Matching Pursuit Based Convolutional Sparse Coding

Plaut, Elad; Giryes, Raja

doi:10.1109/icassp.2018.8461543

Cited by 8 publications

(9 citation statements)

References 15 publications

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“…Significant additional improvements are achieved when learning the local dictionary D l from the corrupted image. The second block in Table I contains the inpainting PSNR obtained in this scenario for the sliced based method [29] and for the weighted 2,∞ − 1 used along the dictionary update proposed in [27]. In this context, the weighting of the stripe dictionary is particularly beneficial as it encourages more atoms to be used and therefore updated (see Figure 5).…”

Section: Methodsmentioning

confidence: 99%

“…Indeed, the patch would then be assumed to stem from the local dictionary alone, disregarding all the contributions of shifted atoms to its reconstruction. We adopt instead a more coherent alternative that was recently proposed in [27] in which standard dictionary update procedures are adapted to a convolutional setting and carried out via conjugate gradient descent [32] in conjunction with fast convolution computations. The proposed method is applied to the test images cat and pineapple, the results of our method are shown in Figure 4 along with the results from the 1 − 2 based method in [29] V. THE 2,∞ − 1 CSC FORMULATION We move on to consider our second formulation, of explicitly incorporating a local control on the CSC model.…”

Section: B Experimentsmentioning

confidence: 99%

“…in which the Lagrange multiplier is set to an optimal value λ * i : the smallest Lagrange multiplier such that the inequality constraint is satisfied. Observe that, while transitioning from Equation (27) to Equation (28), we moved from Ω to D, in order to pose the algorithm w.r.t. the global dictionary.…”

Section: A Proposed Algorithmmentioning

confidence: 99%

“…Running FISTA successively with warm-start initialization allows to estimate the minimizer for different values of λ i with only few extra iterations. This allows to use a binary-search scheme to estimate the optimal Lagrange multiplier λ * i which in turn provides the solution to the proximal operator in Equation (27).…”

Section: A Proposed Algorithmmentioning

confidence: 99%

“…The CSC pursuit formulations proposed in the present work aim at explicitly controlling the sparsity level in these portions of the representation vectors, called stripes. The first formulation employs the 1,∞ norm as the sparsity promoting function, providing a convex relaxation of the 0,∞ pseudo-norm that was introduced in [26] and explored further in [27], [28]. The second formulation controls the sparsity of the stripes by considering the maximum reconstruction error on each patch simultaneously, via an 2,∞ norm.…”

Section: Introductionmentioning

confidence: 99%

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Variations on the CSC model

Rey-Otero,

Sulam,

Elad

2018

Preprint

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Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patchbased, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same 1 − 2 problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. 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 main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.

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Section: Methodsmentioning

confidence: 99%

Section: B Experimentsmentioning

confidence: 99%

Section: A Proposed Algorithmmentioning

confidence: 99%

Section: A Proposed Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variations on the CSC model

Rey-Otero,

Sulam,

Elad

2018

Preprint

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Convolutional Sparse Coding for Time Series Via a ℓ0 Penalty: An Efficient Algorithm With Statistical Guarantees

Truong,

Moreau

2024

Statistical Analysis

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Identifying characteristic patterns in time series, such as heartbeats or brain responses to a stimulus, is critical to understanding the physical or physiological phenomena monitored with sensors. Convolutional sparse coding (CSC) methods, which aim to approximate signals by a sparse combination of short signal templates (also called atoms), are well‐suited for this task. However, enforcing sparsity leads to non‐convex and untractable optimization problems. This article proposes finding the optimal solution to the original and non‐convex CSC problem when the atoms do not overlap. Specifically, we show that the reconstruction error satisfies a simple recursive relationship in this setting, which leads to an efficient detection algorithm. We prove that our method correctly estimates the number of patterns and their localization, up to a detection margin that depends on a certain measure of the signal‐to‐noise ratio. In a thorough empirical study, with simulated and real‐world physiological data sets, our method is shown to be more accurate than existing algorithms at detecting the patterns' onsets.

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Learning the sparse prior: Modern approaches

Peng

2024

WIREs Computational Stats

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The sparse prior has been widely adopted to establish data models for numerous applications. In this context, most of them are based on one of three foundational paradigms: the conventional sparse representation, the convolutional sparse representation, and the multi‐layer convolutional sparse representation. When the data morphology has been adequately addressed, a sparse representation can be obtained by solving the sparse coding problem specified by the data model. This article presents a comprehensive overview of these three models and their corresponding sparse coding problems and demonstrates that they can be solved using convex and non‐convex optimization approaches. When the data morphology is not known or cannot be analyzed, it must be learned from training data, thereby formulating dictionary learning problems. This article addresses two different dictionary learning paradigms. In an unsupervised scenario, dictionary learning involves the alternating or joint resolution of sparse coding and dictionary updating. Another option is to create a recurrent neural network by unrolling algorithms designed to solve sparse coding problems. These networks can then be used in a supervised learning setting to facilitate the training of dictionaries via forward‐backward optimization. This article lists numerous applications in various domains and outlines several directions for future research related to the sparse prior.This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Modeling Methods and Algorithms Statistical Models > Nonlinear Models

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Matching Pursuit Based Convolutional Sparse Coding

Cited by 8 publications

References 15 publications

Variations on the CSC model

Variations on the CSC model

Convolutional Sparse Coding for Time Series Via a ℓ0 Penalty: An Efficient Algorithm With Statistical Guarantees

Learning the sparse prior: Modern approaches

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