The most widely used form of convolutional sparse coding uses an $\ell_1$ regularization term. While this approach has been successful in a variety of applications, a limitation of the $\ell_1$ penalty is that it is homogeneous across the spatial and filter index dimensions of the sparse representation array, so that sparsity cannot be separately controlled across these dimensions. The present paper considers the consequences of replacing the $\ell_1$ penalty with a mixed group norm, motivated by recent theoretical results for convolutional sparse representations. Algorithms are developed for solving the resulting problems, which are quite challenging, and the impact on the performance of the denoising problem is evaluated. The mixed group norms are found to perform very poorly in this application. While their performance is greatly improved by introducing a weighting strategy, such a strategy also improves the performance obtained from the much simpler and computationally cheaper $\ell_1$ norm.
Sparse decomposition has been widely used for different applications, such as source separation, image classification and image denoising. This paper presents a new algorithm for segmentation of an image into background and foreground text and graphics using sparse decomposition. First, the background is represented using a suitable smooth model, which is a linear combination of a few smoothly varying basis functions, and the foreground text and graphics are modeled as a sparse component overlaid on the smooth background. Then the background and foreground are separated using a sparse decompos…
Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is measured by the l2-norm or l1-norm of the coding residual. Such a sparse coding model assumes that the coding residual follows Gaussian or Laplacian distribution, which may not be effective enough to describe the coding residual in practical FR systems. Meanwhile, the sparsity constraint on the coding coefficients makes SRC's computational cost very high. In…
Advanced Research Lab, NavInfo Europe（NavInfo Europe 高级研究实验室）；Department of Mathematics and Computer Science, Eindhoven University of Technology（埃因霍温理工大学数学与计算机科学系）
Efficient continual learning in humans is enabled by a rich set of neurophysiological mechanisms and interactions between multiple memory systems. The brain efficiently encodes information in non-overlapping sparse codes, which facilitates the learning of new associations faster with controlled interference with previous associations. To mimic sparse coding in DNNs, we enforce activation sparsity along with a dropout mechanism which encourages the model to activate similar units for semantically similar inputs and have less overlap with activation patterns of semantically dissimilar inputs. Th…
The Hong Kong Polytechnic University（香港理工大学）；Xidian University（西安电子科技大学）；Microsoft Research Asia（微软亚洲研究院）
By coding a query sample as a sparse linear combination of all training samples and then classifying it by evaluating which class leads to the minimal coding residual, sparse representation based classification (SRC) leads to interesting results for robust face recognition. It is widely believed that the l1- norm sparsity constraint on coding coefficients plays a key role in the success of SRC, while its use of all training samples to collaboratively represent the query sample is rather ignored. In this paper we discuss how SRC works, and show that the collaborative representation mechanism us…
University of Science and Technology of China（中国科学技术大学）；Texas A&M University（得克萨斯农工大学）
The problem of $L_p$-norm constrained coding is to convert signal into code that lies inside an $L_p$-ball and most faithfully reconstructs the signal. Previous works under the name of sparse coding considered the cases of $L_0$ and $L_1$ norms. The cases with $p>1$ values, i.e. non-sparse coding studied in this paper, remain a difficulty. We propose an interpretable deep structure namely Frank-Wolfe Network (F-W Net), whose architecture is inspired by unrolling and truncating the Frank-Wolfe algorithm for solving an $L_p$-norm constrained problem with $p\geq 1$. We show that the Frank-Wolfe s…
In this paper, we explore an efficient variant of convolutional sparse coding with unit norm code vectors where reconstruction quality is evaluated using an inner product (cosine distance). To use these codes for discriminative classification, we describe a model we term Energy-Based Spherical Sparse Coding (EB-SSC) in which the hypothesized class label introduces a learned linear bias into the coding step. We evaluate and visualize performance of stacking this encoder to make a deep layered model for image classification.
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…
This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm Laplacian regularization is defined directly over the eigenvectors of the normalized Laplacian matrix, we successfully formulate semi-supervised learning as an L1-norm linear reconstruction problem which can be effectively solved with sparse coding. By working with only a small subset of eigenvectors, we further develop a fast sparse coding algorithm for our…
We propose in this paper a new paradigm for facial video compression. We leverage the generative capacity of GANs such as StyleGAN to represent and compress a video, including intra and inter compression. Each frame is inverted in the latent space of StyleGAN, from which the optimal compression is learned. To do so, a diffeomorphic latent representation is learned using a normalizing flows model, where an entropy model can be optimized for image coding. In addition, we propose a new perceptual loss that is more efficient than other counterparts. Finally, an entropy model for video inter coding…
University of Electronic Science and Technology of China（电子科技大学）；Chongqing College of Electronic Engineering（重庆电子工程职业学院）；Minnan Normal University（闽南师范大学）
Because of the limitations of the infrared imaging principle and the properties of infrared imaging systems, infrared images have some drawbacks, including a lack of details, indistinct edges, and a large amount of salt-andpepper noise. To improve the sparse characteristics of the image while maintaining the image edges and weakening staircase artifacts, this paper proposes a method that uses the Lp quasinorm instead of the L1 norm and for infrared image deblurring with an overlapping group sparse total variation method. The Lp quasinorm introduces another degree of freedom, better describes i…
Center for Data Science（数据科学中心）；New York University（纽约大学）；Courant Institute（库朗研究所）；Meta AI - FAIR（Meta人工智能实验室——基础人工智能研究团队）
Sparse representations of images are useful in many computer vision applications. Sparse coding with an $l_1$ penalty and a learned linear dictionary requires regularization of the dictionary to prevent a collapse in the $l_1$ norms of the codes. Typically, this regularization entails bounding the Euclidean norms of the dictionary's elements. In this work, we propose a novel sparse coding protocol which prevents a collapse in the codes without the need to regularize the decoder. Our method regularizes the codes directly so that each latent code component has variance greater than a fixed thres…
School of Computer Science and Technology, Soochow University（苏州大学计算机科学与技术学院）；YITU Technology（依图科技）
In this paper, we propose a structured Robust Adaptive Dic-tionary Pair Learning (RA-DPL) framework for the discrim-inative sparse representation learning. To achieve powerful representation ability of the available samples, the setting of RA-DPL seamlessly integrates the robust projective dictionary pair learning, locality-adaptive sparse representations and discriminative coding coefficients learning into a unified learning framework. Specifically, RA-DPL improves existing projective dictionary pair learning in four perspectives. First, it applies a sparse l2,1-norm based metric to encode th…
Soochow University（苏州大学）；Hefei University of Technology（合肥工业大学）；University of Georgia（佐治亚大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；University of Science and Technology of China（中国科学技术大学）
In this paper, we propose a robust representation learning model called Adaptive Structure-constrained Low-Rank Coding (AS-LRC) for the latent representation of data. To recover the underlying subspaces more accurately, AS-LRC seamlessly integrates an adaptive weighting based block-diagonal structure-constrained low-rank representation and the group sparse salient feature extraction into a unified framework. Specifically, AS-LRC performs the latent decomposition of given data into a low-rank reconstruction by a block-diagonal codes matrix, a group sparse locality-adaptive salient feature part …
Neural networks, specifically deep convolutional neural networks, have achieved unprecedented performance in various computer vision tasks, but the rationale for the computations and structures of successful neural networks is not fully understood. Theories abound for the aptitude of convolutional neural networks for image classification, but less is understood about why such models would be capable of complex visual tasks such as inference and anomaly identification. Here, we propose a sparse coding interpretation of neural networks that have ReLU activation and of convolutional neural networ…
In this paper, we propose a novel sparse coding and counting method under Bayesian framwork for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear coefficients of incrementally updated linear basis. The sparsity constraint enables the tracker to effectively handle difficult challenges, such as occlusion or image corruption. To achieve realtime processing, we propose a fast and efficient numerical algorithm for solving the proposed model. Although it is an NP-hard problem, the proposed accelerated proximal gra…
Deep neural networks (DNNs) usually demand a large amount of operations for real-time inference. Especially, fully-connected layers contain a large number of weights, thus they usually need many off-chip memory accesses for inference. We propose a weight compression method for deep neural networks, which allows values of +1 or -1 only at predetermined positions of the weights so that decoding using a table can be conducted easily. For example, the structured sparse (8,2) coding allows at most two non-zero values among eight weights. This method not only enables multiplication-free DNN implemen…
Anomalies in images occur in various scales from a small hole on a carpet to a large stain. However, anomaly detection based on sparse coding, one of the widely used anomaly detection methods, has an issue in dealing with anomalies that are out of the patch size employed to sparsely represent images. A large anomaly can be considered normal if seen in a small scale, but it is not easy to determine a single scale (patch size) that works well for all images. Then, we propose to incorporate multi-scale features to sparse coding and improve the performance of anomaly detection. The proposed method…
