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Convergence of Slice-Based Block Coordinate Descent Algorithm for Convolutional Sparse Coding

Jing Li, Hui Yu, Xiao Wei, Jinjia Wang
2020 Mathematical Problems in Engineering  
Several research studies have addressed the basis pursuit (BP) problem of the CSC model, including the recently proposed local block coordinate descent (LoBCoD) algorithm.  ...  A slice-based multilayer local block coordinate descent (ML-LoBCoD) algorithm is proposed which is motivated by the multilayer basis pursuit (ML-BP) problem and the LoBCoD algorithm.  ...  Slice-Based Multilayer Local Block Coordinate Descent Algorithm Slice-Based Multilayer Convolutional Sparse Coding. e ML-CSC model is a deep extension of the CSC model, since the ML-CSC model assumes  ... 
doi:10.1155/2020/4367515 fatcat:jsuasg4f65bqlls7mv2rmibc4y

A Local Block Coordinate Descent Algorithm for the Convolutional Sparse Coding Model [article]

Ev Zisselman, Jeremias Sulam, Michael Elad
2018 arXiv   pre-print
In this work we maintain the localized strategy of the SBDL, while proposing a new and much simpler approach based on the Block Coordinate Descent algorithm - this method is termed Local Block Coordinate  ...  A recent work by Papyan et al. suggested the SBDL algorithm for the CSC, while operating locally on image patches.  ...  ACKNOWLEDGMENT The research leading to these results has received funding in part from the European Research Council under EUs 7th  ... 
arXiv:1811.00312v1 fatcat:yqxvew5mhbe5rp5b74pna5wohe

Research on Semi-supervised Sound Event Detection Based on Mean Teacher Models Using ML-LoBCoD-NET

Jinjia Wang, Jing Xia, Qian Yang, Yuzhen Zhang
2020 IEEE Access  
The authors thank all anonymous reviewers for their effort and suggestions to improve this paper. VOLUME 4, 2016  ...  The ML-LoBCoD-NET is driven by the multi-layer local block coordinate descent algorithm (ML-LoBCoD) which is extended from the local block coordinate descent (LoBCoD) algorithm. A.  ...  J. (5) The slice-based local block coordinate descent algorithm is extended into the multi-layers. Then, a slice-based multi-layer local block coordinate descent algorithm (ML-LoBCoD) is proposed.  ... 
doi:10.1109/access.2020.2974479 fatcat:lyarmpw3tbcqdpq6xpsnacesxa

Multivariate Convolutional Sparse Coding for Electromagnetic Brain Signals [article]

Tom Dupré La Tour, Thomas Moreau, Mainak Jas, Alexandre Gramfort
2018 arXiv   pre-print
Our algorithm is based on alternated minimization and a greedy coordinate descent solver that leads to state-of-the-art running time on long time series.  ...  In this paper, we propose to learn dedicated representations of such recordings using a multivariate convolutional sparse coding (CSC) algorithm.  ...  Acknowledgment This work was supported by the ERC Starting Grant SLAB ERC-YStG-676943 and by the ANR THALA-MEEG ANR-14-NEUC-0002-01  ... 
arXiv:1805.09654v2 fatcat:b2gmzdbosrghli6dnijlpnxgmu

Variations on the CSC model [article]

Ives Rey-Otero, Jeremias Sulam, Michael Elad
2018 arXiv   pre-print
available algorithms that deploy the CSC model consider the same ℓ_1 - ℓ_2 problem form.  ...  This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints.  ...  The second stage of the block-coordinate descent algorithm consists in updating the estimate of X, the restored image, by solving the least-square problem in closed form [2] according to: X = λI + R  ... 
arXiv:1810.01169v1 fatcat:kvlwq3mgkvd37lhd4rrr27av7a

Distributed Convolutional Dictionary Learning (DiCoDiLe): Pattern Discovery in Large Images and Signals [article]

Thomas Moreau, Alexandre Gramfort
2019 arXiv   pre-print
To address this optimization problem, this work proposes a distributed and asynchronous algorithm, employing locally greedy coordinate descent and an asynchronous locking mechanism that does not require  ...  This algorithm can be used to distribute the computation on a number of workers which scales linearly with the encoded signal's size.  ...  Locally Greedy Coordinate Descent for CSC Coordinate descent (CD) is an algorithm which updates a single coefficient at each iteration.  ... 
arXiv:1901.09235v1 fatcat:uqsaiprxavbzphelgpuv4ipvmy

Consensus Convolutional Sparse Coding

Biswarup Choudhury, Robin Swanson, Felix Heide, Gordon Wetzstein, Wolfgang Heidrich
2017 2017 IEEE International Conference on Computer Vision (ICCV)  
By learning CSC features from large-scale image datasets for the first time, we achieve significant quality improvements in a number of imaging tasks.  ...  Convolutional sparse coding (CSC) is a promising direction for unsupervised learning in computer vision.  ...  Gordon Wetzstein was supported by a Terman Faculty Fellowship, the Intel Compressive Sensing Alliance, the National Science Foundation (IIS 1553333), and the NSF/Intel Partnership on Visual and Experiential  ... 
doi:10.1109/iccv.2017.459 dblp:conf/iccv/ChoudhurySHWH17 fatcat:6tcbbgk47bgbtpkk5hf5fc3dxi

Cogradient Descent for Bilinear Optimization [article]

Li'an Zhuo, Baochang Zhang, Linlin Yang, Hanlin Chen, Qixiang Ye, David Doermann, Guodong Guo, Rongrong Ji
2020 arXiv   pre-print
In this paper, we introduce a Cogradient Descent algorithm (CoGD) to address the bilinear problem, based on a theoretical framework to coordinate the gradient of hidden variables via a projection function  ...  One reason lies in the insufficient training due to the asynchronous gradient descent, which results in vanishing gradients for the coupled variables.  ...  To update the parameters in a bilinear model, they directly utilize the gradient descent algorithm and backpropagate the gradients of the loss.  ... 
arXiv:2006.09142v1 fatcat:h2vvyxczhratlp7jvzictfukti

Fast Convolutional Sparse Coding in the Dual Domain [article]

Lama Affara, Bernard Ghanem, Peter Wonka
2018 arXiv   pre-print
We present two contributions to the state of the art in CSC. First, we significantly speed up the computation by proposing a new optimization framework that tackles the problem in the dual domain.  ...  Convolutional sparse coding (CSC) is an important building block of many computer vision applications ranging from image and video compression to deep learning.  ...  The full algorithm for the CSC problem is shown in Alg. 1. The coordinate descent algorithm above guarantees a monotonically decreasing joint objective.  ... 
arXiv:1709.09479v2 fatcat:vb5qtmtoxjdwbicvydjdo2s574

Fast and flexible convolutional sparse coding

Felix Heide, Wolfgang Heidrich, Gordon Wetzstein
2015 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)  
In this paper, we propose a new approach to solving CSC problems and show that our method converges significantly faster and also finds better solutions than the state of the art.  ...  As opposed to patch-based methods, convolutional sparse coding operates on whole images, thereby seamlessly capturing the correlation between local neighborhoods.  ...  Algorithm 2 CSC learning using coordinate descent 1: Algorithm penalty parameters: ρ d ∈ R + , ρ z ∈ R + 2: Initialize variables: d 0 , z 0 , λ 0 d , λ 0 z 3: repeat {Outer iterations} 4: Kernel update  ... 
doi:10.1109/cvpr.2015.7299149 dblp:conf/cvpr/HeideHW15 fatcat:jxhljvbgbbaodk4wrughvthelu

Cogradient Descent for Dependable Learning [article]

Runqi Wang, Baochang Zhang, Li'an Zhuo, Qixiang Ye, David Doermann
2021 arXiv   pre-print
In this paper, we propose a dependable learning based on Cogradient Descent (CoGD) algorithm to address the bilinear optimization problem, providing a systematic way to coordinate the gradients of coupling  ...  Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative.  ...  Acknowledgments We are thankful for the comments from Prof. Rongrong Ji for their deep and insightful discussion.  ... 
arXiv:2106.10617v1 fatcat:s5gthlcvfzh6jgqx3mwm2obtbq

General Convolutional Sparse Coding with Unknown Noise [article]

Yaqing Wang, James T. Kwok, Lionel M. Ni
2019 arXiv   pre-print
We use the expectation-maximization algorithm to solve the problem and design an efficient method for the weighted CSC problem in maximization step.  ...  In this paper, we propose a general CSC model capable of dealing with complicated unknown noise.  ...  Thus, CSC is mainly solved by alternatively update the codes and dictionary by block coordinate descent (BCD) [18] .  ... 
arXiv:1903.03253v1 fatcat:ygicvrmblvamrbiidhetokjnvm

Scalable training of deep learning machines by incremental block training with intra-block parallel optimization and blockwise model-update filtering

Kai Chen, Qiang Huo
2016 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  
mini-batch based stochastic gradient descent training on a single GPU.  ...  We present a new approach to scalable training of deep learning machines by incremental block training with intra-block parallel optimization to leverage data parallelism and blockwise model-update filtering  ...  It is noted that local models can also be optimized by other algorithms such as natural gradient SGD [30] and even ASGD for workers with multiple GPUs or CPUs.  ... 
doi:10.1109/icassp.2016.7472805 dblp:conf/icassp/ChenH16 fatcat:jg7gvoeznvgp3da2jzezoons34

Scalable Online Convolutional Sparse Coding

Yaqing Wang, Quanming Yao, James T. Kwok, Lionel M. Ni
2018 IEEE Transactions on Image Processing  
Moreover, while existing CSC algorithms can only run on a small number of images, the proposed method can handle at least ten times more images.  ...  Convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data.  ...  Problem (13) can be solved by block coordinate descent [5] , [8] , [16] , [17] , which updates {Z i } and D alternately. 1) Updating {Z i }: GivenD, the {Z i } can be obtained one by one for each  ... 
doi:10.1109/tip.2018.2842152 pmid:29969396 fatcat:3hd2s6pxcneytgnecrr56jqpam

Convolutional Dictionary Learning via Local Processing [article]

Vardan Papyan, Yaniv Romano, Jeremias Sulam, Michael Elad
2017 arXiv   pre-print
A recent work suggested a novel theoretical analysis of this global model, providing guarantees that rely on a localized sparsity measure.  ...  Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations.  ...  Moreover, both iterate this process in a block-coordinate descent manner in order to minimize the overall objective. So, what is the difference between this algorithm and previous approaches?  ... 
arXiv:1705.03239v1 fatcat:dozpli5djjcalnkzz6uu3obql4
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