structure of the signal sparsity such as the Tree-based Orthogonal Matching Pursuit (TOMP) [23] , [24] , [25] . On the other hand, the Multipath Matching Pursuit models the problem of finding the candidate support of the signal as a tree search problem [26] .…”

Section: Introductionmentioning

confidence: 99%