Iterative and greedy algorithms for the sparsity in levels model in compressed sensing

Adcock, Ben; Brugiapaglia, Simone; King-Roskamp, Matthew

doi:10.1117/12.2526373

Cited by 6 publications

(6 citation statements)

References 34 publications

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“…Nonuniform recovery guarantees for the 1 minimization decoder were proven first in [4], with uniform guarantees later in [25]. The IHTL and CoSaMPL algorithms have been previously examined numerically in [3] by the authors, wherein these algorithms were first introduced. However, this previous work contained no theoretical analysis, and did not consider OMPL.…”

Section: Previous Workmentioning

confidence: 99%

“…Finally, we include some numerics to support the claim that OMP also generalizes well to this new setting. The experiments performed are analogous to those in [3], which gives numerical results for IHTL and CoSAMPL.…”

Section: Function X = Omp(a Y S)mentioning

confidence: 99%

“…This is of particular importance to IHTL, where it has been observed that altering the stepsize can drastically effect performance, causing improvement or convergence issues depending on the quality of the stepsize. However, numerically CoSaMP is much more robust to changes in the stepsize [3].…”

Section: Now As Pmentioning

confidence: 99%

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The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees

Adcock,

Brugiapaglia,

King-Roskamp

2020

Preprint

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The sparsity in levels model recently inspired a new generation of effective acquisition and reconstruction modalities for compressive imaging. Moreover, it naturally arises in various areas of signal processing such as parallel acquisition, radar, and the sparse corruptions problem. Reconstruction strategies for sparse in levels signals usually rely on a suitable convex optimization program. Notably, although iterative and greedy algorithms can outperform convex optimization and have been studied extensively in the case of standard sparsity, little is known about their generalizations to the sparse in levels setting. In this paper, we bridge this gap by showing new stable and robust uniform recovery guarantees for sparse in level variants of the iterative hard thresholding and the CoSaMP algorithms. Our theoretical analysis generalizes recovery guarantees currently available in the case of standard sparsity and favorably compare to sparse in levels guarantees for weighted 1 minimization. In addition, we also propose and numerically test an extension of the orthogonal matching pursuit algorithm for sparse in levels signals.

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Section: Previous Workmentioning

confidence: 99%

Section: Function X = Omp(a Y S)mentioning

confidence: 99%

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The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees

Adcock,

Brugiapaglia,

King-Roskamp

2020

Preprint

Self Cite

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show abstract

“…At present, reconstruction algorithms can be broadly divided into two direction including minimization of the l0 and l1 norm.The solving model of the reconstruction algorithm based on l0 norm minimization is 𝑚𝑖𝑛 ||𝑠|| , 𝑠. 𝑡. 𝑦 = 𝐴𝑠 which is an intractable NP-hard problem [5] and needs to be transformed. The common methods include greedy algorithm [6] and SL0 algorithm [7] .…”

Section: Introductionmentioning

confidence: 99%

A reformative algorithm for compressed sensing sparse signal recovery based on smoothed L0 norm

Zhang¹,

Chen²,

Zeng³

et al. 2023

Ninth Symposium on Novel Photoelectronic Detection Technology and Applications

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“…The solving model of the reconstruction algorithm, based on the

norm minimization, is

, which is an intractable NP−hard problem [ 5 ] and must be transformed. The standard methods include the greedy [ 6 ] and SL0 algorithms [ 7 ]. The reconstruction algorithm, based on the

norm minimization, uses the

norm to approximate the

norm, whose solution model is

.…”

Section: Introductionmentioning

confidence: 99%

Compressed Imaging Reconstruction Based on Block Compressed Sensing with Conjugate Gradient Smoothed l0 Norm

Zhang

Chen

Zeng

et al. 2023

Sensors

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Compressed imaging reconstruction technology can reconstruct high-resolution images with a small number of observations by applying the theory of block compressed sensing to traditional optical imaging systems, and the reconstruction algorithm mainly determines its reconstruction accuracy. In this work, we design a reconstruction algorithm based on block compressed sensing with a conjugate gradient smoothed l0 norm termed BCS-CGSL0. The algorithm is divided into two parts. The first part, CGSL0, optimizes the SL0 algorithm by constructing a new inverse triangular fraction function to approximate the l0 norm and uses the modified conjugate gradient method to solve the optimization problem. The second part combines the BCS-SPL method under the framework of block compressed sensing to remove the block effect. Research shows that the algorithm can reduce the block effect while improving the accuracy and efficiency of reconstruction. Simulation results also verify that the BCS-CGSL0 algorithm has significant advantages in reconstruction accuracy and efficiency.

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Iterative and greedy algorithms for the sparsity in levels model in compressed sensing

Cited by 6 publications

References 34 publications

The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees

The benefits of acting locally: Reconstruction algorithms for sparse in levels signals with stable and robust recovery guarantees

A reformative algorithm for compressed sensing sparse signal recovery based on smoothed L0 norm

Compressed Imaging Reconstruction Based on Block Compressed Sensing with Conjugate Gradient Smoothed l0 Norm

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