• Corpus ID: 15372563

On sparsity averaging

@article{Carrillo2013OnSA,
  title={On sparsity averaging},
  author={Rafael E. Carrillo and Jason D. McEwen and Yves Wiaux},
  journal={ArXiv},
  year={2013},
  volume={abs/1307.1360}
}
Recent developments in Carrillo et al. (2012) and Carrillo et al. (2013) introduced a novel regularization method for compressive imaging in the context of compressed sensing with coherent redundant dictionaries. The approach relies on the observation that natural images exhibit strong average sparsity over multiple coherent frames. The associated reconstruction algorithm, based on an analysis prior and a reweighted $\ell_1$ scheme, is dubbed Sparsity Averaging Reweighted Analysis (SARA). We… 
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References

SHOWING 1-10 OF 14 REFERENCES

Sparsity Averaging for Compressive Imaging

We discuss a novel sparsity prior for compressive imaging in the context of the theory of compressed sensing with coherent redundant dictionaries, based on the observation that natural images exhibit

Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio‐interferometric imaging

TLDR
It is shown through simulations that the proposed approach outperforms state-of-the-art imaging methods in the field, which are based on the assumption of signal sparsity in a single basis only.

Enhancing Sparsity by Reweighted ℓ1 Minimization

TLDR
A novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery.

Compressed Sensing with Coherent and Redundant Dictionaries

Compressed Sensing and Redundant Dictionaries

TLDR
It is shown that a matrix, which is a composition of a random matrix of certain type and a deterministic dictionary, has small restricted isometry constants, and signals that are sparse with respect to the dictionary can be recovered via basis pursuit from a small number of random measurements.

Universal and efficient compressed sensing by spread spectrum and application to realistic Fourier imaging techniques

TLDR
The spread spectrum technique remains effective in an analog setting with chirp modulation for application to realistic Fourier imaging and is proved universal in the sense that the required number of measurements for accurate recovery is optimal and independent of the sparsity basis.

Sparse Reverberant Audio Source Separation via Reweighted Analysis

TLDR
It is shown, through theoretical discussions and simulations, that this algorithm is particularly well suited for source separation of realistic reverberation mixtures and outperforms state-of-the-art methods on reverberant mixtures of audio sources by more than 2 dB of signal-to-distortion ratio on the BSS Oracle dataset.

Simultaneously Structured Models With Application to Sparse and Low-Rank Matrices

TLDR
This framework applies to arbitrary structure-inducing norms as well as to a wide range of measurement ensembles, and allows us to give sample complexity bounds for problems such as sparse phase retrieval and low-rank tensor completion.

Morphological Component Analysis: An Adaptive Thresholding Strategy

TLDR
This paper shows how the MCA convergence can be drastically improved using the mutual incoherence of the dictionaries associated to the different components.