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The Benefits of Diversity: Permutation Recovery in Unlabeled Sensing from Multiple Measurement Vectors [article]

Hang Zhang, Martin Slawski, Ping Li
2020 arXiv   pre-print
In this paper, we study the case of multiple noisy measurement vectors (MMVs) resulting from a common permutation and investigate to what extent the number of MMVs m facilitates permutation recovery by  ...  In "Unlabeled Sensing", one observes a set of linear measurements of an underlying signal with incomplete or missing information about their ordering, which can be modeled in terms of an unknown permutation  ...  study the case of multiple noisy measurement vectors (MMVs) resulting from a common permutation and investigate to what extent the number of MMVs m facilitates permutation recovery by "borrowing strength  ... 
arXiv:1909.02496v2 fatcat:qqc4daw6hregne57pe6q4ntzgu

Unlabeled sensing with local permutations [article]

Ahmed Abbasi, Abiy Tasissa, Shuchin Aeron
2020 arXiv   pre-print
Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix  ...  In this setting, namely unlabeled multi-view sensing with local permutation, previous results and algorithms are not directly applicable.  ...  INTRODUCTION Motivated by several practical problems such as sampling in the presence of clock jitter, mobile sensor networks and multiple target tracking in radar, the problem of unlabeled sensing was  ... 
arXiv:1911.06382v3 fatcat:zlohethr3zcztce6pkicr4kivy

Unlabelled Sensing: A Sparse Bayesian Learning Approach [article]

Ranjitha Prasad
2018 arXiv   pre-print
We address the recovery of sparse vectors in an overcomplete, linear and noisy multiple measurement framework, where the measurement matrix is known upto a permutation of its rows.  ...  We derive sparse Bayesian learning (SBL) based updates for joint recovery of the unknown sparse vector and the sensing order, represented using a permutation matrix.  ...  We propose a novel Bayesian approach for joint multiple sparse vector recovery and sensor permutation recovery in an MMV framework.  ... 
arXiv:1802.00559v1 fatcat:gohzs3ifx5g5xf4fmm5rlgmbb4

Permutations Unlabeled beyond Sampling Unknown [article]

Ivan Dokmanić
2019 arXiv   pre-print
We show that this condition on A implies something much stronger: that an unknown vector x can be recovered from measurements y = T A x, when the unknown T belongs to an arbitrary set of invertible, diagonalizable  ...  A recent unlabeled sampling result by Unnikrishnan, Haghighatshoar and Vetterli states that with probability one over iid Gaussian matrices A, any x can be uniquely recovered from an unknown permutation  ...  As a byproduct, we get a simple, geometric proof of the uniqueness result for classical permutation-based unlabeled sensing.  ... 
arXiv:1812.00498v2 fatcat:yde7soua45dd7ldnkui6cutn4e

R-local sensing: A novel graph matching approach for multiview unlabeled sensing under local permutations

Ahmed Abbasi, Abiy Tasissa, Shuchin Aeron
2021 IEEE Open Journal of Signal Processing  
Unlabeled sensing is a linear inverse problem where the measurements are scrambled under an unknown permutation leading to loss of correspondence between the measurements and the rows of the sensing matrix  ...  In this setting, namely multi-view unlabeled sensing under local permutations, previous results and algorithms are not directly applicable.  ...  INTRODUCTION Motivated by several practical problems such as sampling in the presence of clock jitter, mobile sensor networks and multiple target tracking in radar, the problem of unlabeled sensing was  ... 
doi:10.1109/ojsp.2021.3083479 fatcat:m2heshjqxfeexb6liyybdvlcem

Signal Detection from Permutated Observations Using Distributed Sensors

Naiti Jiang, Ning Zhang, Jindong Zhang
2019 Journal of Sensors  
In this paper, distributed constant level detection in wireless sensor networks (WSNs) is investigated.  ...  Numerical simulations are performed, and it is shown that the performance degradation of the GLRT detector is small, compared to the permutation known as Neyman-Pearson (NP) detector.  ...  Vetterli, "Unlabeled sensing with random linear measurements", " Allerton Conference, pp. -, . [ ] A. Pananjady and M. J.  ... 
doi:10.1155/2019/8169404 fatcat:62uwvkknk5hrjivl5afjgudg2u

Unlabeled Sensing with Random Linear Measurements [article]

Jayakrishnan Unnikrishnan, Saeid Haghighatshoar, Martin Vetterli
2015 arXiv   pre-print
We study the problem of solving a linear sensing system when the observations are unlabeled.  ...  In terms of applications, the unlabeled sensing problem is related to data association problems encountered in different domains including robotics where it is appears in a method called "simultaneous  ...  . • We introduce the problem of unlabeled sensing and demonstrate that for signals of arbitrary dimensions, there exist sensing matrices that allow perfect recovery of a signal from unlabeled linear measurements  ... 
arXiv:1512.00115v1 fatcat:gg2dpbhlsbhfpaxa5h4ucgzyce

Unlabeled Sensing With Random Linear Measurements

Jayakrishnan Unnikrishnan, Saeid Haghighatshoar, Martin Vetterli
2018 IEEE Transactions on Information Theory  
We study the problem of solving a linear sensing system when the observations are unlabeled.  ...  In terms of applications, the unlabeled sensing problem is related to data association problems encountered in different domains including robotics where it is appears in a method called "simultaneous  ...  . • We introduce the problem of unlabeled sensing and demonstrate that for signals of arbitrary dimensions, there exist sensing matrices that allow perfect recovery of a signal from unlabeled linear measurements  ... 
doi:10.1109/tit.2018.2809002 fatcat:njse6bvvjbee3mkz5bffep7jre

Unlabeled sensing: Reconstruction algorithm and theoretical guarantees

Golnoosh Elhami, Adam Scholefield, Benjamin Bejar Haro, Martin Vetterli
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
It often happens that we are interested in reconstructing an unknown signal from partial measurements.  ...  In this paper, we consider the situation in which the order of noisy samples, taken from a linear measurement system, is missing.  ...  Unlabeled sensing is similar to compressed sensing in the sense that they both deal with partially revealed information in a linear measurement system.  ... 
doi:10.1109/icassp.2017.7953021 dblp:conf/icassp/ElhamiSHV17 fatcat:n3rncycodbhcvecxodtx73vs5e

Homomorphic Sensing [article]

Manolis C. Tsakiris, Liangzu Peng
2019 arXiv   pre-print
A recent line of research termed unlabeled sensing and shuffled linear regression has been exploring under great generality the recovery of signals from subsampled and permuted measurements; a challenging  ...  In this paper we introduce an abstraction of this problem which we call homomorphic sensing.  ...  INTRODUCTION In a recent line of research termed unlabeled sensing, it has been established that uniquely recovering a signal from shuffled and subsampled measurements is possible as long as the number  ... 
arXiv:1901.07852v3 fatcat:55himfjobnha3ienq3nowrjpyq

Homomorphic Sensing: Sparsity and Noise

Liangzu Peng, Boshi Wang, Manolis C. Tsakiris
2021 International Conference on Machine Learning  
It was generalized to the homomorphic sensing problem by replacing the unknown permutation with an unknown linear map from a given finite set of linear maps.  ...  Sparsity in the context of unlabeled sensing leads to the problem of unlabeled compressed sensing, and a consequence of our general theory is the existence under mild conditions of a unique sparsest solution  ...  Indeed, the number 2k is the threshold for unique recovery of x * in compressed sensing (recall §1.1), but this number remains the same in unlabeled compressed sensing, even though there could be m!  ... 
dblp:conf/icml/PengWT21 fatcat:jwuxytfy3fgabhmv36mtjqwvpa

Multiview Sensing With Unknown Permutations: An Optimal Transport Approach [article]

Yanting Ma, Petros T. Boufounos, Hassan Mansour, Shuchin Aeron
2021 arXiv   pre-print
In several applications, including imaging of deformable objects while in motion, simultaneous localization and mapping, and unlabeled sensing, we encounter the problem of recovering a signal that is measured  ...  In particular, we recognize that in most practical applications the unknown permutations are not arbitrary but some are more likely to occur than others.  ...  A generalization of the unlabeled sensing problem, introducing an optional linear operator measuring the permuted data.  ... 
arXiv:2103.07458v1 fatcat:lcdn4gskbrah3b2d3cfz3d4osq

Signal Amplitude Estimation and Detection From Unlabeled Binary Quantized Samples

Guanyu Wang, Jiang Zhu, Rick S. Blum, Peter Willett, Stefano Marano, Vincenzo Matta, Paolo Braca
2018 IEEE Transactions on Signal Processing  
In addition, an accurate approximation to the probability of successful permutation matrix recovery is derived, and explicit expressions are provided to reveal the relationship between the number of signal  ...  Signal amplitude estimation and detection from unlabeled quantized binary samples are studied, assuming that the order of the time indexes is completely unknown.  ...  In the noiseless case with a random linear sensing matrix, it is shown that the permutation matrix can be recovered correctly with probability 1, given that the number of measurements is twice the number  ... 
doi:10.1109/tsp.2018.2849704 fatcat:x5xwdocgajhqzolqjkgk2ezw7i

Ladder Matrix Recovery from Permutations [article]

Manolis C. Tsakiris
2022 arXiv   pre-print
We give unique recovery guarantees for matrices of bounded rank that have undergone permutations of their entries. We even do this for a more general matrix structure that we call ladder matrices.  ...  In unlabeled sensing, we have a linear subspace W -the column-space of A ∈ R m×r -and a permuted version y of a point b ∈ W inside that subspace, and we ask for unique recovery of b from A and y.  ...  In [21] Yao, Peng and the author considered a natural extension of unlabeled sensing, termed unlabeled principal component analysis, from vector spaces to algebraic varieties of matrices of bounded rank  ... 
arXiv:2207.10864v1 fatcat:jmkw4gg5nzgcpdcoih6yjyhvpe

Homomorphic Sensing of Subspace Arrangements [article]

Liangzu Peng, Manolis C. Tsakiris
2021 arXiv   pre-print
It has been successful in interpreting such a recovery in the case of permutations composed by coordinate projections, an important instance in applications known as unlabeled sensing, which models data  ...  Similarly, our noise result also implies that the unique recovery in unlabeled sensing is locally stable.  ...  ., matrices whose rows are formed by r distinct standard basis vectors of R m , unique recovery in unlabeled sensing is equivalent to hsp(R n , S r,m A).  ... 
arXiv:2006.05158v3 fatcat:5suyhejferemdcqkamxf5ja5jq
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