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First- and Second-Order Methods for Online convolutional Dictionary Learning

SIAM JOURNAL ON IMAGING SCIENCES 2018年第2期11卷 1589-1628页

作者： Liu, Jialin Garcia-Cardona, Cristina Wohlbereg, Brendt Yin, Wotao UCLA Dept Math Los Angeles CA 90095 USA Los Alamos Natl Lab CCS Div Los Alamos NM 87545 USA Los Alamos Natl Lab Theoret Div Los Alamos NM 87545 USA

convolutional sparse representations are a form of sparse representation with a structured, translation-invariant dictionary. Most convolutional dictionary learning algorithms to date operate in batch mode, requiring simultaneous access to all training images during the learning process, which results in very high memory usage and severely limits the training data size that can be used. Very recently, however, a number of authors have considered the design of online convolutional dictionary learning algorithms that offer far better scaling of memory and computational cost with training set size than batch methods. This paper extends our prior work, improving a number of aspects of our previous algorithm;proposing an entirely new one, with better performance, that supports the inclusion of a spatial mask for learning from incomplete data;and providing a rigorous theoretical analysis of these methods.

关键词： convolutional sparse coding convolutional dictionary learning online dictionary learning stochastic gradient descent recursive least squares

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An improved method for single image super-resolution based on deep learning

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SIGNAL IMAGE AND VIDEO PROCESSING 2019年第3期13卷 557-565页

作者： Xie, Chao Liu, Ying Zeng, Weili Lu, Xiaobo Nanjing Forestry Univ Coll Mech & Elect Engn Nanjing 210037 Jiangsu Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Civil Aviat Nanjing 210016 Jiangsu Peoples R China Southeast Univ Sch Automat Nanjing 210096 Jiangsu Peoples R China

This paper strives for presenting an improved method for single image super-resolution based on deep learning, and therefore, a well-designed network structure is proposed by simultaneously considering the merits of convolutional sparse coding (CSC) and deep convolutional neural networks (CNN). In our model, contrary to most existing methods that directly operate on the raw input, we first perform a global decomposition on the input based on CSC for the purpose of extracting two specific components from it. Since the generated components are designed to have predefined physical meanings (i.e., residual or smooth), they can be discriminatively super-resolved according to their distinctive appearances. Specifically, a strong preference is given to the residual one as it is much more crucial to our task, while the other should just provide a quick reference. Based on this analysis, deep CNN and plain interpolation are selected to map them, respectively. In all, the proposed model integrates the above procedures into a completely end-to-end trainable deep network. Thorough experimental results demonstrate that our proposed network is able to gain considerable accuracy from this deep and delicate architecture, thereby outperforming many recently published baselines in terms of both objective evaluation and visual fidelity.

关键词： Single image super-resolution Deep learning convolutional sparse coding Deep convolutional neural networks

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convolutional Dictionary Learning: Acceleration and Convergence

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2018年第4期27卷 1697-1712页

作者： Chun, Il Yong Fessler, Jeffrey A. Univ Michigan Dept Elect Engn & Comp Sci Ann Arbor MI 48019 USA

convolutional dictionary learning (CDL or sparsifying CDL) has many applications in image processing and computer vision. There has been growing interest in developing efficient algorithms for CDL, mostly relying on the augmented Lagrangian (AL) method or the variant alternating direction method of multipliers (ADMM). When their parameters are properly tuned, AL methods have shown fast convergence in CDL. However, the parameter tuning process is not trivial due to its data dependence and, in practice, the convergence of AL methods depends on the AL parameters for nonconvex CDL problems. To moderate these problems, this paper proposes a new practically feasible and convergent Block Proximal Gradient method using a Majorizer (BPG-M) for CDL. The BPG-M-based CDL is investigated with different block updating schemes and majorization matrix designs, and further accelerated by incorporating some momentum coefficient formulas and restarting techniques. All of the methods investigated incorporate a boundary artifacts removal (or, more generally, sampling) operator in the learning model. Numerical experiments show that, without needing any parameter tuning process, the proposed BPG-M approach converges more stably to desirable solutions of lower objective values than the existing state-of-the-art ADMM algorithm and its memory-efficient variant do. Compared with the ADMM approaches, the BPG-M method using a multi-block updating scheme is particularly useful in single-threaded CDL algorithm handling large data sets, due to its lower memory requirement and no polynomial computational complexity. Image denoising experiments show that, for relatively strong additive white Gaussian noise, the filters learned by BPG-M-based CDL outperform those trained by the ADMM approach.

关键词： convolutional dictionary learning convolutional sparse coding block proximal gradient method majorization matrix design convergence guarantee

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Learning a Non-Locally Regularized convolutional sparse Representation for Joint Chromatic and Polarimetric Demosaicking

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2024年 33卷 5029-5044页

作者： Luo, Yidong Zhang, Junchao Shao, Jianbo Tian, Jiandong Ma, Jiayi Cent South Univ Sch Automat Hunan Prov Key Lab Opt Elect Intelligent Measureme Changsha 410083 Peoples R China Chinese Acad Sci Shenyang Inst Automat State Key Lab Robot Shenyang 110016 Peoples R China Wuhan Univ Elect Informat Sch Wuhan 430072 Peoples R China

Division of focal plane color polarization camera becomes the mainstream in polarimetric imaging for it directly captures color polarization mosaic image by one snapshot, so image demosaicking is an essential task. Current color polarization demosaicking (CPDM) methods are prone to unsatisfied results since it's difficult to recover missed 15 or 14 pixels out of 16 pixels in color polarization mosaic images. To address this problem, a non-locally regularized convolutional sparse regularization model, which is advantaged in denoising and edge maintaining, is proposed to recall more information for CPDM task, and the CPDM task is transformed into an energy function to be solved by ADMM optimization. Finally, the optimal model generates informative and clear results. The experimental results, including reconstructed synthetic and real-world scenes, demonstrate that our proposed method outperforms the current state-of-the-art methods in terms of quantitative measurements and visual quality. The source code is available at https://***/roydon-luo/NLCSR-CPDM.

关键词： Image color analysis Imaging Image edge detection Polarization Correlation Cameras Image reconstruction Color polarization demosaicking convolutional sparse coding non-local self-similarity unsupervised learning global optimization

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convolutional Dictionary Learning With Grid Refinement

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2020年 68卷 2558-2573页

作者： Song, Andrew H. Flores, Francisco J. Ba, Demba MIT Elect Engn & Comp Sci 77 Massachusetts Ave Cambridge MA 02139 USA Massachusetts Gen Hosp MGH Boston MA 02114 USA Harvard Med Sch Boston MA 02114 USA Harvard Univ Sch Engn & Appl Sci Cambridge MA 02138 USA

Given a continuous-domain signal that can be modeled as the superposition of localized events from multiple sources, the goal of convolutional Dictionary Learning (CDL) is to identify the location of the events-by convolutional sparse coding (CSC)-and learn the template for each source-through a convolutional Dictionary Update (CDU) step. In practice, because we observe samples of the continuous-domain signal on a discrete grid, classical CSC methods can only produce estimates of the locations of the events on this grid, which degrades the performance of the CDU step. We introduce a CDL framework that significantly reduces the errors arising from performing the estimation on the grid. Specifically, we construct an expanded dictionary that comprises, not only discrete shifts of the templates, but also variants shifted by a non-integer amount and smoothly interpolated, that enable CSC and CDU to operate at a finer resolution than that of the original sampling grid. We term this approach CDL with grid refinement. For CSC, we develop a novel computationally efficient algorithm, termed convolutional Orthogonal Matching Pursuit with an interpolated dictionary (COMP-INTERP). We use simulated data to compare COMP-INTERP to state-of-the-art CSC algorithms for estimating off-the-grid events, and demonstrate that it 1) achieves a competitive level of accuracy, and 2) is one order of magnitude faster. For CDU, we derive a novel procedure to update the templates given sparse codes that can occur both on and off the sampling grid. We also show that 3) dictionary update with the overcomplete dictionary yields more accurate templates. Finally, we demonstrate the competitive performance of the algorithms in two applications, namely spike sorting and super-resolution microscopy.

关键词： Convolution Dictionaries convolutional codes Signal processing algorithms Matching pursuit algorithms Brain modeling Machine learning convolutional dictionary learning convolutional sparse coding convolutional orthogonal matching pursuit non-integer shift grid refinement

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sparse Overcomplete Denoising: Aggregation Versus Global Optimization

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IEEE SIGNAL PROCESSING LETTERS 2017年第10期24卷 1468-1472页

作者： Carrera, Diego Boracchi, Giacomo Foi, Alessandro Wohlberg, Brendt Politecn Milan I-20133 Milan Italy Tampere Univ Technol Tampere 33720 Finland Los Alamos Natl Lab Los Alamos NM 87545 USA

Denoising is often addressed via sparse coding with respect to an overcomplete dictionary. There are two main approaches when the dictionary is composed of translates of an orthonormal basis. The first, traditionally employed by techniques such as wavelet cycle spinning, separately seeks sparsity w.r.t. each translate of the orthonormal basis, solving multiple partial optimizations and obtaining a collection of sparse approximations of the noise-free image, which are aggregated together to obtain a final estimate. The second approach, recently employed by convolutional sparse representations, instead seeks sparsity over the entire dictionary via a global optimization. It is tempting to view the former approach as providing a suboptimal solution of the latter. In this letter, we analyze whether global sparsity is a desirable property, and under what conditions the global optimization provides a better solution to the denoising problem. In particular, our experimental analysis shows that the two approaches attain comparable performance in case of natural images and global optimization outperforms the simpler aggregation of partial estimates only when the image admits an extremely sparse representation. We explain this phenomenon by separately studying the bias and variance of these solutions, and by noting that the variance of the global solution increases very rapidly as the original signal becomes less and less sparse.

关键词： convolutional sparse coding denoising overcomplete representations sparse representations

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Edge-assisted Object Segmentation Using Multimodal Feature Aggregation and Learning

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ACM TRANSACTIONS ON SENSOR NETWORKS 2024年第1期20卷 1-22页

作者： Li, Jianbo Yuan, Genji Yang, Heng Qingdao Univ 308 Ningxia Rd Qingdao Peoples R China Tsinghua Univ 30 Shuangqing Rd Beijing Peoples R China

Object segmentation aims to perfectly identify objects embedded in the surrounding environment and has a wide range of applications. Most previous methods of object segmentation only use RGB images and ignore geometric information from disparity images. Making full use of heterogeneous data from different devices has proved to be a very effective strategy for improving segmentation performance. The key challenge of the multimodal fusion-based object segmentation task lies in the learning, transformation, and fusion of multimodal information. In this article, we focus on the transformation of disparity images and the fusion of multimodal features. We develop a multimodal fusion object segmentation framework, termed the Hybrid Fusion Segmentation Network (HFSNet). Specifically, HFSNet contains three key components, i.e., disparity convolutional sparse coding (DCSC), asymmetric dense projection feature aggregation (ADPFA), and multimodal feature fusion (MFF). The DCSC is designed based on convolutional sparse coding. It not only has better interpretability but also preserves the key geometric information of the object. ADPFA is designed to enhance texture and geometric information to fully exploit nonadjacent features. MFF is used to perform multimodal feature fusion. Extensive experiments show that our HFSNet outperforms existing state-of-the-art models on two challenging datasets.

关键词： Object segmentation convolutional sparse coding dense projection feature aggregation multimodal fusion

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Learning Multiscale convolutional Dictionaries for Image Reconstruction

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2022年 8卷 425-437页

作者： Liu, Tianlin Chaman, Anadi Belius, David Dokmanic, Ivan Univ Basel Dept Math & Comp Sci CH-4001 Basel Switzerland Univ Illinois Dept Elect Comp Engn Urbana IL 61801 USA

convolutional neural networks (CNNs) have been tremendously successful in solving imaging inverse problems. To understand their success, an effective strategy is to construct simpler and mathematically more tractable convolutional sparse coding (CSC) models that share essential ingredients with CNNs. Existing CSC methods, however, underperform leading CNNs in challenging inverse problems. We hypothesize that the performance gap may be attributed in part to how they process images at different spatial scales: While many CNNs use multiscale feature representations, existing CSC models mostly rely on single-scale dictionaries. To close the performance gap, we thus propose a multiscale convolutional dictionary structure. The proposed dictionary structure is derived from the U-Net, arguably the most versatile and widely used CNN for image-to-image learning problems. We show that incorporating the proposed multiscale dictionary in an otherwise standard CSC framework yields performance competitive with state-of-the-art CNNs across a range of challenging inverse problems including CT and MRI reconstruction. Our work thus demonstrates the effectiveness and scalability of the multiscale CSC approach in solving challenging inverse problems.

关键词： Computed tomography convolutional neural networks convolutional sparse coding dictionary learning inverse problems multiscale representation U-Net

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Single Image Deraining With Continuous Rain Density Estimation

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IEEE TRANSACTIONS ON MULTIMEDIA 2023年 25卷 443-456页

作者： Yu, Lei Wang, Bishan He, Jingwei Xia, Gui-Song Yang, Wen Wuhan Univ Sch Elect Informat Wuhan 430072 Peoples R China Wuhan Univ Sch Comp Sci Wuhan 430072 Peoples R China

Single image deraining (SIDR) often suffers from over/under deraining due to the nonuniformity of rain densities and the variety of raindrop scales. In this paper, we propose a continuous density-guided network (CODE-Net) for SIDR. Particularly, it is composed of a rain streak extractor and a denoiser, where the convolutional sparse coding (CSC) is exploited to filter out noises from the extracted rain streaks. Inspired by the reweighted iterative soft-threshold (ISTA) for CSC, we address the problem of continuous rain density estimation by learning the weights with channel attention blocks from sparse codes. We further develop a multiscale strategy to depict rain streaks appearing at different scales. Experiments on synthetic and real-world data demonstrate the superiority of our methods over recent state-of-the-arts, in terms of both quantitative and qualitative results. Additionally, instead of quantizing rain density with several levels, our CODE-Net can provide continuous-valued estimations of rain densities, which is more desirable in real applications.

关键词： Rain convolutional codes Estimation Encoding convolutional neural networks Minimization Mathematical models convolutional sparse coding image deraining rain density estimation

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Factorized Tensor Dictionary Learning for Visual Tensor Data Completion

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IEEE TRANSACTIONS ON MULTIMEDIA 2021年 23卷 1225-1238页

作者： Xu, Ruotao Xu, Yong Quan, Yuhui South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Peng Cheng Lab Shenzhen 518055 Peoples R China Commun & Comp Network Lab Guangdong Guangzhou 510006 Peoples R China Guangdong Prov Key Lab Computat Intelligence & Cy Guangzhou 510006 Peoples R China

This paper aims at developing a dictionary-learning-based method for completing the visual tensor data with missing elements. Traditional dictionary learning approaches suffer from very high computational costs when processing high-dimensional tensor data. Some existing approaches for acceleration impose orthogonality constraints or rank-one decompositions on dictionary atoms;however, the expressibility of the resulting dictionary is rather limited. To address such issues, we propose a convolutional analysis model for tensor dictionary learning, where the update of sparse coefficients during dictionary learning is simple and fast. Furthermore, we propose an orthogonality-constrained convolutional factorization scheme for dictionary construction, in which each tensor dictionary atom is factorized by the convolution of two atoms selected from two orthogonal factor dictionaries respectively. This factorization scheme enables us to efficiently learn an expressive dictionary with over-completeness and non-rank-one atoms. Based on our convolutional analysis model and factorization scheme, an effective yet efficient dictionary learning method is proposed for visual tensor completion. Extensive experiments show that, our method not only outperforms existing dictionary-based approaches with relatively-low time cost, but also outperforms recent low-rank approaches.

关键词： Tensile stress Dictionaries Machine learning Visualization convolutional codes Encoding Analytical models Tensor dictionary learning tensor completion convolutional sparse coding factorized dictionary learning

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