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Multi-Layer Convolutional Sparse Modeling: Pursuit and Dictionary Learning

Jeremias Sulam, Vardan Papyan, Yaniv Romano, Michael Elad
2018 IEEE Transactions on Signal Processing  
The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs  ...  Our work represents a bridge between matrix factorization, sparse dictionary learning and sparse auto-encoders, and we analyze these connections in detail.  ...  Multi Layer CSC The Multi-Layer Convolutional Sparse Coding (ML-CSC) model is a natural extension of the CSC described above, as it assumes that a signal can be expressed by sparse representations at different  ... 
doi:10.1109/tsp.2018.2846226 fatcat:tjxqlzo54bgt3iacu2czacff3q

Sparse Pursuit and Dictionary Learning for Blind Source Separation in Polyphonic Music Recordings [article]

Sören Schulze, Emily J. King
2020 arXiv   pre-print
We develop a novel sparse pursuit algorithm that can match the discrete spectra from the recorded signal with the continuous spectra delivered by the model.  ...  We then make use of the pitch-invariant properties of that representation in order to identify the sounds of the instruments via the same sparse pursuit method.  ...  Bodmann, Gitta Kutyniok, and Monika Dörfler for engaging discussions on the subject and Kara Tober for playing the clarinet samples. Author details  ... 
arXiv:1806.00273v4 fatcat:uhblpu3qivf43ekk7v7tr3no3m

Adversarial Noise Attacks of Deep Learning Architectures – Stability Analysis via Sparse Modeled Signals [article]

Yaniv Romano, Aviad Aberdam, Jeremias Sulam, Michael Elad
2019 arXiv   pre-print
We start with convolutional sparsity and then proceed to its multi-layered version, which is tightly connected to CNNs.  ...  In addition, we offer similar stability theorems for two practical pursuit algorithms, which are posed as two different deep-learning architectures - the layered Thresholding and the layered Basis Pursuit  ...  We commence by analyzing a shallow convolutional sparse model and then proceed to its multi-layer extension.  ... 
arXiv:1805.11596v3 fatcat:taob5csjpvgwxjugmc575l3fsq

Rethinking the CSC Model for Natural Images [article]

Dror Simon, Michael Elad
2019 arXiv   pre-print
In recent years, the Convolutional Sparse Coding (CSC) model, in which the dictionary consists of shift-invariant filters, has gained renewed interest.  ...  Sparse representation with respect to an overcomplete dictionary is often used when regularizing inverse problems in signal and image processing.  ...  Acknowledgement The research leading to these results has received funding from the Technion Hiroshi Fujiwara Cyber Security Research Center and the Israel Cyber Directorate.  ... 
arXiv:1909.05742v1 fatcat:c25n24s5hjcejk5ywtcxsjwfsu

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

Ev Zisselman, Jeremias Sulam, Michael Elad
2018 arXiv   pre-print
Contemporary methods for pursuit and learning the CSC dictionary often rely on the Alternating Direction Method of Multipliers (ADMM) in the Fourier domain for the computational convenience of convolutions  ...  The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities.  ...  The CSC model handles the signal globally, and yet pursuit and dictionary learning are feasible due to the specific structure of the dictionary involved.  ... 
arXiv:1811.00312v1 fatcat:yqxvew5mhbe5rp5b74pna5wohe

Improved Image Generation via Sparse Modeling [article]

Roy Ganz, Michael Elad
2022 arXiv   pre-print
More specifically, we show that generators can be viewed as manifestations of the Convolutional Sparse Coding (CSC) and its Multi-Layered version (ML-CSC) synthesis processes.  ...  In this paper, we aim to provide a better understanding and design of the image generation process. We interpret existing generators as implicitly relying on sparsity-inspired models.  ...  To do so, we utilize the convolutional sparse coding (CSC) and its Multi-Layer version (ML-CSC) models.  ... 
arXiv:2104.00464v2 fatcat:fkgcsxjpcng43emokttcbexocq

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 dictionary and sparse code of multi-layer convolutional sparse coding (ML-CSC) also inherit the same prior knowledge [19] .  ...  algorithm for the multi-layer basis pursuit.  ... 
doi:10.1109/access.2020.2974479 fatcat:lyarmpw3tbcqdpq6xpsnacesxa

Dataless Model Selection with the Deep Frame Potential [article]

Calvin Murdock, Simon Lucey
2020 arXiv   pre-print
Building upon theoretical connections between deep learning and sparse approximation, we propose the deep frame potential: a measure of coherence that is approximately related to representation stability  ...  We validate its use as a criterion for model selection and demonstrate correlation with generalization error on a variety of common residual and densely connected network architectures.  ...  solution of a multi-layer sparse coding model [26] .  ... 
arXiv:2003.13866v1 fatcat:ctvt43qmzrdohk6uti7qm4uscq

Sparse and deep generalizations of the FRAME model

Ying Nian Wu, Jianwen Xie, Yang Lu, Song-Chun Zhu
2018 Annals of Mathematical Sciences and Applications  
We can recruit a generator model as a direct and approximate sampler of the deep energy-based model to speed up the sampling step, and the two models can be learned simultaneously by a cooperative learning  ...  The model can be learned by an "analysis by synthesis" algorithm that iterates a sampling step for synthesis and a learning step for analysis.  ...  Acknolwedgment The work is supported by NSF DMS 1310391, DARPA SIMPLEX N66001-15-C-4035, ONR MURI N00014-16-1-2007, and DARPA ARO W911NF-16-1-0579.  ... 
doi:10.4310/amsa.2018.v3.n1.a7 fatcat:te7aw7vmnze3fbaotkqwzaf3uq

On Multi-Layer Basis Pursuit, Efficient Algorithms and Convolutional Neural Networks [article]

Jeremias Sulam, Aviad Aberdam, Amir Beck, Michael Elad
2018 arXiv   pre-print
Motivated by the recent Multi-Layer Convolutional Sparse Coding (ML-CSC) model, we herein generalize the traditional Basis Pursuit problem to a multi-layer setting, introducing similar sparse enforcing  ...  penalties at different representation layers in a symbiotic relation between synthesis and analysis sparse priors.  ...  ), but the multi-layer sparse model provides a convenient way to study deep learning architectures in terms of pursuit algorithms [?] .  ... 
arXiv:1806.00701v5 fatcat:hj5nar6whbf73edlehvn2zgmem

Multi-layer Basis Pursuit for Compressed Sensing MR Image Reconstruction

Abdul Wahid, Jawad Shah, Adnan Umar Khan, Manzoor Ahmed, Hanif Razali
2020 IEEE Access  
ACKNOWLEDGMENT Authors would like to thank Electronics Section, Universiti Kuala Lumpur British Malaysia Institute, Radiology department Hospital Kuala Lumpur (HKL), and the higher education commission  ...  LAYERED BASIS PURSUIT The layered basis pursuit in context of sparse models and deep learning has been proposed addressing pursuit problems of the form: x i ← arg min xi ||x i−1 − Dx i || 2 2 + λ i ||x  ...  CONCLUSION In this work, we proposed a CS-MRI restoration framework based on multi-layer convolutional sparse coding, employing iterative thresholding algorithms for basis pursuits to learn parameters  ... 
doi:10.1109/access.2020.3028877 fatcat:wdbm7fsngjgu5m5aaauudqsdze

Sparse Models for Computer Vision [chapter]

Laurent U. Perrinet
2015 Biologically Inspired Computer Vision  
More specifically, we will propose that bio-inspired approaches may be applied to computer vision using predictive coding schemes, sparse models being one simple and efficient instance of such schemes.  ...  Then, we will outline a complete multi-scale framework ---SparseLets--- implementing a biologically inspired sparse representation of natural images.  ...  Correspondence and requests for materials should be addressed to the author 6 . Code and supplementary material available at  ... 
doi:10.1002/9783527680863.ch14 fatcat:h7d5a6fyvba2rhat5qo7gaokny

Multi-layer Residual Sparsifying Transform (MARS) Model for Low-dose CT Image Reconstruction [article]

Xikai Yang, Yong Long, Saiprasad Ravishankar
2021 arXiv   pre-print
In this work, we develop a new image reconstruction approach based on a novel multi-layer model learned in an unsupervised manner by combining both sparse representations and deep models.  ...  We propose new formulations for multi-layer transform learning and image reconstruction.  ...  For example, the multi-layer convolutional (synthesis) sparse coding model 15, 16 provides a new interpretation of convolutional neural networks (CNNs), where the pursuit of sparse representation from  ... 
arXiv:2010.06144v3 fatcat:pdxxjadjevhohm4cqgo3eng2de

Multi-Layer Sparse Coding: The Holistic Way [article]

Aviad Aberdam, Jeremias Sulam, Michael Elad
2018 arXiv   pre-print
The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN).  ...  We then show that this multi-layer construction admits a brand new interpretation in a unique symbiosis between synthesis and analysis models: while the deepest layer indeed provides a synthesis representation  ...  This construction, termed Multi-Layer Convolutional Sparse Coding (ML-CSC), raises particular interest because of its tight connection to deep learning.  ... 
arXiv:1804.09788v2 fatcat:2fb4lxfomffkfne3d3yqgofwry

Learning Sparse FRAME Models for Natural Image Patterns

Jianwen Xie, Wenze Hu, Song-Chun Zhu, Ying Nian Wu
2014 International Journal of Computer Vision  
The sparse FRAME model can be written as a shared sparse coding model, which motivates us to propose a twostage algorithm for learning the model.  ...  Our experiments show that the sparse FRAME models are capable of representing a wide variety of object patterns in natural images and that the learned models are useful for object classification.  ...  After learning one layer of sparse FRAME models, we can treat these models as re-usable parts, and continue to compose them into higher layers of sparse FRAME models. Compositional models.  ... 
doi:10.1007/s11263-014-0757-x fatcat:t5hq3upqlvd7jg2tvtilajxlgy
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