Subproblem coupling in convolutional dictionary learning

Garcia-Cardona, Cristina; Wohlberg, Brendt

doi:10.1109/icip.2017.8296571

Cited by 23 publications

(55 citation statements)

References 11 publications

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“…2 presents a comparison of the objective value as a function of time for each of the competing algorithms, showing that our method achieves the 6 All our notations are in accordance with those presented in [29] Fig. 2: Run time comparison between our method and the batch methods: the SBDL algorithm [1], the algorithm of Wohlberg [40] and the algorithm by Garcia et al [41].…”

Section: A Run Time Comparisonmentioning

confidence: 82%

A Local Block Coordinate Descent Algorithm for the CSC Model

Zisselman

Sulam²,

Elad

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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The Convolutional Sparse Coding (CSC) model has recently gained considerable traction in the signal and image processing communities. By providing a global, yet tractable, model that operates on the whole image, the CSC was shown to overcome several limitations of the patch-based sparse model while achieving superior performance in various applications. 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, while ignoring the local characterizations of the image. A recent work by Papyan et al. [1] suggested the SBDL algorithm for the CSC, while operating locally on image patches. SBDL demonstrates better performance compared to the Fourier-based methods, albeit still relying on the ADMM.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 Descent (LoBCoD). Furthermore, we introduce a novel stochastic gradient descent version of LoBCoD for training the convolutional filters. The Stochastic-LoBCoD leverages the benefits of online learning, while being applicable to a single training image. We demonstrate the advantages of the proposed algorithms for image inpainting and multi-focus image fusion, achieving state-of-the-art results.

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Section: A Run Time Comparisonmentioning

confidence: 82%

A Local Block Coordinate Descent Algorithm for the CSC Model

Zisselman

Sulam²,

Elad

2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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“…First, a synthesis dictionary D is obtained, which satisfies X0: N −1 ≈ DY0: N −1, by using CSC instead of giving an analysis map Ψ as in Sect. 2 [9][10][11][12]. Fig.…”

Section: Convolutional-sparse-coded Dmdmentioning

confidence: 98%

“…Atom termination is applied to the boundary [20,21]. The sparse approximation in (11) and (13) used ISTA [18]. In the dictionary update step (12), a stochastic gradient descent method with AdaGrad was adopted [22][23][24], where 128 patches of size 32 × 128 × 2 voxels were randomly extracted from the ST training data.…”

Section: Experimental River Setupmentioning

confidence: 99%

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Convolutional-sparse-coded Dynamic Mode Decomposition and Its Application to River State Estimation

Kaneko

Muramatsu

Yasuda

et al. 2019

ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data-driven method of analysis used to describe a nonlinear dynamical system with a linear time-evolution equation. Compared with existing EDMD methods, CSC-DMD has the advantage of reflecting the spatial structure of a target. As an example, the proposed method is applied to river bed shape estimation from the water surface observation. This estimation problem is reduced to sparsityaware signal restoration with a hard constraint given by the CSC-DMD prediction, where the algorithm is derived by the primal-dual splitting method. A time series set of water surface and bed shape measured through an experimental river setup is used to train and test the system. From the result, the efficacy of the proposed method is verified.Index Terms-Extended dynamic mode decomposition, Convolutional sparse coding, Primal-dual splitting, NSOLT

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“…A final remark is that the reviewed DL techniques are designated for flat-fading channels. Multipath scenarios would require convolutional dictionary learning [38], and would be the topic of a future study.…”

Section: B Channel Estimationmentioning

confidence: 99%

Blind Sparse Estimation of Intermittent Sources Over Unknown Fading Channels

Dong

Simeone

Haimovich

et al. 2019

IEEE Trans. Veh. Technol.

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Radio frequency sources are observed at a fusion center via sensor measurements made over slow flat-fading channels. The number of sources may be larger than the number of sensors, but their activity is sparse and intermittent with bursty transmission patterns. To account for this, sources are modeled as hidden Markov models with known or unknown parameters. The problem of blind source estimation in the absence of channel state information is tackled via a novel algorithm, consisting of a dictionary learning (DL) stage and a per-source stochastic filtering (PSF) stage. The two stages work in tandem, with the latter operating on the output produced by the former. Both stages are designed so as to account for the sparsity and memory of the sources. To this end, smooth LASSO is integrated with DL, while the forward-backward algorithm and Expectation Maximization (EM) algorithm are leveraged for PSF. It is shown that the proposed algorithm can enhance the detection and the estimation performance of the sources, and that it is robust to the sparsity level. Index TermsBlind source separation, Wireless networks, Dictionary learning, Intermittent and sparse sources, Hidden Markov model I. INTRODUCTIONBlind source separation (BSS) refers to the separation of a set of source signals from a set of mixed signals, without resorting to any a priori information about the source signals or the mixing process [1]. BSS exploits only the information carried by the received signals themselves, hence the term blind. BSS has numerous applications in speech recognition [2,3], image extraction [4,5], and surveillance [6,7]. Different metrics are used to evaluate the performance of BSS methods depending on the applications. For example, signal-to-interference ratio is used in [2] for speech separation, and a performance index is introduced in [4] for image feature extraction. Based on these metrics, many approaches have been proposed to solve BSS problems, such as independent component analysis (ICA) [8], principal component analysis (PCA) [9], and singular value decomposition (SVD) [10].This paper addresses BSS in wireless networks. We are specifically interested in the set-up illustrated in Fig. 1, in which a fusion center observes a number of radio sources via noisy sensor measurements over unknown channels. The system may model an Internet-of-Things (IoT) system, such as LoRa, Sigfox, or Narrow Band-IoT (NB-IoT) [11,12].In wireless networks involving multiple terminals operating over flat fading channels, the signals received at a terminal are linear mixtures of the signals emitted by the transmitting terminals. The need for BSS arises in non-collaborative applications in which the signals and the channels through which they are received at a terminal are both unknown. ICA has been widely applied to solve BSS problems in wireless networks [13][14][15][16], since it yields a useful decomposition with only scaling, and permutation ambiguities [17]. To achieve signal separation, ICA relies on the statistical independence and on the non-...

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Subproblem coupling in convolutional dictionary learning

Cited by 23 publications

References 11 publications

A Local Block Coordinate Descent Algorithm for the CSC Model

A Local Block Coordinate Descent Algorithm for the CSC Model

Convolutional-sparse-coded Dynamic Mode Decomposition and Its Application to River State Estimation

Blind Sparse Estimation of Intermittent Sources Over Unknown Fading Channels

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