A lower bound guaranteeing exact matrix completion via singular value thresholding algorithm

The singular value thresholding (SVT) algorithm plays an important role in the well-known matrix reconstruction problem, and it has many applications in computer vision and recommendation systems. In this paper, an SVT with diagonal-update (D-SVT) algorithm was put forward, which allows the algorithm to make use of simple arithmetic operation and keep the computational cost of each iteration low. The low-rank matrix would be reconstructed well. The convergence of the new algorithm was discussed in detail. Finally, the numerical experiments show the effectiveness of the new algorithm for low-rank matrix completion.

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An optimized 2D-Robust Adaptive Beamforming algorithm based on Matrix Completion in sparse array

MATEC Web of Conferences ◽

10.1051/matecconf/201820801003 ◽

2018 ◽

Vol 208 ◽

pp. 01003

Author(s):

Jiaying Di ◽

Wen Hu ◽

Mengxia Li ◽

Hongtao Li

Keyword(s):

Matrix Completion ◽

Adaptive Beamforming ◽

Singular Value ◽

Spectral Norm ◽

Sparse Array ◽

Robust Adaptive Beamforming ◽

Robust Adaptive ◽

Singular Value Thresholding ◽

Beamforming Algorithm ◽

Norm Error

The sparse arrays can reduce the cost of beamforming, it greatly reduces the number of actual array elements. However, it also brings about the problem of information loss. A 2D-robust adaptive beamforming algorithm in sparse array based on Singular Value Thresholding algorithm is proposed. At first, a signal model of planar array is established based on Matrix Completion, which can be proved to meet Null Space Property. Then the Genetic Algorithm is used to optimize the sparse array, which is determined to reduce the Spectral Norm Error of Matrix Completion and make the array recovered closer to the full array. In the case of sparse array, the missing information is restored by using the theory of Singular Value Thresholding, and then the restored signal is used to design the digital beamformer weights. This algorithm significantly reduces the Spectral Norm Error and forms robust adaptive beam.

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A Singular Value Thresholding Algorithm for Order Estimation

2021 American Control Conference (ACC) ◽

10.23919/acc50511.2021.9482743 ◽

2021 ◽

Author(s):

Ahmad S. Al-Tawaha ◽

Khaled Aljanaideh ◽

Ahmad Alshorman

Keyword(s):

Singular Value ◽

Order Estimation ◽

Thresholding Algorithm ◽

Singular Value Thresholding

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Matrix completion by singular value thresholding: Sharp bounds

Electronic Journal of Statistics ◽

10.1214/15-ejs1076 ◽

2015 ◽

Vol 9 (2) ◽

pp. 2348-2369 ◽

Cited By ~ 9

Author(s):

Olga Klopp

Keyword(s):

Matrix Completion ◽

Singular Value ◽

Sharp Bounds ◽

Singular Value Thresholding

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Optimized quantum singular value thresholding algorithm based on a hybrid quantum computer

Chinese Physics B ◽

10.1088/1674-1056/ac40fb ◽

2021 ◽

Author(s):

Yangyang Ge ◽

Zhimin Wang ◽

Wen Zheng ◽

Yu Zhang ◽

Xiangmin Yu ◽

...

Keyword(s):

Quantum Computer ◽

Singular Values ◽

Singular Value ◽

Low Rank ◽

Continuous Variables ◽

Rank Matrix ◽

Near Term ◽

Thresholding Algorithm ◽

Low Rank Matrix ◽

Singular Value Thresholding

Abstract Quantum singular value thresholding (QSVT) algorithm, as a core module of many mathematical models, seeks the singular values of a sparse and low rank matrix exceeding a threshold and their associated singular vectors. The existing all-qubit QSVT algorithm demands lots of ancillary qubits, remaining a huge challenge for realization on near-term intermediate-scale quantum computers. In this paper, we propose a hybrid QSVT (HQSVT) algorithm utilizing both discrete variables (DVs) and continuous variables (CVs). In our algorithm, raw data vectors are encoded into a qubit system and the following data processing is fulfilled by hybrid quantum operations. Our algorithm requires O[log(MN)] qubits with O(1) qumodes and totally performs O(1) operations, which significantly reduces the space and runtime consumption.

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