Convolutional sparse coding improves on the standard sparse approximation by incorporating a global shift-invariant model. The most efficient convolutional sparse coding methods are based on the alternating direction method of multipliers and the convolution theorem. The only major difference between these methods is how they approach a convolutional least-squares fitting subproblem. This letter presents a solution to this subproblem, which improves the efficiency of the state-of-the-art algorithms. We also use the same approach for developing an efficient convolutional dictionary learning method. Furthermore, we propose a novel algorithm for convolutional sparse coding with a constraint on the approximation error.
Rochester Institute of Technology（罗切斯特理工学院）；University of South Florida（南佛罗里达大学）
In this work, we develop convolutional neural generative coding (Conv-NGC), a generalization of predictive coding to the case of convolution/deconvolution-based computation. Specifically, we concretely implement a flexible neurobiologically-motivated algorithm that progressively refines latent state feature maps in order to dynamically form a more accurate internal representation/reconstruction model of natural images. The performance of the resulting sensory processing system is evaluated on complex datasets such as Color-MNIST, CIFAR-10, and Street House View Numbers (SVHN). We study the eff…
The State Key Laboratory of Integrated Service Networks, Xidian University（西安电子科技大学综合业务网理论及关键技术国家重点实验室）；Department of Computer Science and Informatics, Emory University（埃默里大学计算机科学与信息学系）；Department of Computer Science, George Mason University（乔治梅森大学计算机科学系）
The Graph Convolutional Network (GCN) has been successfully applied to many graph-based applications. Training a large-scale GCN model, however, is still challenging: Due to the node dependency and layer dependency of the GCN architecture, a huge amount of computational time and memory is required in the training process. In this paper, we propose a parallel and distributed GCN training algorithm based on the Alternating Direction Method of Multipliers (ADMM) to tackle the two challenges simultaneously. We first split GCN layers into independent blocks to achieve layer parallelism. Furthermore…
Peking University（北京大学）；National Tsinghua University（国立清华大学）；UC San Diego（加州大学圣地亚哥分校）
We propose an adversarial defense method that achieves state-of-the-art performance among attack-agnostic adversarial defense methods while also maintaining robustness to input resolution, scale of adversarial perturbation, and scale of dataset size. Based on convolutional sparse coding, we construct a stratified low-dimensional quasi-natural image space that faithfully approximates the natural image space while also removing adversarial perturbations. We introduce a novel Sparse Transformation Layer (STL) in between the input image and the first layer of the neural network to efficiently proj…
Convolutional sparse representation (CSR), shift-invariant model for inverse problems, has gained much attention in the fields of signal/image processing, machine learning and computer vision. The most challenging problems in CSR implies the minimization of a composite function of the form $min_x \sum_i f_i(x) + g(x)$, where a direct and low-cost solution can be difficult to achieve. However, it has been reported that semi-distributed formulations such as ADMM consensus can provide important computational benefits. In the present work, we derive and detail a thorough theoretical analysis of an…
University of Chinese Academy of Sciences（中国科学院大学）
Convolutional neural network (CNN) and its variants have led to many state-of-art results in various fields. However, a clear theoretical understanding about them is still lacking. Recently, multi-layer convolutional sparse coding (ML-CSC) has been proposed and proved to equal such simply stacked networks (plain networks). Here, we think three factors in each layer of it including the initialization, the dictionary design and the number of iterations greatly affect the performance of ML-CSC. Inspired by these considerations, we propose two novel multi-layer models--residual convolutional spars…
School of Information Technology, University of Cincinnati（辛辛那提大学信息技术学院）；School of Computing and Informatics, University of Louisiana at Lafayette（路易斯安那大学拉法叶分校计算与信息学院）
Spatiotemporal sequence prediction is an important problem in deep learning. We study next-frame(s) video prediction using a deep-learning-based predictive coding framework that uses convolutional, long short-term memory (convLSTM) modules. We introduce a novel reduced-gate convolutional LSTM(rgcLSTM) architecture that requires a significantly lower parameter budget than a comparable convLSTM. By using a single multi-function gate, our reduced-gate model achieves equal or better next-frame(s) prediction accuracy than the original convolutional LSTM while using a smaller parameter budget, there…
University of Bristol（布里斯托大学）；NHS Trust Foundation（NHS信托基金会）
In representation learning, Convolutional Sparse Coding (CSC) enables unsupervised learning of features by jointly optimising both an \(\ell_2\)-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 I…
CMLA, ENS Paris-Saclay, Université Paris-Saclay（巴黎萨克雷高等师范学院、巴黎萨克雷大学数学与应用数学中心）；L2TI, Université Paris 13（巴黎第十三大学信息处理与交互技术实验室）
In this paper, we introduce DICOD, a convolutional sparse coding algorithm which builds shift invariant representations for long signals. This algorithm is designed to run in a distributed setting, with local message passing, making it communication efficient. It is based on coordinate descent and uses locally greedy updates which accelerate the resolution compared to greedy coordinate selection. We prove the convergence of this algorithm and highlight its computational speed-up which is super-linear in the number of cores used. We also provide empirical evidence for the acceleration propertie…
We apply the latest advances in machine learning with deep neural networks to the tasks of radio modulation recognition, channel coding recognition, and spectrum monitoring. This paper first proposes an identification algorithm for space-time block coding of a signal. The feature between spatial multiplexing and Alamouti signals is extracted by adapting convolutional neural networks after preprocessing the received sequence. Unlike other algorithms, this method requires no prior information of channel coefficients and noise power, and consequently is well-suited for noncooperative contexts. Re…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；Bedford Veterans Affairs Medical Center（贝德福德退伍军人事务医疗中心）；University of Massachusetts Medical School（马萨诸塞大学医学院）
Automated ICD coding, which assigns the International Classification of Disease codes to patient visits, has attracted much research attention since it can save time and labor for billing. The previous state-of-the-art model utilized one convolutional layer to build document representations for predicting ICD codes. However, the lengths and grammar of text fragments, which are closely related to ICD coding, vary a lot in different documents. Therefore, a flat and fixed-length convolutional architecture may not be capable of learning good document representations. In this paper, we proposed a M…
Ecole Normale Supérieure de Cachan（卡尚高等师范学院）；CNRS（法国国家科学研究中心）；Université Paris-Saclay（巴黎-萨克雷大学）；Université Paris 13（巴黎第十三大学）
This paper introduces a new multivariate convolutional sparse coding based on tensor algebra with a general model enforcing both element-wise sparsity and low-rankness of the activations tensors. By using the CP decomposition, this model achieves a significantly more efficient encoding of the multivariate signal-particularly in the high order/ dimension setting-resulting in better performance. We prove that our model is closely related to the Kruskal tensor regression problem, offering interesting theoretical guarantees to our setting. Furthermore, we provide an efficient optimization algorith…
The pursuit algorithms integrated in multi-layer convolutional sparse coding (ML-CSC) can interpret the convolutional neural networks (CNNs). However, many current state-of-art (SOTA) pursuit algorithms require multiple iterations to optimize the solution of ML-CSC, which limits their applications to deeper CNNs due to high computational cost and large number of resources for getting very tiny gain of performance. In this study, we focus on the 0th iteration in pursuit algorithm by introducing an effective initialization strategy for each layer, by which the solution for ML-CSC can be improved…
D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing
School of Electronic and Computer Engineering, Peking University（北京大学电子与计算机工程学院）；Graduate School at Shenzhen, Tsinghua University（清华大学深圳研究生院）；ByteDance Inc（字节跳动公司）；School of Software Engineering, Tongji University（同济大学软件学院）；School of Computer Science and Technology, Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳）计算机科学与技术学院）
Technion -– Israel Institute of Technology（以色列理工学院）
Convolutional neural networks (CNN) have led to many state-of-the-art results spanning through various fields. However, a clear and profound theoretical understanding of the forward pass, the core algorithm of CNN, is still lacking. In parallel, within the wide field of sparse approximation, Convolutional Sparse Coding (CSC) has gained increasing attention in recent years. A theoretical study of this model was recently conducted, establishing it as a reliable and stable alternative to the commonly practiced patch-based processing. Herein, we propose a novel multi-layer model, ML-CSC, in which …
CSC-Unet: A Novel Convolutional Sparse Coding Strategy Based Neural Network for Semantic Segmentation
Jiangsu Ocean University（江苏海洋大学）；Suzhou Institute of Trade & Commerce（苏州经贸职业技术学院）；Suzhou University of Science and Technology（苏州科技大学）；Affiliated Lianyungang Hospital of Xuzhou Medical University（徐州医科大学附属连云港医院）；ShanghaiTech University（上海科技大学）；The Hong Kong Polytechnic University（香港理工大学）
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Zhejiang University（浙江大学）
Positron emission tomography (PET) is widely used for clinical diagnosis. As PET suffers from low resolution and high noise, numerous efforts try to incorporate anatomical priors into PET image reconstruction, especially with the development of hybrid PET/CT and PET/MRI systems. In this work, we proposed a novel 3D structural convolutional sparse coding (CSC) concept for penalized-likelihood PET image reconstruction, named 3D PET-CSC. The proposed 3D PET-CSC takes advantage of the convolutional operation and manages to incorporate anatomical priors without the need of registration or supervise…
It has recently been observed that certain extremely simple feature encoding techniques are able to achieve state of the art performance on several standard image classification benchmarks including deep belief networks, convolutional nets, factored RBMs, mcRBMs, convolutional RBMs, sparse autoencoders and several others. Moreover, these "triangle" or "soft threshold" encodings are ex- tremely efficient to compute. Several intuitive arguments have been put forward to explain this remarkable performance, yet no mathematical justification has been offered. The main result of this report is to sh…
Sun Yat-sen University（中山大学）；National Engineering Research Center of Digital Life, Sun Yat-sen University（中山大学国家数字生活工程技术研究中心）；Central China Normal University（华中师范大学）
Tensor data often suffer from missing value problem due to the complex high-dimensional structure while acquiring them. To complete the missing information, lots of Low-Rank Tensor Completion (LRTC) methods have been proposed, most of which depend on the low-rank property of tensor data. In this way, the low-rank component of the original data could be recovered roughly. However, the shortcoming is that the detail information can not be fully restored, no matter the Sum of the Nuclear Norm (SNN) nor the Tensor Nuclear Norm (TNN) based methods. On the contrary, in the field of signal processing…
Hong Kong University of Science and Technology（香港科技大学）
Convolutional sparse coding (CSC) can learn representative shift-invariant patterns from multiple kinds of data. However, existing CSC methods can only model noises from Gaussian distribution, which is restrictive and unrealistic. In this paper, we propose a general CSC model capable of dealing with complicated unknown noise. The noise is now modeled by Gaussian mixture model, which can approximate any continuous probability density function. We use the expectation-maximization algorithm to solve the problem and design an efficient method for the weighted CSC problem in maximization step. The …
New York University Tandon School of Engineering（纽约大学坦登工程学院）
We propose an efficient algorithm for the generalized sparse coding (SC) inference problem. The proposed framework applies to both the single dictionary setting, where each data point is represented as a sparse combination of the columns of one dictionary matrix, as well as the multiple dictionary setting as given in morphological component analysis (MCA), where the goal is to separate a signal into additive parts such that each part has distinct sparse representation within a corresponding dictionary. Both the SC task and its generalization via MCA have been cast as $\ell_1$-regularized least…
Technion – Israel Institute of Technology（以色列理工学院）；GeoEnergy, Inc.（GeoEnergy公司）
In sparse coding, we attempt to extract features of input vectors, assuming that the data is inherently structured as a sparse superposition of basic building blocks. Similarly, neural networks perform a given task by learning features of the training data set. Recently both data-driven and model-driven feature extracting methods have become extremely popular and have achieved remarkable results. Nevertheless, practical implementations are often too slow to be employed in real-life scenarios, especially for real-time applications. We propose a speed-up upgraded version of the classic iterative…
University of Oxford（牛津大学）；The Alan Turing Institute（阿兰·图灵研究所）
Deep Convolutional Sparse Coding (D-CSC) is a framework reminiscent of deep convolutional neural networks (DCNNs), but by omitting the learning of the dictionaries one can more transparently analyse the role of the activation function and its ability to recover activation paths through the layers. Papyan, Romano, and Elad conducted an analysis of such an architecture, demonstrated the relationship with DCNNs and proved conditions under which the D-CSC is guaranteed to recover specific activation paths. A technical innovation of their work highlights that one can view the efficacy of the ReLU n…
Centre Borelli（博雷利中心）；CNRS（法国国家科学研究中心）；ENS Paris Saclay（巴黎-萨克雷高等师范学院）；Université de Paris（巴黎大学）；SSA（法国武装部队卫生服务局）；Hôpital Necker-Enfants Malades（内克尔-患病儿童医院）；AP-HP（巴黎公立医院集团）；Université Sorbonne Paris Nord（索邦巴黎北大学）；University Paris-Saclay（巴黎-萨克雷大学）；Inria（法国国家信息与自动化研究所）；CEA（法国原子能和替代能源委员会）
The analysis of the Nystagmus waveforms from eye-tracking records is crucial for the clinicial interpretation of this pathological movement. A major issue to automatize this analysis is the presence of natural eye movements and eye blink artefacts that are mixed with the signal of interest. We propose a method based on Convolutional Dictionary Learning that is able to automaticcaly highlight the Nystagmus waveforms, separating the natural motion from the pathological movements. We show on simulated signals that our method can indeed improve the pattern recovery rate and provide clinical exampl…
Sparse coding techniques for image processing traditionally rely on a 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 $\ell_0$ "norm" or the $\ell_1$ norm of the whole image, which may create an imbalanced sparsity across various regions in the image. In order to …
University of Oxford（牛津大学）；MRC Brain Network Dynamics Unit（医学研究理事会脑网络动力学单元）；Hebei University of Technology（河北工业大学）
Predictive coding networks (PCNs) are an influential model for information processing in the brain. They have appealing theoretical interpretations and offer a single mechanism that accounts for diverse perceptual phenomena of the brain. On the other hand, backpropagation (BP) is commonly regarded to be the most successful learning method in modern machine learning. Thus, it is exciting that recent work formulates inference learning (IL) that trains PCNs to approximate BP. However, there are several remaining critical issues: (i) IL is an approximation to BP with unrealistic/non-trivial requir…
Convergence Analysis for Deep Sparse Coding via Convolutional Neural Networks
Department of Mathematics, Ludwig-Maximilians-Universität München（慕尼黑莱布尼茨-马克斯大学数学系）；Department of Mathematics, City University of Hong Kong（香港城市大学数学系）；Department of Mathematics, The University of Sydney（悉尼大学数学系）
King Abdullah University of Science and Technology (KAUST)（沙特阿拉伯国王 Abdullah 科技大学(KAUST)（注：此处“King Abdullah University of Science and Technology”的中文常见译名为“沙特国王 Abdullah 科技大学”，但根据原文本括号内缩写“KAUST”，保留“国王 Abdullah 科技大学(KAUST)”或更简洁的“沙特国王 Abdullah 科技大学”均可，此处按原文括号内缩写整合为“沙特阿拉伯国王 Abdullah 科技大学(KAUST)”以确保准确对应））
State-of-the-art methods for Convolutional Sparse Coding usually employ Fourier-domain solvers in order to speed up the convolution operators. However, this approach is not without shortcomings. For example, Fourier-domain representations implicitly assume circular boundary conditions and make it hard to fully exploit the sparsity of the problem as well as the small spatial support of the filters. In this work, we propose a novel stochastic spatial-domain solver, in which a randomized subsampling strategy is introduced during the learning sparse codes. Afterwards, we extend the proposed strate…
LTCI, Télécom ParisTech, Université Paris-Saclay（LTCI，巴黎高等电信学院，巴黎萨克雷大学）；INRIA, Université Paris Saclay（法国国家信息与自动化研究所，巴黎萨克雷大学）
Frequency-specific patterns of neural activity are traditionally interpreted as sustained rhythmic oscillations, and related to cognitive mechanisms such as attention, high level visual processing or motor control. While alpha waves (8-12 Hz) are known to closely resemble short sinusoids, and thus are revealed by Fourier analysis or wavelet transforms, there is an evolving debate that electromagnetic neural signals are composed of more complex waveforms that cannot be analyzed by linear filters and traditional signal representations. In this paper, we propose to learn dedicated representations…
Technische Universität Berlin (TU Berlin)（柏林工业大学）；Univ. Grenoble Alpes, CNRS, Grenoble INP, GIPSA-lab（格勒诺布尔阿尔卑斯大学、法国国家科学研究中心、格勒诺布尔国立理工学院、GIPSA实验室）；University of California, Los Angeles (UCLA)（加利福尼亚大学洛杉矶分校）；RIKEN Center for Advanced Intelligence Project (AIP), RIKEN（理化学研究所先进智能项目中心）
Interferometric phase restoration has been investigated for decades and most of the state-of-the-art methods have achieved promising performances for InSAR phase restoration. These methods generally follow the nonlocal filtering processing chain aiming at circumventing the staircase effect and preserving the details of phase variations. In this paper, we propose an alternative approach for InSAR phase restoration, i.e. Complex Convolutional Sparse Coding (ComCSC) and its gradient regularized version. To our best knowledge, this is the first time that we solve the InSAR phase restoration proble…
Université Paris-Saclay（巴黎萨克雷大学）；CNRS（法国国家科学研究中心）；ENS Paris-Saclay（巴黎萨克雷高等师范学校）；Centre Borelli（博雷利中心）；Université Sorbonne Paris Nord（索邦巴黎北大学）；L2TI（L2TI实验室）；eXascale Infolab；University of Fribourg（弗里堡大学）
Recently, there has been growing interest in the analysis of spectrograms of ElectroEncephaloGram (EEG), particularly to study the neural correlates of (un)-consciousness during General Anesthesia (GA). Indeed, it has been shown that order three tensors (channels x frequencies x times) are a natural and useful representation of these signals. However this encoding entails significant difficulties, especially for convolutional sparse coding (CSC) as existing methods do not take advantage of the particularities of tensor representation, such as rank structures, and are vulnerable to the high lev…
Drexel University（德雷塞尔大学）；University of Delaware（特拉华大学）
Artificial neural networks (ANNs), specifically deep learning networks, have often been labeled as black boxes due to the fact that the internal representation of the data is not easily interpretable. In our work, we illustrate that an ANN, trained using sparse coding under specific sparsity constraints, yields a more interpretable model than the standard deep learning model. The dictionary learned by sparse coding can be more easily understood and the activations of these elements creates a selective feature output. We compare and contrast our sparse coding model with an equivalent feed forwa…
Speech coding facilitates the transmission of speech over low-bandwidth networks with minimal distortion. Neural-network based speech codecs have recently demonstrated significant improvements in quality over traditional approaches. While this new generation of codecs is capable of synthesizing high-fidelity speech, their use of recurrent or convolutional layers often restricts their effective receptive fields, which prevents them from compressing speech efficiently. We propose to further reduce the bitrate of neural speech codecs through the use of pretrained Transformers, capable of exploiti…
Harbin Engineering University（哈尔滨工程大学）；University of California, Los Angeles（加州大学洛杉矶分校）
We introduce an explainable generative model by applying sparse operation on the feature maps of the generator network. Meaningful hierarchical representations are obtained using the proposed generative model with sparse activations. The convolutional kernels from the bottom layer to the top layer of the generator network can learn primitives such as edges and colors, object parts, and whole objects layer by layer. From the perspective of the generator network, we propose a method for inducing both sparse coding and the AND-OR grammar for images. Experiments show that our method is capable of …
College of Electronic and Optical Engineering & College of Microelectronics, Nanjing University of Posts and Telecommunications（南京邮电大学电子与光学工程学院、微电子学院）；College of Telecommunications & Information Engineering, Nanjing University of Posts and Telecommunications（南京邮电大学通信与信息工程学院）
Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with each group contains low-rank property. In this paper, we propose a novel low-rank minimization based denoising model for IR tasks under the perspective of GSC, an important connection between our denoising model and rank minimization problem has been put forward. To overcome the bias problem caused by convex nuclear norm minimization (NNM) for rank approximat…
Video coding is a critical step in all popular methods of streaming video. Marked progress has been made in video quality, compression, and computational efficiency. Recently, there has been an interest in finding ways to apply techniques form the fast-progressing field of machine learning to further improve video coding. We present a method that uses convolutional neural networks to help refine the output of various standard coding methods. The novelty of our approach is to train multiple different sets of network parameters, with each set corresponding to a specific, short segment of video. …
Filter banks are a popular tool for the analysis of piecewise smooth signals such as natural images. Motivated by the empirically observed properties of scale and detail coefficients of images in the wavelet domain, we propose a hierarchical deep generative model of piecewise smooth signals that is a recursion across scales: the low pass scale coefficients at one layer are obtained by filtering the scale coefficients at the next layer, and adding a high pass detail innovation obtained by filtering a sparse vector. This recursion describes a linear dynamic system that is a non-Gaussian Markov p…
First Affiliation（第一隶属机构）；Second Affiliation（第二隶属机构）；hw.ac.uk（爱丁堡大学（注：hw.ac.uk通常是University of Edinburgh的域名，这里可能是缩写或未完整显示，按要求保留原文并翻译））
In this research, we propose ImmuNetNAS, a novel Neural Architecture Search (NAS) approach inspired by the immune network theory. The core of ImmuNetNAS is built on the original immune network algorithm, which iteratively updates the population through hypermutation and selection, and eliminates the self-generation individuals that do not meet the requirements through comparing antibody affinity and inter-specific similarity. In addition, in order to facilitate the mutation operation, we propose a novel two-component based neural structure coding strategy. Furthermore, an improved mutation str…
The recently proposed multi-layer sparse model has raised insightful connections between sparse representations and convolutional neural networks (CNN). In its original conception, this model was restricted to a cascade of convolutional synthesis representations. In this paper, we start by addressing a more general model, revealing interesting ties to fully connected networks. We then show that this multi-layer construction admits a brand new interpretation in a unique symbiosis between synthesis and analysis models: while the deepest layer indeed provides a synthesis representation, the mid-l…
