An Orthogonal Method for Measurement Matrix Optimization

Pan, Jinfeng; Qiu, Yuehong

doi:10.1007/s00034-015-0107-4

Cited by 7 publications

(3 citation statements)

References 25 publications

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“…From (8) and (9) we see that increasing H(y) results in reducing ν, and hence M eff ≃ M. Hence, as ν decreases, the lower bound 2K + ν on M comes close to 2K. Thus, maximisation of H(y) leads to unique recovery with a reduced number of measurements M close to 2K.…”

Section: Definitionmentioning

confidence: 83%

“…In [5], Elad introduced a structured sensing matrix along with a method to construct it by reducing the mutual coherence

μ false(A false)

of the columns of the matrix

A

. Subsequently, many techniques were proposed to construct the sensing matrix by reducing

μ false(A false)

[6–9]. In [10, 11], the sensing matrices were constructed by applying multidimensional scaling (MDS) on a sparsifying dictionary

Ψ

.…”

Section: Introductionmentioning

confidence: 99%

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Entropy‐based learning of sensing matrices

Parthasarathy

Abhilash

2019

IET signal process.

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This paper proposes a learning method to construct an efficient sensing (measurement) matrix, having orthogonal rows, for compressed sensing of a class of signals. The learning scheme identifies the sensing matrix by maximizing the entropy of measurement vectors. The bounds on the entropy of the measurement vector necessary for the unique recovery of a signal are also proposed. A comparison of the performance of the designed sensing matrix and the sensing matrices constructed using other existing methods is also presented. The simulation results on the recovery of synthetic, speech, and image signals, compressively sensed using the sensing matrix identified, shows an improvement in the accuracy of recovery. The reconstruction quality is better, using less number of measurements, than those measured using sensing matrices identified by other methods.

show abstract

Section: Definitionmentioning

confidence: 83%

“…In [5], Elad introduced a structured sensing matrix along with a method to construct it by reducing the mutual coherence

μ false(A false)

of the columns of the matrix

A

. Subsequently, many techniques were proposed to construct the sensing matrix by reducing

μ false(A false)

[6–9]. In [10, 11], the sensing matrices were constructed by applying multidimensional scaling (MDS) on a sparsifying dictionary

Ψ

.…”

Section: Introductionmentioning

confidence: 99%

Entropy‐based learning of sensing matrices

Parthasarathy

Abhilash

2019

IET signal process.

View full text Add to dashboard Cite

show abstract

“…Abolghasemi et al [17], [18] utilized the idea of gradient descent to optimize the mutual coherence of the Gaussian random matrix and improved the performance of sparse recovery. Pan and Qiu [19] gave an orthogonal optimization method for reducing the mutual coherence of the random measurement matrix based on QR factorization. Li et al [20] designed a projection matrix using the estimated sparse representation to decrease the local cumulative coherence of the measurement dictionary.…”

Section: Introductionmentioning

confidence: 99%

An Improved Reweighted Method for Optimizing the Sensing Matrix of Compressed Sensing

Shi,

2024

IEEE Access

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In compressed sensing (CS), coherence is a simple and practical measure of the quality of a sensing matrix. The smaller the coherence of the sensing matrix, the better the reconstruction result. Most strategies for optimizing the coherence of a sensing matrix are only applicable to gray-value matrices and are not to binary matrices with fast computation speed and smaller storage space. Under a certain condition, the coherence can be improved by weighting the sensing matrix to make its condition number equal to 1, i.e., all non-zero singular values become the same. In this paper, we propose a method for reweighting CS models to reduce the condition number of the sensing matrix so as to improve its coherence, prove that the condition number decreases monotonically to 1 as the weighting times approaches infinity, and then obtain a coherence improvement model equivalent to the original CS model. Finally, we give the RwOMP recovery algorithm based on the proposed reweighted method and verify its superiority by using different binary sensing matrices for CS experiments.

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Sparse Recovery of Sound Fields Using Measurements from Moving Microphones

Katzberg

Mertins

2022

Applied and Numerical Harmonic Analysis

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An Orthogonal Method for Measurement Matrix Optimization

Cited by 7 publications

References 25 publications

Entropy‐based learning of sensing matrices

Entropy‐based learning of sensing matrices

An Improved Reweighted Method for Optimizing the Sensing Matrix of Compressed Sensing

Sparse Recovery of Sound Fields Using Measurements from Moving Microphones

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