Learning Fast Dictionaries for Sparse Representations Using Low-Rank Tensor Decompositions

Dantas, Cassio F.; Cohen, Jérémy E.; Gribonval, Rémi

doi:10.1007/978-3-319-93764-9_42

Cited by 8 publications

(5 citation statements)

References 18 publications

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“…Earlier results in [14] are similar to SuKro and also propose a non-separable version based on CP decomposition. The latest in this line of work is a DL algorithm to learn sums of R Kronecker products of K terms [22].…”

Section: Methodsmentioning

confidence: 99%

Efficient and Parallel Separable Dictionary Learning

Rusu¹,

Irofti²

2020

Preprint

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Separable, or Kronecker product, dictionaries provide natural decompositions for 2D signals, such as images. In this paper, we describe an algorithm to learn such dictionaries which is highly parallelizable and which reaches sparse representations competitive with the previous state of the art dictionary learning algorithms from the literature. We highlight the performance of the proposed method to sparsely represent image data and for image denoising applications.

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Section: Methodsmentioning

confidence: 99%

Efficient and Parallel Separable Dictionary Learning

Rusu¹,

Irofti²

2020

Preprint

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“…To address this problem, the tensor-based dictionary learning algorithms [183,184,185,186,187] are considered as an alternative approach to this type of training data. Additional algorithms in this category are CPD-based dictionary learning [188,189,190,191] and Tucker-based dictionary learning [192,193,194,195] where the algorithms utilize similar formulations of Equation (3.8) or Equation (3.9) based on multi-dimensional representations with sparsity constraints.…”

Section: Dictionary Learningmentioning

confidence: 99%

Data-Driven Approaches for Sparse Reflectance Modeling and Acquisition

Tongbuasirilai

2023

Linköping Studies in Science and Technology. Dissertations

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Description of the cover imageThe front cover of this thesis illustrates BRDFs in the form of multiple rendered spheres along BRDF curves (RGB signals) where the glossy BRDF curves are placed above the diffuse BRDF curves. The front illustration portrays the results of the thesis contents. The blue wave signals in the back cover represent sparse signals which serve as the BRDF encoding process (thesis's contributions) to reconstruct the BRDF signals in the front cover. The orange abstract waves in the background indicate that the BRDF is a type of signals around us. The materials used to render all the spheres are measured isotropic BRDFs from Mitsubishi Electric Research Laboratories (MERL).

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“…The other batch algorithm we propose, named TeFDiL, learns subdictionaries of the LSR dictionary by exploiting the connection to tensor recovery and using tensor CPD. Recently, Dantas et al [33] proposed an algorithm for learning an LSR dictionary for tensor data in which the dictionary update stage is a projected gradient descent algorithm that involves a CPD after every gradient step. In contrast, TeFDiL only requires a single CPD at the end of each dictionary update stage.…”

Section: B Relation To Prior Workmentioning

confidence: 99%

Learning Mixtures of Separable Dictionaries for Tensor Data: Analysis and Algorithms

Ghassemi

Shakeri

Sarwate

et al. 2020

IEEE Trans. Signal Process.

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This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing the separable dictionary learning model. Two different approaches for learning mixture of separable dictionaries are explored and sufficient conditions for local identifiability of the underlying dictionary are derived in each case. Moreover, computational algorithms are developed to solve the problem of learning mixture of separable dictionaries in both batch and online settings. Numerical experiments are used to show the usefulness of the proposed model and the efficacy of the developed algorithms.

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Learning Fast Dictionaries for Sparse Representations Using Low-Rank Tensor Decompositions

Cited by 8 publications

References 18 publications

Efficient and Parallel Separable Dictionary Learning

Efficient and Parallel Separable Dictionary Learning

Data-Driven Approaches for Sparse Reflectance Modeling and Acquisition

Learning Mixtures of Separable Dictionaries for Tensor Data: Analysis and Algorithms

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