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Rapid, Robust, and Reliable Blind Deconvolution via Nonconvex Optimization [article]

Xiaodong Li, Shuyang Ling, Thomas Strohmer, Ke Wei
2016 arXiv   pre-print
To the best of our knowledge, our algorithm is the first blind deconvolution algorithm that is numerically efficient, robust against noise, and comes with rigorous recovery guarantees under certain subspace  ...  This problem, known as blind deconvolution, pervades many areas of science and technology, including astronomy, medical imaging, optics, and wireless communications.  ...  Strohmer, and K. Wei acknowledge support from the NSF via grant dtra-dms 1322393.  ... 
arXiv:1606.04933v1 fatcat:y5uw4je2jneddaurz6xqioddx4

Rapid, robust, and reliable blind deconvolution via nonconvex optimization

Xiaodong Li, Shuyang Ling, Thomas Strohmer, Ke Wei
2018 Applied and Computational Harmonic Analysis  
To the best of our knowledge, our algorithm is the first blind deconvolution algorithm that is numerically efficient, robust against noise, and comes with rigorous recovery guarantees under certain subspace  ...  This problem, known as blind deconvolution, pervades many areas of science and technology, including astronomy, medical imaging, optics, and wireless communications.  ...  [4] considers an interesting blind calibration problem with a special type of measurement matrix via nonconvex optimization.  ... 
doi:10.1016/j.acha.2018.01.001 fatcat:c2lmxxfbe5ejnpsfpdeluwpdny

Finding the Sparsest Vectors in a Subspace: Theory, Algorithms, and Applications [article]

Qing Qu, Zhihui Zhu, Xiao Li, Manolis C. Tsakiris, John Wright, and René Vidal
2020 arXiv   pre-print
recovery, dictionary learning, sparse blind deconvolution, and many other problems in signal processing and machine learning.  ...  for solving the associated nonconvex optimization problem, to applications in machine intelligence, representation learning, and imaging sciences.  ...  Strohmer, and K. Wei, “Rapid, robust, and reliable blind deconvolution via nonconvex optimization,” Applied and computational harmonic analysis, vol. 47, no. 3, pp. 893–934, 2019. [102] Z.  ... 
arXiv:2001.06970v1 fatcat:zluhhl3635bzrnnk7fjw5tvi7a

A Nonconvex Approach for Exact and Efficient Multichannel Sparse Blind Deconvolution [article]

Qing Qu, Xiao Li, Zhihui Zhu
2020 arXiv   pre-print
We formulate the task as a nonconvex optimization problem over the sphere.  ...  We study the multi-channel sparse blind deconvolution (MCS-BD) problem, whose task is to simultaneously recover a kernel a and multiple sparse inputs {x_i}_i=1^p from their circulant convolution y_i =  ...  Acknowledgement Part of this work is done when QQ, XL and ZZ were attending "Computational Imaging" workshop at ICERM Brown in Spring 2019. We would like to thank the National Science  ... 
arXiv:1908.10776v3 fatcat:ku5mxr7ppfhejlh6kdyuuppspm

Convex and Nonconvex Optimization Are Both Minimax-Optimal for Noisy Blind Deconvolution under Random Designs [article]

Yuxin Chen, Jianqing Fan, Bingyan Wang, Yuling Yan
2021 arXiv   pre-print
We investigate the effectiveness of convex relaxation and nonconvex optimization in solving bilinear systems of equations under two different designs (i.e.a sort of random Fourier design and Gaussian design  ...  The current paper makes two contributions by demonstrating that: (1) a two-stage nonconvex algorithm attains minimax-optimal accuracy within a logarithmic number of iterations. (2) convex relaxation also  ...  , IIS-2100158 and DMS-2014279, and by the Princeton SEAS innovation award.  ... 
arXiv:2008.01724v2 fatcat:u6j7gazbpnd6dfpwa3zh7pzpki

Learning to do multiframe wavefront sensing unsupervised: Applications to blind deconvolution

A. Asensio Ramos, N. Olspert
2021 Astronomy and Astrophysics  
Leveraging the linear image formation theory and a probabilistic approach to the blind deconvolution problem produces a physically motivated loss function.  ...  The network model is roughly three orders of magnitude faster than applying standard deconvolution based on optimization and shows potential to be used on real-time at the telescope.  ...  We thank Álex Oscoz, Roberto López and Jorge Andrés Prieto for providing the FastCam@NOT datasets and Jaime de la Cruz Rodríguez for providing the CRISP@SST datasets.  ... 
doi:10.1051/0004-6361/202038552 fatcat:5f5vr7jn3fdn7fyicmmldadh4m

Implicit Regularization in Nonconvex Statistical Estimation: Gradient Descent Converges Linearly for Phase Retrieval, Matrix Completion, and Blind Deconvolution [article]

Cong Ma, Kaizheng Wang, Yuejie Chi, Yuxin Chen
2019 arXiv   pre-print
Focusing on three fundamental statistical estimation problems, i.e. phase retrieval, low-rank matrix completion, and blind deconvolution, we establish that gradient descent achieves near-optimal statistical  ...  In particular, by marrying statistical modeling with generic optimization theory, we develop a general recipe for analyzing the trajectories of iterative algorithms via a leave-one-out perturbation argument  ...  Chi is supported in part by the grants AFOSR FA9550-15-1-0205, ONR N00014-15-1-2387, NSF CCF-1527456, ECCS-1650449 and CCF-1704245. Y.  ... 
arXiv:1711.10467v3 fatcat:qmqqujn55nhtbncwcy3c7ka66m

Characterization of Gradient Dominance and Regularity Conditions for Neural Networks [article]

Yi Zhou, Yingbin Liang
2017 arXiv   pre-print
These two landscape properties are desirable for the optimization around the global minimizers of the loss function for these neural networks.  ...  the regularity condition along certain directions and within the neighborhood of their global minimizers.  ...  Rapid, robust, and reliable blind deconvolution via nonconvex optimization. Arxiv: 1606.04933. Lippmann, R. (1988). An introduction to computing with neural nets.  ... 
arXiv:1710.06910v2 fatcat:2xsjin6eybeedoy3usliy7uf4a

Understanding the Impact of Model Incoherence on Convergence of Incremental SGD with Random Reshuffle [article]

Shaocong Ma, Yi Zhou
2020 arXiv   pre-print
Specifically, minimizer incoherence measures the discrepancy between the global minimizers of a sample loss and those of the total loss and affects the convergence error of SGD with random reshuffle.  ...  With model incoherence, our results show that SGD has a faster convergence rate and smaller convergence error under random reshuffle than those under random sampling, and hence provide justifications to  ...  ., and Wei, K. Rapid, robust, and reliable blind deconvolution via nonconvex optimization. Applied and Computational Harmonic Analysis, 2018. Ma, S., Bassily, R., and Belkin, M.  ... 
arXiv:2007.03509v1 fatcat:ylglnxk5zzfmbc7xrwdhkp4vf4

Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval [article]

Yuxin Chen, Yuejie Chi, Jianqing Fan, Cong Ma
2019 arXiv   pre-print
All of these are achieved by exploiting the statistical models in analyzing optimization algorithms, via a leave-one-out approach that enables the decoupling of certain statistical dependency between the  ...  gradient descent iterates and the data.  ...  Fan is supported in part by the NSF grants DMS-1662139 and DMS-1712591, the ONR grant N00014-19-1-2120, and the NIH grant 2R01-GM072611-13.  ... 
arXiv:1803.07726v2 fatcat:jemo7c7olzg2natul5n5adrc3y

Accelerating Ill-Conditioned Low-Rank Matrix Estimation via Scaled Gradient Descent [article]

Tian Tong, Cong Ma, Yuejie Chi
2021 arXiv   pre-print
A popular approach in practice is to factorize the matrix into two compact low-rank factors, and then optimize these factors directly via simple iterative methods such as gradient descent and alternating  ...  With tailored variants for low-rank matrix sensing, robust principal component analysis and matrix completion, we theoretically show that ScaledGD achieves the best of both worlds: it converges linearly  ...  Tong and Y.  ... 
arXiv:2005.08898v4 fatcat:fi4mfkd45fcvjhdlepfwmyuh2u

Spatial Sparsity-Induced Prediction (SIP) for Images and Video: A Simple Way to Reject Structured Interference

Gang Hua, Onur G. Guleryuz
2011 IEEE Transactions on Image Processing  
None of the interference parameters are estimated as our algorithm provides completely blind and automated operation.  ...  We provide a general formulation that allows for nonlinearities in the prediction loop and we consider prediction optimal decompositions.  ...  (26) Hence, as long as the optimal deconvolution filter, f −1 , can be closely approximated via f −1 ∼   1 p 2 p 2 q=1 α q φ ′ q * φ q   , (27) for some α q , q = 1, . . . , p 2 , the assumption requirements  ... 
doi:10.1109/tip.2010.2082991 pmid:20923739 fatcat:6fzq3lddezeoddqtywqwouhyha

2019 Index IEEE Transactions on Industrial Informatics Vol. 15

2019 IEEE Transactions on Industrial Informatics  
., +, TII April 2019 2083-2090 Robust Faulted Line Identification in Power Distribution Networks via Hybrid State Estimator.  ...  ., +, TII March 2019 1521-1531 Robust Faulted Line Identification in Power Distribution Networks via Hybrid State Estimator.  ... 
doi:10.1109/tii.2020.2968165 fatcat:utk3ywxc6zgbdbfsys5f4otv7u

2021 Index IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing Vol. 14

2021 IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing  
The primary entry includes the coauthors' names, the title of the paper or other item, and its location, specified by the publication abbreviation, year, month, and inclusive pagination.  ...  The Subject Index contains entries describing the item under all appropriate subject headings, plus the first author's name, the publication abbreviation, month, and year, and inclusive pages.  ...  Nonconvex and TV Regularization.  ... 
doi:10.1109/jstars.2022.3143012 fatcat:dnetkulbyvdyne7zxlblmek2qy

2020 Index IEEE Transactions on Instrumentation and Measurement Vol. 69

2020 IEEE Transactions on Instrumentation and Measurement  
Meenalochani, M., and Sudha, S., Influence of Received Signal Strength on Prediction of Cluster Head and Number of Rounds; TIM June 2020 3739-3749 Hendeby, G., see Kasebzadeh, P., TIM Aug. 2020 5862  ...  Converter Using All-Digital Nested Delay-Locked Loops With 50-ps Resolution and High Throughput for LiDAR TIM Nov. 2020 9262-9271 Helsen, J., see Huchel, L., TIM July 2020 4145-4153 Hemavathi, N.,  ...  Li, N., +, TIM March 2020 770-781 Nonconvex Group Sparsity Signal Decomposition via Convex Optimization for Bearing Fault Diagnosis.  ... 
doi:10.1109/tim.2020.3042348 fatcat:a5f4fsqs45fbbetre6zwsg3dly
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