Gridless compressed sensing for fully augmentable arrays

Suleiman, Wassim; Sandor, Christian; Sorg, Alexander; Pesavento, Marius

doi:10.23919/eusipco.2017.8081557

Cited by 6 publications

(1 citation statement)

References 24 publications

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“…Unlike Problem ( 14) the dimension of ( 16) does not grow with the number of measurements [43]. Gridless variants of the method for uniform linear arrays (ULAs), shift-invariant arrays and augmentable arrays are reported in [43,55,44,3,63]. In the case of DoA estimation in partly calibrated subarray systems with unknown DoAs 𝝂 and subarray position parameters 𝜼, the recovery problem can be formulated as a rank-and block-sparse regularization problem [41].…”

Section: Theorem 3 (Problem Equivalence 1)mentioning

confidence: 99%

Recovery under Side Constraints

Ardah¹,

Haardt²,

Liu³

et al. 2021

Preprint

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This chapter addresses sparse signal reconstruction under various types of structural side constraints with applications in multi-antenna systems. Side constraints may result from prior information on the measurement system and the sparse signal structure. They may involve the structure of the sensing matrix, the structure of the non-zero support values, the temporal structure of the sparse representation vector, and the nonlinear measurement structure. First, we demonstrate how a priori information in form of structural side constraints influence recovery guarantees (null space properties) using ℓ 1 -minimization. Furthermore, for constant modulus signals, signals with row-, block-and rank-sparsity, as well as non-circular signals, we illustrate how structural prior information can be used to devise efficient algorithms with improved recovery performance and reduced computational complexity. Finally, we address the measurement system design for linear and nonlinear measurements of sparse signals. Moreover, we discuss the linear mixing matrix design based on coherence minimization. Then we extend our focus to nonlinear measurement systems where we design parallel optimization algorithms to efficiently compute stationary points in the sparse phase retrieval problem with and without dictionary learning.

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Section: Theorem 3 (Problem Equivalence 1)mentioning

confidence: 99%

Recovery under Side Constraints

Ardah¹,

Haardt²,

Liu³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Recovery Under Side Constraints

Ardah

Haardt

Liu

et al. 2022

Compressed Sensing in Information Processing

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A Compact Formulation for the $\ell _{2,1}$ Mixed-Norm Minimization Problem

Sandor

Pesavento

Pfetsch

2018

IEEE Trans. Signal Process.

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Abstract-Parameter estimation from multiple measurement vectors (MMVs) is a fundamental problem in many signal processing applications, e.g., spectral analysis and direction-ofarrival estimation. Recently, this problem has been address using prior information in form of a jointly sparse signal structure. A prominent approach for exploiting joint sparsity considers mixednorm minimization in which, however, the problem size grows with the number of measurements and the desired resolution, respectively. In this work we derive an equivalent, compact reformulation of the 2,1 mixed-norm minimization problem which provides new insights on the relation between different existing approaches for jointly sparse signal reconstruction. The reformulation builds upon a compact parameterization, which models the row-norms of the sparse signal representation as parameters of interest, resulting in a significant reduction of the MMV problem size. Given the sparse vector of row-norms, the jointly sparse signal can be computed from the MMVs in closed form. For the special case of uniform linear sampling, we present an extension of the compact formulation for gridless parameter estimation by means of semidefinite programming. Furthermore, we derive in this case from our compact problem formulation the exact equivalence between the 2,1 mixed-norm minimization and the atomic-norm minimization. Additionally, for the case of irregular sampling or a large number of samples, we present a low complexity, grid-based implementation based on the coordinate descent method.

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Gridless compressed sensing for fully augmentable arrays

Cited by 6 publications

References 24 publications

Recovery under Side Constraints

Recovery under Side Constraints

Recovery Under Side Constraints

A Compact Formulation for the $\ell _{2,1}$ Mixed-Norm Minimization Problem

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