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Fast convolutional sparse coding using matrix inversion lemma

DIGITAL SIGNAL PROCESSING 2016年 55卷 44-51页

作者： Sorel, Michal Sroubek, Filip Czech Acad Sci Inst Informat Theory & Automat Vodarenskou Vezi 4 Prague 18208 Czech Republic

convolutional sparse coding is an interesting alternative to standard sparse coding in modeling shift invariant signals, giving impressive results for example in unsupervised learning of visual features. In state-of-the-art methods, the most time-consuming parts include inversion of a linear operator related to convolution. In this article we show how these inversions can be computed non-iteratively in the Fourier domain using the matrix inversion lemma. This greatly speeds up computation and makes convolutional sparse coding computationally feasible even for large problems. The algorithm is derived in three variants, one of them especially suitable for parallel implementation. We demonstrate algorithms on two-dimensional image data but all results hold for signals of arbitrary dimension. (C) 2016 Elsevier Inc. All rights reserved.

关键词： convolutional sparse coding Feature learning Deconvolution networks Shift-invariant sparse coding

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Ultrasonic defect characterization using time-domain scattering matrices and convolutional sparse coding

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NDT & E INTERNATIONAL 2022年第0期131卷

作者： Bai, Long Liu, Nanxin Guo, Changrong Xu, Jianfeng Huazhong Univ Sci & Technol Sch Mech Sci & Engn State Key Lab Digital Mfg Equipment & Technol Wuhan 430074 Peoples R China

In this paper, the use of the time-domain scattering matrix for ultrasonic characterization of defects is explored. An approach based on convolutional sparse coding is proposed for extraction of the shift-invariant features of the time-domain scattering matrix. The results of a simulation show that the proposed approach can be reliably used for classification of the rough cracks. In addition, the mean sizing error and its standard deviation are also reduced compared with the use of the frequency domain scattering matrix. In experiments, a 1.5 mm slot and 1.5 mm elliptical defect were sized to within 0.25 mm using a 2.5 MHz, 64 element linear array with an element pitch of 0.5 mm. Excellent sizing results were obtained for inclined slots with a large orientation angle (i.e. 60 degrees).

关键词： Defect characterization Scattering matrix convolutional sparse coding Rough cracks Volumetric defects

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Representation Learning via Cauchy convolutional sparse coding

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IEEE ACCESS 2021年 9卷 100447-100459页

作者： Mayo, Perla Karakus, Oktay Holmes, Robin Achim, Alin Univ Bristol Visual Informat Lab Bristol BS1 5DD Avon England

In representation learning, convolutional sparse coding (CSC) enables unsupervised learning of features by jointly optimising both an l(2)-norm fidelity term and a sparsity enforcing penalty. This work investigates using a regularisation term derived from an assumed Cauchy prior for the coefficients of the feature maps of a CSC generative model. The sparsity penalty term resulting from this prior is solved via its proximal operator, which is then applied iteratively, element-wise, on the coefficients of the feature maps to optimise the CSC cost function. The performance of the proposed Iterative Cauchy Thresholding (ICT) algorithm in reconstructing natural images is compared against algorithms based on minimising standard penalty functions via soft and hard thresholding as well as against the Iterative Log-Thresholding (ILT) method. ICT outperforms the Iterative Hard Thresholding (IHT), Iterative Soft Thresholding (IST), and ILT algorithms in most of our reconstruction experiments across various datasets, with an average Peak Signal to Noise Ratio (PSNR) of up to 11.30 dB, 7.04 dB, and 7.74 dB over IST, IHT, and ILT respectively. The source code for the implementation of the proposed approach is publicly available at https://***/p-mayo/cauchycsc

关键词： Encoding Data models Task analysis Image reconstruction convolutional codes Convolution Thresholding (Imaging) Cauchy-based penalty function convolutional sparse coding proximal splitting

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Accelerating convolutional sparse coding for Curvilinear Structures Segmentation by Refining SCIRD-TS Filter Banks

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IEEE TRANSACTIONS ON MEDICAL IMAGING 2016年第11期35卷 2381-2392页

作者： Annunziata, Roberto Trucco, Emanuele Univ Dundee Sch Sci & Engn Comp Dundee DD1 4HN Scotland

Deep learning has shown great potential for curvilinear structure (e.g., retinal blood vessels and neurites) segmentation as demonstrated by a recent auto-context regression architecture based on filter banks learned by convolutional sparse coding. However, learning such filter banks is very time-consuming, thus limiting the amount of filters employed and the adaptation to other data sets (i.e., slow re-training). We address this limitation by proposing a novel acceleration strategy to speed-up convolutional sparse coding filter learning for curvilinear structure segmentation. Our approach is based on a novel initialisation strategy (warm start), and therefore it is different from recent methods improving the optimisation itself. Our warm-start strategy is based on carefully designed hand-crafted filters (SCIRD-TS), modelling appearance properties of curvilinear structures which are then refined by convolutional sparse coding. Experiments on four diverse data sets, including retinal blood vessels and neurites, suggest that the proposed method reduces significantly the time taken to learn convolutional filter banks (i.e., up to -82%) compared to conventional initialisation strategies. Remarkably, this speed-up does not worsen performance;in fact, filters learned with the proposed strategy often achieve a much lower reconstruction error and match or exceed the segmentation performance of random and DCT-based initialisation, when used as input to a random forest classifier.

关键词： convolutional sparse coding neurites retinal blood vessels segmentation

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Scalable Online convolutional sparse coding

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2018年第10期27卷 4850-4859页

作者： Wang, Yaqing Yao, Quanming Kwok, James T. Ni, Lionel M. Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Peoples R China 4Paradigm Inc Beijing Peoples R China Univ Macau Dept Comp & Informat Sci Macau Peoples R China

convolutional sparse coding (CSC) improves sparse coding by learning a shift-invariant dictionary from the data. However, most existing CSC algorithms operate in the batch mode and are computationally expensive. In this paper, we alleviate this problem by online learning. The key is a reformulation of the CSC objective so that convolution can be handled easily in the frequency domain, and much smaller history matrices are needed. To solve the resultant optimization problem, we use the alternating direction method of multipliers (ADMMs), and its subproblems have efficient closed-form solutions. Theoretical analysis shows that the learned dictionary converges to a stationary point of the optimization problem. Extensive experiments are performed on both the standard CSC benchmark data sets and much larger data sets such as the ImageNet. Results show that the proposed algorithm outperforms the state-of-the-art batch and online CSC methods. It is more scalable, has faster convergence, and better reconstruction performance.

关键词： Online learning convolutional sparse coding dictionary learning

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Deep Content-Dependent 3-D convolutional sparse coding for Hyperspectral Image Denoising

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IEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 2024年 17卷 4125-4138页

作者： Yin, Haitao Chen, Hao Nanjing Univ Posts & Telecommun Coll Automat Coll ArtificialIntelligence Nanjing 210023 Peoples R China

Despite the significant successes in hyperspectral image (HSI) denoising, pure data-driven HSI denoising networks still suffer from limited understanding of inference. Deep unfolding (DU) is a feasible way to improve the interpretability of deep network. However, the specialized spatial-spectral DU methods are seldom studied, and the simple spatial-spectral extension leads to unpleasant spectral distortion. To tackle these issues, we first propose a content-dependent 3-D convolutional sparse coding (CD-CSC) to jointly represent spatial-spectral feature. Specifically, the 3-D filters used in CD-CSC for each HSI are unique, which are determined by linear combination of base 3-D filters. Then, we develop a novel CD-CSC-inspired DU network for HSI denoising, called CD-CSCNet. Furthermore, by exploiting the lightweight of separable convolution and the adaptability of hypernetwork, we design a separable content-dependent 3D Convolution (SCD-Conv) to carry out CD-CSCNet. SCD-Conv not only reduces computational complexity, but also can be viewed as the convolutional sparse coding with spatial and spectral dictionaries. Extensive experimental results on the ICVL, Zhuhai-1 OHS-3C, and GaoFen-5 datasets demonstrate that CD-CSCNet outperforms several recent pure data-driven and DU-based networks quantitatively and visually.

关键词： Hyperspectral image denoising deep network convolutional sparse coding deep unfolding 3-D convolution separable convolution

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Image super-resolution by learning weighted convolutional sparse coding

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SIGNAL IMAGE AND VIDEO PROCESSING 2021年第5期15卷 967-975页

作者： He, Jingwei Yu, Lei Liu, Zhou Yang, Wen Wuhan Univ Elect Informat Sch Wuhan 430072 Peoples R China

Single image super-resolution (SISR) has witnessed substantial progress recently by deep learning-based methods, due to the data-driven end-to-end training. However, most existing DL-based models are built intuitively, with little thought on priors. And the lack of interpretability limits their further improvements. To avoid this, this paper presents an end-to-end trainable unfolding network which leverages both DL- and prior-based methods. Specifically, we introduce the reweighted algorithm into CSC model and solve it by learning weighted iterative soft thresholding algorithm in a convolutional manner. Based on this, we present a SISR model by learning weighted convolutional sparse coding, in which the channel attention is resorted to learn the weight. Extensive experiments demonstrate the superiority of our method to recent state-of-the-art SISR methods, in terms of both quantitative and qualitative results.

关键词： convolutional sparse coding ISTA Iterative reweighted l(1)-minimization Image super-resolution

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Interpretable convolutional sparse coding method of Lamb waves for damage identification and localization

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STRUCTURAL HEALTH MONITORING-AN INTERNATIONAL JOURNAL 2022年第4期21卷 1790-1804页

作者： Zhang, Han Lin, Jing Hua, Jiadong Tong, Tong Beihang Univ Sch Reliabil & Syst Engn Beijing Peoples R China Beihang Univ Sci & Technol Reliabil & Environm Engn Lab Beijing Peoples R China Beihang Univ Beijing Adv Discipline Ctr Unmanned Aircraft Syst Beijing Peoples R China

Lamb wave-based damage identification and localization methods hold the potential for nondestructive evaluation and structural health monitoring. Dispersive and multimodal characteristics lead to complicated Lamb wave signals that are challenging to be analyzed. Deep learning architectures could identify damage-related features effectively. convolutional neural network (CNN) is a promising architecture that has been widely applied in recent years. However, this data-driven approach still lacks a certain degree of physical interpretability and requires a large number of parameters. In this article, an interpretable Lamb wave convolutional sparse coding (LW-CSC) method is proposed for structural damage identification and localization. First, toneburst signals at different center frequencies are considered in the first convolutional layer. The network convolves the waveforms with a set of parametrized functions that implement band-pass filters, which performs more physical interpretability compared to conventional CNN model. Subsequently, the damage features are extracted according to the multi-layer iterative soft thresholding algorithm for multi-layer CSC model, which could realize a deeper network without adding parameters unlike CNN. Finally, Lamb wave-based damage localization is visualized using an imaging algorithm. The experimental results demonstrate that the proposed method not only enables improvement of the classification accuracy but also achieves structural damage localization accurately.

关键词： Lamb wave interpretability convolutional sparse coding damage localization structural health monitoring

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A Greedy Approach to l0,∞-Based convolutional sparse coding

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SIAM JOURNAL ON IMAGING SCIENCES 2019年第1期12卷 186-210页

作者： Plaut, Elad Giryes, Raja Tel Aviv Univ Sch Elect Engn IL-6997801 Tel Aviv Israel

sparse coding techniques for image processing traditionally rely on the processing of small overlapping patches separately, followed by averaging. This has the disadvantage that the reconstructed image no longer obeys the sparsity prior used in the processing. For this purpose convolutional sparse coding has been introduced, where a shift-invariant dictionary is used and the sparsity of the recovered image is maintained. Most such strategies target the l(0) "norm" or the l(1) norm of the whole image, which may create an imbalanced sparsity across various regions in the image. In order to face this challenge, the l(0,infinity) "norm" has been proposed as an alternative that "operates locally while thinking globally." The approaches taken for tackling the nonconvexity of these optimization problems have been using either a convex relaxation or local pursuit algorithms. In this paper, we present an efficient greedy method for sparse coding and dictionary learning, which is specifically tailored to l(0,infinity) and is based on matching pursuit. We demonstrate the usage of our approach in salt-and-pepper noise removal and image inpainting.

关键词： convolutional sparse coding global modeling local processing greedy algorithms sparse representations

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Single image super-resolution based on adaptive convolutional sparse coding and convolutional neural networks

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JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION 2019年第Jan.期58卷 651-661页

作者： Zhao, Jianwei Chen, Chen Zhou, Zhenghua Cao, Feilong China Jiliang Univ Dept Informat Sci & Math Hangzhou 310018 Zhejiang Peoples R China

The convolutional sparse coding-based super-resolution (CSC-SR) method has shown its good performance in single image super-resolution. It divides the low-resolution (LR) image into low-frequency part and the high-frequency part, and reconstructs their corresponding high-resolution (HR) image with bicubic interpolation and convolutional sparse coding (CSC) method, respectively. This paper is devoted to improve the performance of CSC-SR method. As convolutional neural network (CNN) can reveal the mapping relation between the LR image and the HR image for the low-frequency part better, we replace the bicubic interpolation with CNN to reconstruct the HR image for the low-frequency part. In addition, we propose an adaptive CSC method to reconstruct the HR image for the high-frequency part. We name our proposed super-resolution method as hybrid adaptive convolutional sparse coding-based super-resolution (HACSC-SR) method. Many comparison experiments illustrate that our proposed HACSC-SR method is superior to CSC-SR, CNN as well as several existing super-resolution methods. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Super-resolution convolutional sparse coding convolutional neural network Adaptive

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