scholarly journals Uniform approximation property of frames with applications to erasure recovery

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ting Chen ◽  
Fusheng Lv ◽  
Wenchang Sun
Keyword(s):  
Computational Complexity ◽  
Uniform Approximation ◽  
Approximation Property ◽  
Recovery Algorithm ◽  
Recovery Error

<p style='text-indent:20px;'>In this paper, we introduce frames with the uniform approximation property (UAP). We show that with a UAP frame, it is efficient to recover a signal from its frame coefficients with one erasure while the recovery error is smaller than that with the ordinary recovery algorithm. In fact, our approach gives a balance between the recovery accuracy and the computational complexity.</p>

Adaptive Sparse Recovery of Moving Targets for Distributed MIMO Radar

2014 ◽  
Vol 933 ◽  
pp. 450-455
Author(s):  
Hui Yu ◽  
Guang Hua Lu ◽  
Hai Long Zhang
Keyword(s):  
High Resolution ◽  
Sparse Recovery ◽  
Mimo Radar ◽  
Moving Target ◽  
Recovery Algorithm ◽  
Low Snr ◽  
Computation Efficiency ◽  
Target Imaging ◽  
Moving Target Imaging ◽  
Recovery Error

The high resolution and better recovery performance with distributed MIMO radar would be significantly degraded when the target moves at an unknown velocity. In this paper, we propose an adaptive sparse recovery algorithm for moving target imaging to estimate the velocity and image jointly with high computation efficiency. With an iteration mechanism, the proposed method updates the image and estimates the velocity alternately by sequentially minimizing the norm and the recovery error. Numerical simulations are carried out to demonstrate that the proposed algorithm can retrieve high-resolution image and accurate velocity simultaneously even in low SNR.

scholarly journals CHAOTIC COMPRESSIVE SENSING OF TV –UHF BAND IN IRAQ USING CHEBYSHEV GRAM SCHMIDT SENSING MATRIX

2021 ◽  
Vol 1 (1) ◽  
pp. 134-145
Author(s):  
Hadeel S. Abed ◽  
Hikmat N. Abdullah
Keyword(s):  
Compressive Sensing ◽  
Probability Of Detection ◽  
Main Step ◽  
Mutual Coherence ◽  
Sensing Matrix ◽  
Recovery Algorithm ◽  
Low Snr ◽  
Chebyshev Map ◽  
Recovery Error ◽  
Three Stages

Cognitive radio (CR) is a promising technology for solving spectrum sacristy problem. Spectrum sensing  is the main step of CR.  Sensing the wideband spectrum produces more challenges. Compressive sensing (CS) is a technology used as spectrum sening  in CR to solve these challenges. CS consists of three stages: sparse representation, encoding and decoding. In encoding stage sensing matrix are required, and it plays an important role for performance of CS. The design of efficient sensing matrix requires achieving low mutual coherence . In decoding stage the recovery algorithm is applied to reconstruct a sparse signal. İn this paper a new chaotic matrix is proposed based on Chebyshev map and modified gram Schmidt (MGS). The CS based proposed matrix is applied for sensing  real TV signal as a PU. The proposed system is tested under two types of recovery algorithms. The performance of CS based proposed matrix is measured using recovery error (Re), mean square error (MSE), and probability of detection (Pd) and evaluated by comparing it with Gaussian, Bernoulli and chaotic matrix in the literature. The simulation results show that the proposed system has low Re and high Pd under low SNR values and has low MSE with high compression.

The uniform approximation property in Orlicz spaces

1976 ◽  
Vol 23 (2) ◽  
pp. 142-155 ◽  
Author(s):  
J. Lindenstrauss ◽  
L. Tzafriri
Keyword(s):  
Uniform Approximation ◽  
Approximation Property ◽  
Orlicz Spaces

scholarly journals Tensor Recovery from Noisy and Multi-Level Quantized Measurements

2020 ◽  
Author(s):  
Ren Wang ◽  
Meng Wang ◽  
Jinjun Xiong
Keyword(s):  
Gradient Descent ◽  
Optimization Problems ◽  
Low Rank ◽  
Quantization Rule ◽  
Descent Algorithm ◽  
Recovery Algorithm ◽  
Gradient Descent Algorithm ◽  
Tensor Recovery ◽  
Recovery Error ◽  
Multi Level

Abstract Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

scholarly journals Tensor recovery from noisy and multi-level quantized measurements

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Ren Wang ◽  
Meng Wang ◽  
Jinjun Xiong
Keyword(s):  
Gradient Descent ◽  
Optimization Problems ◽  
Low Rank ◽  
Quantization Rule ◽  
Descent Algorithm ◽  
Recovery Algorithm ◽  
Gradient Descent Algorithm ◽  
Tensor Recovery ◽  
Recovery Error ◽  
Multi Level

Abstract Higher-order tensors can represent scores in a rating system, frames in a video, and images of the same subject. In practice, the measurements are often highly quantized due to the sampling strategies or the quality of devices. Existing works on tensor recovery have focused on data losses and random noises. Only a few works consider tensor recovery from quantized measurements but are restricted to binary measurements. This paper, for the first time, addresses the problem of tensor recovery from multi-level quantized measurements by leveraging the low CANDECOMP/PARAFAC (CP) rank property. We study the recovery of both general low-rank tensors and tensors that have tensor singular value decomposition (TSVD) by solving nonconvex optimization problems. We provide the theoretical upper bounds of the recovery error, which diminish to zero when the sizes of dimensions increase to infinity. We further characterize the fundamental limit of any recovery algorithm and show that our recovery error is nearly order-wise optimal. A tensor-based alternating proximal gradient descent algorithm with a convergence guarantee and a TSVD-based projected gradient descent algorithm are proposed to solve the nonconvex problems. Our recovery methods can also handle data losses and do not necessarily need the information of the quantization rule. The methods are validated on synthetic data, image datasets, and music recommender datasets.

scholarly journals The translation invariant uniform approximation property for compact groups

1988 ◽  
Vol 90 (1) ◽  
pp. 27-35
Author(s):  
Jarosław Krawczyk
Keyword(s):  
Uniform Approximation ◽  
Approximation Property ◽  
Compact Groups ◽  
Translation Invariant

scholarly journals On the duality of the uniform approximation property in Banach spaces

1991 ◽  
Vol 35 (2) ◽  
pp. 191-197 ◽  
Author(s):  
Vania Mascioni
Keyword(s):  
Banach Spaces ◽  
Uniform Approximation ◽  
Approximation Property

scholarly journals Some remarks on the uniform approximation property in Banach spaces

1990 ◽  
Vol 96 (3) ◽  
pp. 243-253 ◽  
Author(s):  
Vania Mascioni
Keyword(s):  
Banach Spaces ◽  
Uniform Approximation ◽  
Approximation Property

On the uniform approximation property in Banach spaces

1984 ◽  
Vol 49 (4) ◽  
pp. 343-359 ◽  
Author(s):  
A. Szankowski
Keyword(s):  
Banach Spaces ◽  
Uniform Approximation ◽  
Approximation Property

scholarly journals Cross Validation Based Distributed Greedy Sparse Recovery for Multiview Through-the-Wall Radar Imaging

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Lele Qu ◽  
Shimiao An ◽  
Yanpeng Sun
Keyword(s):  
Cross Validation ◽  
Matching Pursuit ◽  
Measurement Data ◽  
Radar Imaging ◽  
Sparse Recovery ◽  
Imaging Algorithm ◽  
Recovery Algorithm ◽  
Recovery Error ◽  
Cv Measurements ◽  
Imaging Performance

Multiview through-the-wall radar imaging (TWRI) can improve the imaging quality and target detection by exploiting the measurement data acquired from various views. Based on the established joint sparsity signal model for multiview TWRI, a cross validation (CV) based distributed greedy sparse recovery algorithm which combines the strengths of the CV technique and censored simultaneous orthogonal matching pursuit algorithm (CSOMP) is proposed in this paper. The developed imaging algorithm named by CV-CSOMP which separates the total measurements into reconstruction measurements and CV measurements is able to achieve the accurate imaging reconstruction and estimation of recovery error tolerance by the iterative CSOMP calculation. The proposed CV-CSOMP imaging algorithm not only can reduce the communication costs among radar units, but also can provide the desirable imaging performance without the prior information such as the sparsity or noise level. The experimental results have verified the validity and effectiveness of the proposed imaging algorithm.

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