In this paper, we introduce a Deep Convolutional Analysis Dictionary Model (DeepCAM) by learning convolutional dictionaries instead of unstructured dictionaries as in the case of deep analysis dictionary model introduced in the companion paper. Convolutional dictionaries are more suitable for processing high-dimensional signals like for example images and have only a small number of free parameters. By exploiting the properties of a convolutional dictionary, we present an efficient convolutional analysis dictionary learning approach. A L-layer DeepCAM consists of L layers of convolutional analysis dictionary and element-wise soft-thresholding pairs and a single layer of convolutional synthesis dictionary. Similar to DeepAM, each convolutional analysis dictionary is composed of a convolutional Information Preserving Analysis Dictionary (IPAD) and a convolutional Clustering Analysis Dictionary (CAD). The IPAD and the CAD are learned using variations of the proposed learning algorithm. We demonstrate that DeepCAM is an effective multilayer convolutional model and, on single image super-resolution, achieves performance comparable with other methods while also showing good generalization capabilities.
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学（KAUST））
Convolutional Sparse Coding (CSC) is a well-established image representation model especially suited for image restoration tasks. In this work, we extend the applicability of this model by proposing a supervised approach to convolutional sparse coding, which aims at learning discriminative dictionaries instead of purely reconstructive ones. We incorporate a supervised regularization term into the traditional unsupervised CSC objective to encourage the final dictionary elements to be discriminative. Experimental results show that using supervised convolutional learning results in two key advant…
Université catholique de Louvain（鲁汶天主教大学）；Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Computational imaging methods that can exploit multiple modalities have the potential to enhance the capabilities of traditional sensing systems. In this paper, we propose a new method that reconstructs multimodal images from their linear measurements by exploiting redundancies across different modalities. Our method combines a convolutional group-sparse representation of images with total variation (TV) regularization for high-quality multimodal imaging. We develop an online algorithm that enables the unsupervised learning of convolutional dictionaries on large-scale datasets that are typical…
Inspired by the recent success of deep neural networks and the recent efforts to develop multi-layer dictionary models, we propose a Deep Analysis dictionary Model (DeepAM) which is optimized to address a specific regression task known as single image super-resolution. Contrary to other multi-layer dictionary models, our architecture contains L layers of analysis dictionary and soft-thresholding operators to gradually extract high-level features and a layer of synthesis dictionary which is designed to optimize the regression task at hand. In our approach, each analysis dictionary is partitione…
Recently, the Magnetic Resonance Imaging (MRI) images have limited and unsatisfactory resolutions due to various constraints such as physical, technological and economic considerations. Super-resolution techniques can obtain high-resolution MRI images. The traditional methods obtained the resolution enhancement of brain MRI by interpolations, affecting the accuracy of the following diagnose process. The requirement for brain image quality is fast increasing. In this paper, we propose an image super-resolution (SR) method based on overcomplete dictionaries and inherent similarity of an image to…
National Engineering Laboratory for Video Technology, Peking University（北京大学视频技术国家工程实验室）
In this letter, we propose a novel image denoising method based on correlation preserving sparse coding. Because the instable and unreliable correlations among basis set can limit the performance of the dictionary-driven denoising methods, two effective regularized strategies are employed in the coding process. Specifically, a graph-based regularizer is built for preserving the global similarity correlations, which can adaptively capture both the geometrical structures and discriminative features of textured patches. In particular, edge weights in the graph are obtained by seeking a nonnegativ…
University College London（伦敦大学学院）；Imperial College London（帝国理工学院）；Heriot-Watt University（赫瑞瓦特大学）；Vrije Universiteit Brussel（布鲁塞尔自由大学）；imec（校际微电子中心）
Real-world data processing problems often involve various image modalities associated with a certain scene, including RGB images, infrared images or multi-spectral images. The fact that different image modalities often share certain attributes, such as certain edges, textures and other structure primitives, represents an opportunity to enhance various image processing tasks. This paper proposes a new approach to construct a high-resolution (HR) version of a low-resolution (LR) image given another HR image modality as reference, based on joint sparse representations induced by coupled dictionar…
Digital cameras transform sensor RAW readings into RGB images by means of their Image Signal Processor (ISP). Computational photography tasks such as image denoising and colour constancy are commonly performed in the RAW domain, in part due to the inherent hardware design, but also due to the appealing simplicity of noise statistics that result from the direct sensor readings. Despite this, the availability of RAW images is limited in comparison with the abundance and diversity of available RGB data. Recent approaches have attempted to bridge this gap by estimating the RGB to RAW mapping: hand…
Astronomical images suffer a constant presence of multiple defects that are consequences of the intrinsic properties of the acquisition equipments, and atmospheric conditions. One of the most frequent defects in astronomical imaging is the presence of additive noise which makes a denoising step mandatory before processing data. During the last decade, a particular modeling scheme, based on sparse representations, has drawn the attention of an ever growing community of researchers. Sparse representations offer a promising framework to many image and signal processing tasks, especially denoising…
We solve the compressive sensing problem via convolutional factor analysis, where the convolutional dictionaries are learned {\em in situ} from the compressed measurements. An alternating direction method of multipliers (ADMM) paradigm for compressive sensing inversion based on convolutional factor analysis is developed. The proposed algorithm provides reconstructed images as well as features, which can be directly used for recognition ($e.g.$, classification) tasks. When a deep (multilayer) model is constructed, a stochastic unpooling process is employed to build a generative model. During re…
We propose a non-convex variational model for the super-resolution of Optical Coherence Tomography (OCT) images of the murine eye, by enforcing sparsity with respect to suitable dictionaries learnt from high-resolution OCT data. The statistical characteristics of OCT images motivate the use of α-stable distributions for learning dictionaries, by considering the non-Gaussian case, α=1. The sparsity-promoting cost function relies on a non-convex penalty - Cauchy-based or Minimax Concave Penalty (MCP) - which makes the problem particularly challenging. We propose an efficient algorithm for minimi…
Sparse representations with learned dictionaries have been successful in several image analysis applications. In this paper, we propose and analyze the framework of ensemble sparse models, and demonstrate their utility in image restoration and unsupervised clustering. The proposed ensemble model approximates the data as a linear combination of approximations from multiple \textit{weak} sparse models. Theoretical analysis of the ensemble model reveals that even in the worst-case, the ensemble can perform better than any of its constituent individual models. The dictionaries corresponding to the…
Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model grap…
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…
Technion-Israel Institute of Technology（以色列理工学院）；Stanford University（斯坦福大学）
The recently proposed Multi-Layer Convolutional Sparse Coding (ML-CSC) model, consisting of a cascade of convolutional sparse layers, provides a new interpretation of Convolutional Neural Networks (CNNs). Under this framework, the computation of the forward pass in a CNN is equivalent to a pursuit algorithm aiming to estimate the nested sparse representation vectors -- or feature maps -- from a given input signal. Despite having served as a pivotal connection between CNNs and sparse modeling, a deeper understanding of the ML-CSC is still lacking: there are no pursuit algorithms that can serve …
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）
Convolutional dictionary learning (CDL), the problem of estimating shift-invariant templates from data, is typically conducted in the absence of a prior/structure on the templates. In data-scarce or low signal-to-noise ratio (SNR) regimes, learned templates overfit the data and lack smoothness, which can affect the predictive performance of downstream tasks. To address this limitation, we propose GPCDL, a convolutional dictionary learning framework that enforces priors on templates using Gaussian Processes (GPs). With the focus on smoothness, we show theoretically that imposing a GP prior is e…
Personalized Convolutional Dictionary Learning of Physiological Time Series
Centre Borelli（博雷利中心）；Thales AVS（泰雷兹AVS公司）；ENS Paris-Saclay（巴黎萨克雷高等师范学校）；University of Pennsylvania（宾夕法尼亚大学）；CMAP（应用数学与计算机科学中心）；CNRS（法国国家科学研究中心）；Ecole polytechnique（巴黎综合理工学院）
Swiss Federal Office of Meteorology and Climatology (MeteoSwiss)（瑞士联邦气象与气候办公室（MeteoSwiss））；ETH Zurich（苏黎世联邦理工学院）
Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables t…
Sparse dictionary learning (SDL) has become a popular method for adaptively identifying parsimonious representations of a dataset, a fundamental problem in machine learning and signal processing. While most work on SDL assumes a training dataset of independent and identically distributed samples, a variant known as convolutional sparse dictionary learning (CSDL) relaxes this assumption, allowing more general sequential data sources, such as time series or other dependent data. Although recent work has explored the statistical properties of classical SDL, the statistical properties of CSDL rema…
The Research Institute of the University of Bucharest (ICUB), University of Bucharest（布加勒斯特大学布加勒斯特大学研究院（ICUB））；University of Bucharest（布加勒斯特大学）
Anomaly detection in networks often boils down to identifying an underlying graph structure on which the abnormal occurrence rests on. Financial fraud schemes are one such example, where more or less intricate schemes are employed in order to elude transaction security protocols. We investigate the problem of learning graph structure representations using adaptations of dictionary learning aimed at encoding connectivity patterns. In particular, we adapt dictionary learning strategies to the specificity of network topologies and propose new methods that impose Laplacian structure on the diction…
Princeton University（普林斯顿大学）；Microsoft Research（微软研究院）；Massachusetts Institute of Technology（麻省理工学院）；Institute for Advanced Study（高等研究院）
In sparse recovery we are given a matrix $A$ (the dictionary) and a vector of the form $A X$ where $X$ is sparse, and the goal is to recover $X$. This is a central notion in signal processing, statistics and machine learning. But in applications such as sparse coding, edge detection, compression and super resolution, the dictionary $A$ is unknown and has to be learned from random examples of the form $Y = AX$ where $X$ is drawn from an appropriate distribution --- this is the dictionary learning problem. In most settings, $A$ is overcomplete: it has more columns than rows. This paper presents …
ARM Machine Learning Research Lab（ARM机器学习研究实验室）；University of California, San Diego（加州大学圣地亚哥分校）
This paper addresses the problem of learning dictionaries for multimodal datasets, i.e. datasets collected from multiple data sources. We present an algorithm called multimodal sparse Bayesian dictionary learning (MSBDL). MSBDL leverages information from all available data modalities through a joint sparsity constraint. The underlying framework offers a considerable amount of flexibility to practitioners and addresses many of the shortcomings of existing multimodal dictionary learning approaches. In particular, the procedure includes the automatic tuning of hyperparameters and is unique in tha…
Luleå University of Technology（吕勒奥理工大学）；SKF-LTU University Technology Center（SKF-吕勒奥理工大学技术中心）
Condition monitoring is central to the efficient operation of wind farms due to the challenging operating conditions, rapid technology development and large number of aging wind turbines. In particular, predictive maintenance planning requires the early detection of faults with few false positives. Achieving this type of detection is a challenging problem due to the complex and weak signatures of some faults, particularly the faults that occur in some of the drivetrain bearings. Here, we investigate recently proposed condition monitoring methods based on unsupervised dictionary learning using …
The success of Convolutional Neural Networks (CNNs) in image classification has prompted efforts to study their use for classifying image data obtained in Particle Physics experiments. Here, we discuss our efforts to apply CNNs to 2D and 3D image data from particle physics experiments to classify signal from background. In this work we present an extensive convolutional neural architecture search, achieving high accuracy for signal/background discrimination for a HEP classification use-case based on simulated data from the Ice Cube neutrino observatory and an ATLAS-like detector. We demonstrat…
