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44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Yuan, Weitao Wang, Shengbei Li, Xiangrui Unoki, Masashi Wang, Wenwu Tianjin Polytech Univ Tianjin Key Lab Autonomous Intelligence Technol & Tianjin Peoples R China Japan Adv Inst Sci & Technol Nomi Japan Univ Surrey Guildford Surrey England

ISBN: (纸本)9781479981311

The recent deep learning methods can offer state-of-the-art performance for Monaural Singing Voice Separation (MSVS). In these deep methods, the recurrent neural network (RNN) is widely employed. This work proposes a novel type of Deep RNN (DRNN), namely proximal DRNN (P-DRNN) for MSVS, which improves the conventional Stacked RNN (S-RNN) by introducing a novel interlayer structure. The interlayer structure is derived from an optimization problem for Monaural Source Separation (MSS). Accordingly, this enables a new hierarchical processing in the proposed P-DRNN with the explicit state transfers between different layers and the skip connections from the inputs, which are efficient for source separation. Finally, the proposed approach is evaluated on the MIR-1K dataset to verify its effectiveness. The numerical results show that the P-DRNN performs better than the conventional S-RNN and several recent MSVS methods.

关键词： proximal algorithm Monaural Source Separation Recurrent Neural Network

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Large-Scale Low-Rank Matrix Learning with Nonconvex Regularizers

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 2019年第11期41卷 2628-2643页

作者： Yao, Quanming Kwok, James T. Wang, Taifeng Liu, Tie-Yan 4Paradigm Inc Beijing 100089 Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Clear Water Bay Hong Kong Peoples R China Microsoft Res Asia Machine Learning Grp Beijing 100010 Peoples R China Microsoft Res Asia Beijing 100010 Peoples R China

Low-rank modeling has many important applications in computer vision and machine learning. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has demonstrated better empirical performance. However, the resulting optimization problem is much more challenging. Recent state-of-the-art requires an expensive full SVD in each iteration. In this paper, we show that for many commonly-used nonconvex low-rank regularizers, the singular values obtained from the proximal operator can be automatically threshold. This allows the proximal operator to be efficiently approximated by the power method. We then develop a fast proximal algorithm and its accelerated variant with inexact proximal step. It can be guaranteed that the squared distance between consecutive iterates converges at a rate of O(1/T), where T is the number of iterations. Furthermore, we show the proposed algorithm can be parallelized, and the resultant algorithm achieves nearly linear speedup w.r.t. the number of threads. Extensive experiments are performed on matrix completion and robust principal component analysis. Significant speedup over the state-of-the-art is observed.

关键词： Low-rank matrix learning nonconvex regularization proximal algorithm parallel algorithm matrix completion

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Linearized ADMM for Nonconvex Nonsmooth Optimization With Convergence Analysis

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IEEE ACCESS 2019年 7卷 76131-76144页

作者： Liu, Qinghua Shen, Xinyue Gu, Yuantao Tsinghua Univ Bejing Natl Res Ctr Informat Sci & Technol BNRist Beijing 100084 Peoples R China Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

Linearized alternating direction method of multipliers (ADMM) as an extension of ADMM has been widely used to solve linearly constrained problems in signal processing, machine learning, communications, and many other fields. Despite its broad applications in nonconvex optimization, for a great number of nonconvex and nonsmooth objective functions, its theoretical convergence guarantee is still an open problem. In this paper, we propose a two-block linearized ADMM and a multi-block parallel linearized ADMM for problems with nonconvex and nonsmooth objectives. Mathematically, we present that the algorithms can converge for a broader class of objective functions under less strict assumptions compared with previous works. Furthermore, our proposed algorithm can update coupled variables in parallel and work for less restrictive nonconvex problems, where the traditional ADMM may have difficulties in solving subproblems.

关键词： Linearized ADMM multi-block ADMM nonconvex optimization parallel computation proximal algorithm

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ADAPTIVE FISTA FOR NONCONVEX OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2019年第4期29卷 2482-2503页

作者： Ochs, Peter Pock, Thomas Saarland Univ Fac Math & Comp Sci Campus E1-7 D-66123 Saarbrucken Germany Graz Univ Technol Inst Comp Graph & Vis Inffeldgasse 16-2 A-8010 Graz Austria

In this paper we propose an adaptively extrapolated proximal gradient method, which is based on the accelerated proximal gradient method (also known as FISTA);however, we locally optimize the extrapolation parameter by carrying out an exact (or inexact) line search. It turns out that in some situations, the proposed algorithm is equivalent to a class of SR1 (identity minus rank 1) proximal quasi-Newton methods. Convergence is proved in a general nonconvex setting, and hence, as a byproduct, we also obtain new convergence guarantees for proximal quasi-Newton methods. The efficiency of the new method is shown in numerical experiments on a sparsity regularized nonlinear inverse problem.

关键词： FISTA proximal algorithm proximal quasi-Newton SR1 quasi-Newton

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Improving POI Recommendation via Non-Convex Regularized Tensor Completion

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Journal of Information Hiding and Privacy Protection 2020年第3期2卷 125-134页

作者： Ming Zhao Tao Liu School of Computer Science and Engineering Central South UniversityChangsha410000China

The problem of low accuracy of POI(Points of Interest)recommendation in LBSN(Location-Based Social Networks)has not been effectively *** this paper,a POI recommendation algorithm based on non-convex regularized tensor completion is *** fourth-order tensor is constructed by using the current location category,the next location category,time and season,the regularizer is added to the objective function of tensor completion to prevent over-fitting and reduce the error of the *** proximal algorithm is used to solve the objective function,and the adaptive momentum is introduced to improve the efficiency of the *** experimental results show that the algorithm can improve recommendation accuracy while reducing the time cost.

关键词： POI recommendation tensor completion proximal algorithm adaptive momentum

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A cubic spline penalty for sparse approximation under tight frame balanced model

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2020年第2期46卷 36-36页

作者： Pang, Tongyao Wu, Chunlin Liu, Zhifang Natl Univ Singapore Dept Math Singapore 119076 Singapore Nankai Univ Sch Math Sci Tianjin 300071 Peoples R China Tianjin Normal Univ Sch Math Sci Tianjin 300387 Peoples R China

The study of non-convex penalties has recently received considerable attentions in sparse approximation. The existing non-convex penalties are proposed on the principle of seeking for a continuous alternative to the l(0)-norm penalty. In this paper, we come up with a cubic spline penalty (CSP) which is also continuous but closer to l(0)-norm penalty compared to the existing ones. As a result, it produces the weakest bias among them. Wavelet tight frames are efficient for sparse approximation due to its redundancy and fast implementation algorithm. We adopt a tight frame balanced model with our proposed cubic spline penalty since the balanced model takes the advantages of both analysis and synthesis model. To solve the non-convex CSP penalized problem, we employ a proximal local linear approximation (PLLA) algorithm and prove the generated sequence converges to a stationary point of the model if it is bounded. Under additional conditions, we find that the limit point behaves as well as the oracle solution, which is obtained by using the exact support of the ground truth signal. The efficiency of our cubic spline penalty are further demonstrated in applications of variable selection and image deblurring.

关键词： Sparse approximation Thresholding rule Concave penalty proximal algorithm Oracle property Wavelet tight frame

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CALIBRATIONLESS OSCAR-BASED IMAGE RECONSTRUCTION IN COMPRESSED SENSING PARALLEL MRI 16

CALIBRATIONLESS OSCAR-BASED IMAGE RECONSTRUCTION IN COMPRESS...

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16th IEEE International Symposium on Biomedical Imaging (ISBI)

作者： El Gueddari, L. Ciuciu, P. Chouzenoux, E. Vignaud, A. Pesquet, J-C CEA NeuroSpin Bat 145 F-91191 Gif Sur Yvette France Univ Paris Saclay Parietal Team INRIA CEA Saclay Ile de France St Aubin France Univ Paris Saclay Cent Supelec CVN St Aubin France Paris Est Univ LIGM Champs Sur Marne France

ISBN: (纸本)9781538636411

Reducing acquisition time is a crucial issue in MRI especially in the high resolution context. Compressed sensing has faced this problem for a decade. However, to maintain a high signal-to-noise ratio (SNR), CS must be combined with parallel imaging. This leads to harder reconstruction problems that usually require the knowledge of coil sensitivity profiles. In this work, we introduce a calibrationless image reconstruction approach that no longer requires this knowledge. The originality of this work lies in using for reconstruction a group sparsity structure (called OSCAR) across channels that handles SNR inhomogeneities across receivers. We compare this reconstruction with other calibrationless approaches based on group LASSO and its sparse variation as well as with the auto-calibrated method called l(1)-ESPIRiT. We demonstrate that OSCAR outperforms its competitors and provides similar results to l(1)-ESPIRiT. This suggests that the sensitivity maps are no longer required to perform combined CS and parallel imaging reconstruction.

关键词： Compressed Sensing Parallel MRI Group Sparsity proximal algorithm

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LEARNING COMPACT PARTIAL DIFFERENTIAL EQUATIONS FOR COLOR IMAGES WITH EFFICIENCY 44

LEARNING COMPACT PARTIAL DIFFERENTIAL EQUATIONS FOR COLOR IM...

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44th IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

作者： Zhao, Zhenyu Hou, Chenping Lin, Bo Fang, Cong Natl Univ Def Technol Coll Liberal Arts & Sci Changsha Hunan Peoples R China Peking Univ Sch EECS Key Lab Machine Percept MOE Beijing Peoples R China

ISBN: (纸本)9781479981311

Learning Partial Differential Equations (LPDEs) from training data for particular tasks has been successfully applied to many image processing problems. In this paper, we aim to learn compact Partial Differential Equations (LCPDEs) for color image tasks by proposing a more effective algorithm. The LCPDEs system is formulated as a linear combination of fundamental differential invariants and simplified by omitting the PDE which works as an indicate function. We replace L2-norm with L1-norm to regularize the coefficients with respect to the invariants. As the objective function is non-smooth, we resort to proximal algorithm to optimize it, which ensures convergence in an at least sub-linear rate. Experiments demonstrate the advantages of the proposed method over other PDE-based methods in terms of both quality and efficiency.

关键词： Partial differential equations L1-norm regularization proximal algorithm Color images

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Error Bounds, Quadratic Growth, and Linear Convergence of proximal Methods

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MATHEMATICS OF OPERATIONS RESEARCH 2018年第3期43卷 919-948页

作者： Drusvyatskiy, Dmitriy Lewis, Adrian S. Univ Washington Dept Math Seattle WA 98195 USA Cornell Univ Sch Operat Res & Informat Engn Ithaca NY 14853 USA

The proximal gradient algorithm for minimizing the sum of a smooth and nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may linearly bound the " error"-the distance to the solution set. We explain the observed linear convergence intuitively by proving the equivalence of such an error bound to a natural quadratic growth condition. Our approach generalizes to linear and quadratic convergence analysis for proximal methods (of Gauss-Newton type) for minimizing compositions of nonsmooth functions with smooth mappings. We observe incidentally that short step-lengths in the algorithm indicate near-stationarity, suggesting a reliable termination criterion.

关键词： proximal algorithm error bound quadratic growth linear convergence subregularity subdifferential tilt-stability

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Consistent learning by composite proximal thresholding

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MATHEMATICAL PROGRAMMING 2018年第1期167卷 99-127页

作者： Combettes, Patrick L. Salzo, Saverio Villa, Silvia North Carolina State Univ Dept Math Box 8205 Raleigh NC 27695 USA MIT Lab Computat & Stat Learning I-16163 Genoa Italy Ist Italiano Tecnol I-16163 Genoa Italy Politecn Milan Dipartimento Matemat I-20133 Milan Italy

We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite dictionary of functions. We propose a novel flexible composite regularization model, which makes it possible to incorporate various priors on the coefficients of the prediction function, including sparsity and hard constraints. We show that the estimators obtained by minimizing the regularized empirical risk are consistent in a statistical sense, and we design an error-tolerant composite proximal thresholding algorithm for computing such estimators. New results on the asymptotic behavior of the proximal forward-backward splitting method are derived and exploited to establish the convergence properties of the proposed algorithm. In particular, our method features a o(1 / m) convergence rate in objective values.

关键词： Consistent estimator Convex optimization Forward-backward splitting proximal algorithm Sparse data representation

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