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 nonnegative low-rank construction. Besides, a robust locality-constrained coding can automatically preserve not only spatial neighborhood information but also internal consistency present in noisy patches while learning overcomplete dictionary. Experimental results demonstrate that our proposed method achieves state-of-the-art denoising performance in terms of both PSNR and subjective visual quality.
In this paper, we propose a new multimodal image denoising approach to attenuate white Gaussian additive noise in a given image modality under the aid of a guidance image modality. The proposed coupled image denoising approach consists of two stages: coupled sparse coding and reconstruction. The first stage performs joint sparse transform for multimodal images with respect to a group of learned coupled dictionaries, followed by a shrinkage operation on the sparse representations. Then, in the second stage, the shrunken representations, together with coupled dictionaries, contribute to the reco…
This paper introduces a new rain removal model based on the shrinkage of the sparse codes for a single image. Recently, dictionary learning and sparse coding have been widely used for image restoration problems. These methods can also be applied to the rain removal by learning two types of rain and non-rain dictionaries and forcing the sparse codes of the rain dictionary to be zero vectors. However, this approach can generate unwanted edge artifacts and detail loss in the non-rain regions. Based on this observation, a new approach for shrinking the sparse codes is presented in this paper. To e…
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…
Group sparse representation has shown promising results in image debulrring and image inpainting in GSR [3] , the main reason that lead to the success is by exploiting Sparsity and Nonlocal self-similarity (NSS) between patches on natural images, and solve a regularized optimization problem. However, directly adapting GSR[3] in image denoising yield very unstable and non-satisfactory results, to overcome these issues, this paper proposes a progressive image denoising algorithm that successfully adapt GSR [3] model and experiments shows the superior performance than some of the state-of-the-art…
The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；The Hong Kong Polytechnic University（香港理工大学）
Most of existing image denoising methods assume the corrupted noise to be additive white Gaussian noise (AWGN). However, the realistic noise in real-world noisy images is much more complex than AWGN, and is hard to be modelled by simple analytical distributions. As a result, many state-of-the-art denoising methods in literature become much less effective when applied to real-world noisy images captured by CCD or CMOS cameras. In this paper, we develop a trilateral weighted sparse coding (TWSC) scheme for robust real-world image denoising. Specifically, we introduce three weight matrices into t…
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…
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…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately, the applicability of such methods is severely hampered by the computational burden of sparse approximation: these algorithms are linear or super-linear in both the data dimensionality and size of the dictionary. We propose a framework for learning the hierarchical structure of over-complete dictionaries that enables fast computation of sparse representations…
The Hong Kong Polytechnic University（香港理工大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
Most of existing image denoising methods learn image priors from either external data or the noisy image itself to remove noise. However, priors learned from external data may not be adaptive to the image to be denoised, while priors learned from the given noisy image may not be accurate due to the interference of corrupted noise. Meanwhile, the noise in real-world noisy images is very complex, which is hard to be described by simple distributions such as Gaussian distribution, making real-world noisy image denoising a very challenging problem. We propose to exploit the information in both ext…
Nanjing University（南京大学）；Southeast University（东南大学）；Nokia Bell Labs（诺基亚贝尔实验室）
Inspired by group-based sparse coding, recently proposed group sparsity residual (GSR) scheme has demonstrated superior performance in image processing. However, one challenge in GSR is to estimate the residual by using a proper reference of the group-based sparse coding (GSC), which is desired to be as close to the truth as possible. Previous researches utilized the estimations from other algorithms (i.e., GMM or BM3D), which are either not accurate or too slow. In this paper, we propose to use the Non-Local Samples (NLS) as reference in the GSR regime for image denoising, thus termed GSR-NLS…
Deep Equilibrium Convolutional Sparse Coding for Hyperspectral Image Denoising
School of Computer Science and Engineering, Nanjing University of Science and Technology（南京理工大学计算机科学与工程学院）；College of Computer Science, Zhejiang University（浙江大学计算机科学学院）
Since the first success of Dong et al., the deep-learning-based approach has become dominant in the field of single-image super-resolution. This replaces all the handcrafted image processing steps of traditional sparse-coding-based methods with a deep neural network. In contrast to sparse-coding-based methods, which explicitly create high/low-resolution dictionaries, the dictionaries in deep-learning-based methods are implicitly acquired as a nonlinear combination of multiple convolutions. One disadvantage of deep-learning-based methods is that their performance is degraded for images created …
Virginia Tech（弗吉尼亚理工大学）；New Mexico Tech（新墨西哥理工学院）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）
Neural networks are analogous in many ways to spin glasses, systems which are known for their rich set of dynamics and equally complex phase diagrams. We apply well-known techniques in the study of spin glasses to a convolutional sparsely encoding neural network and observe power law finite-size scaling behavior in the sparsity and reconstruction error as the network denoises 32$\times$32 RGB CIFAR-10 images. This finite-size scaling indicates the presence of a continuous phase transition at a critical value of this sparsity. By using the power law scaling relations inherent to finite-size sca…
Nanjing University of Science and Technology（南京理工大学）；University of Macau（澳门大学）；Griffith University（格里菲斯大学）；Zhejiang University（浙江大学）
Deep learning (DL) based hyperspectral images (HSIs) denoising approaches directly learn the nonlinear mapping between observed noisy images and underlying clean images. They normally do not consider the physical characteristics of HSIs, therefore making them lack of interpretability that is key to understand their denoising mechanism.. In order to tackle this problem, we introduce a novel model guided interpretable network for HSI denoising. Specifically, fully considering the spatial redundancy, spectral low-rankness and spectral-spatial properties of HSIs, we first establish a subspace base…
In this work we propose a novel postprocessing technique for compression-artifact reduction. Our approach is based on posing this task as an inverse problem, with a regularization that leverages on existing state-of-the-art image denoising algorithms. We rely on the recently proposed Plug-and-Play Prior framework, suggesting the solution of general inverse problems via Alternating Direction Method of Multipliers (ADMM), leading to a sequence of Gaussian denoising steps. A key feature in our scheme is a linearization of the compression-decompression process, so as to get a formulation that can …
University of Science and Technology of China（中国科学技术大学）
K-SVD algorithm has been successfully applied to image denoising tasks dozens of years but the big bottleneck in speed and accuracy still needs attention to break. For the sparse coding stage in K-SVD, which involves $\ell_{0}$ constraint, prevailing methods usually seek approximate solutions greedily but are less effective once the noise level is high. The alternative $\ell_{1}$ optimization is proved to be powerful than $\ell_{0}$, however, the time consumption prevents it from the implementation. In this paper, we propose a new K-SVD framework called K-SVD$_P$ by applying the Primal-dual ac…
The Johns Hopkins University（约翰霍普金斯大学）；West Virginia University（西弗吉尼亚大学）
In this paper, we describe the deep sparse coding network (SCN), a novel deep network that encodes intermediate representations with nonnegative sparse coding. The SCN is built upon a number of cascading bottleneck modules, where each module consists of two sparse coding layers with relatively wide and slim dictionaries that are specialized to produce high dimensional discriminative features and low dimensional representations for clustering, respectively. During training, both the dictionaries and regularization parameters are optimized with an end-to-end supervised learning algorithm based o…
Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has proven to be very effective in many image processing tasks. Traditionally, the dictionary is an unstructured "flat" set of atoms. In this paper, we study structured dictionaries which are obtained from an epitome, or a set of epitomes. The epitome is itself a small image, and the atoms are all the patches of a chosen size inside this image. This considerably …
In this study, the problem of computing a sparse representation of multi-dimensional visual data is considered. In general, such data e.g., hyperspectral images, color images or video data consists of signals that exhibit strong local dependencies. A new computationally efficient sparse coding optimization problem is derived by employing regularization terms that are adapted to the properties of the signals of interest. Exploiting the merits of the learnable regularization techniques, a neural network is employed to act as structure prior and reveal the underlying signal dependencies. To solve…
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…
UNC Chapel Hill/BRIC（北卡罗来纳大学教堂山分校/生物医学影像中心）；Microsoft Research Cambridge（微软研究院剑桥）；University of Delaware（特拉华大学）
Correlative microscopy is a methodology combining the functionality of light microscopy with the high resolution of electron microscopy and other microscopy technologies. Image registration for correlative microscopy is quite challenging because it is a multi-modal, multi-scale and multi-dimensional registration problem. In this report, I introduce two methods of image registration for correlative microscopy. The first method is based on fiducials (beads). I generate landmarks from the fiducials and compute the similarity transformation matrix based on three pairs of nearest corresponding land…
Sparse coding (SC) is an automatic feature extraction and selection technique that is widely used in unsupervised learning. However, conventional SC vectorizes the input images, which breaks apart the local proximity of pixels and destructs the elementary object structures of images. In this paper, we propose a novel two-dimensional sparse coding (2DSC) scheme that represents the input images as the tensor-linear combinations under a novel algebraic framework. 2DSC learns much more concise dictionaries because it uses the circular convolution operator, since the shifted versions of atoms learn…
In this paper, we propose sparse coding-based approaches for segmentation of tumor regions from MR images. Sparse coding with data-adapted dictionaries has been successfully employed in several image recovery and vision problems. The proposed approaches obtain sparse codes for each pixel in brain magnetic resonance images considering their intensity values and location information. Since it is trivial to obtain pixel-wise sparse codes, and combining multiple features in the sparse coding setup is not straightforward, we propose to perform sparse coding in a high-dimensional feature space where…
Nonlocal self-similarity and group sparsity have been widely utilized in image compressive sensing (CS). However, when the sampling rate is low, the internal prior information of degraded images may be not enough for accurate restoration, resulting in loss of image edges and details. In this paper, we propose a joint group and residual sparse coding method for CS image recovery (JGRSC-CS). In the proposed JGRSC-CS, patch group is treated as the basic unit of sparse coding and two dictionaries (namely internal and external dictionaries) are applied to exploit the sparse representation of each g…
In this paper a new dictionary learning algorithm for multidimensional data is proposed. Unlike most conventional dictionary learning methods which are derived for dealing with vectors or matrices, our algorithm, named KTSVD, learns a multidimensional dictionary directly via a novel algebraic approach for tensor factorization as proposed in [3, 12, 13]. Using this approach one can define a tensor-SVD and we propose to extend K-SVD algorithm used for 1-D data to a K-TSVD algorithm for handling 2-D and 3-D data. Our algorithm, based on the idea of sparse coding (using group-sparsity over multidi…
HRL Laboratories, LLC（HRL实验室有限责任公司）；University of Pennsylvania（宾夕法尼亚大学）
A classic approach toward zero-shot learning (ZSL) is to map the input domain to a set of semantically meaningful attributes that could be used later on to classify unseen classes of data (e.g. visual data). In this paper, we propose to learn a visual feature dictionary that has semantically meaningful atoms. Such dictionary is learned via joint dictionary learning for the visual domain and the attribute domain, while enforcing the same sparse coding for both dictionaries. Our novel attribute aware formulation provides an algorithmic solution to the domain shift/hubness problem in ZSL. Upon le…
PetroChina Research Institute of Petroleum Exploration and Development (RIPED)-Northwest（中国石油勘探开发研究院（西北））；University of Electronic Science and Technology of China（电子科技大学）；Columbia University（哥伦比亚大学）
Seismic data denoising is vital to geophysical applications and the transform-based function method is one of the most widely used techniques. However, it is challenging to design a suit- able sparse representation to express a transform-based func- tion group due to the complexity of seismic data. In this paper, we apply a seismic data denoising method based on learning- type overcomplete dictionaries which uses two-dimensional sparse coding (2DSC). First, we model the input seismic data and dictionaries as third-order tensors and introduce tensor- linear combinations for data approximation. …
SAMSUNG Research Institute（三星研究院）；School of Electrical and Computing Engineering, University of Campinas (Unicamp)（坎皮纳斯大学（Unicamp）电气与计算机工程学院）；Institute of Computing, University of Campinas (Unicamp)（坎皮纳斯大学（Unicamp）计算研究所）
Visual dictionaries are a critical component for image classification/retrieval systems based on the bag-of-visual-words (BoVW) model. Dictionaries are usually learned without supervision from a training set of images sampled from the collection of interest. However, for large, general-purpose, dynamic image collections (e.g., the Web), obtaining a representative sample in terms of semantic concepts is not straightforward. In this paper, we evaluate the impact of semantics in the dictionary quality, aiming at verifying the importance of semantic diversity in relation visual diversity for visua…
Over the last decades, images have become an important source of information in many domains, thus their high quality has become necessary to acquire better information. One of the important issues that arise is image denoising, which means recovering a signal from inaccurately and/or partially measured samples. This interpretation is highly correlated to the compressive sensing theory, which is a revolutionary technology and implies that if a signal is sparse then the original signal can be obtained from a few measured values, which are much less, than the ones suggested by other used theorie…
Southwest Jiaotong University（西南交通大学）；Shenzhen Institutes of Advanced Technology（深圳先进技术研究院）；Chinese Academy of Sciences（中国科学院）
Many efforts have been devoted to develop alternative methods to traditional vector quantization in image domain such as sparse coding and soft-assignment. These approaches can be split into a dictionary learning phase and a feature encoding phase which are often closely connected. In this paper, we investigate the effects of these phases by separating them for video-based action classification. We compare several dictionary learning methods and feature encoding schemes through extensive experiments on KTH and HMDB51 datasets. Experimental results indicate that sparse coding performs consisten…
Beyond FACS: Data-driven Facial Expression Dictionaries, with Application to Predicting Autism
Center for Autism Research, The Children’s Hospital of Philadelphia（儿童医院费城医院自闭症研究中心）；Department of Psychiatry, University of Pennsylvania（宾夕法尼亚大学精神病学系）；Deliberate AI
Hyperspectral imaging offers new perspectives for diverse applications, ranging from the monitoring of the environment using airborne or satellite remote sensing, precision farming, food safety, planetary exploration, or astrophysics. Unfortunately, the spectral diversity of information comes at the expense of various sources of degradation, and the lack of accurate ground-truth "clean" hyperspectral signals acquired on the spot makes restoration tasks challenging. In particular, training deep neural networks for restoration is difficult, in contrast to traditional RGB imaging problems where d…
Center for Imaging Science, Johns Hopkins University（约翰霍普金斯大学成像科学中心）
Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers in the brain, $\textit{in vivo}$, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tensor imaging, but the high number of samples needed to estimate diffusivity requires longer patient scan times. To accelerate dMRI, compressed sensing (CS) has been utilized by exploiting a sparse dictionary representation of the data, discovered through sparse coding. The sparser …
University of Minnesota（明尼苏达大学）；Universidad de la Republica, Uruguay（乌拉圭共和国大学）
A collaborative framework for detecting the different sources in mixed signals is presented in this paper. The approach is based on C-HiLasso, a convex collaborative hierarchical sparse model, and proceeds as follows. First, we build a structured dictionary for mixed signals by concatenating a set of sub-dictionaries, each one of them learned to sparsely model one of a set of possible classes. Then, the coding of the mixed signal is performed by efficiently solving a convex optimization problem that combines standard sparsity with group and collaborative sparsity. The present sources are ident…
Sparse coding with dictionary learning (DL) has shown excellent classification performance. Despite the considerable number of existing works, how to obtain features on top of which dictionaries can be better learned remains an open and interesting question. Many current prevailing DL methods directly adopt well-performing crafted features. While such strategy may empirically work well, it ignores certain intrinsic relationship between dictionaries and features. We propose a framework where features and dictionaries are jointly learned and optimized. The framework, named joint non-negative pro…
Hong Kong University of Science and Technology University（香港科技大学）；Paradigm Inc（第四范式有限公司）；University of Macau（澳门大学）
Convolutional sparse coding (CSC) has been popularly used for the learning of shift-invariant dictionaries in image and signal processing. However, existing methods have limited scalability. In this paper, instead of convolving with a dictionary shared by all samples, we propose the use of a sample-dependent dictionary in which filters are obtained as linear combinations of a small set of base filters learned from the data. This added flexibility allows a large number of sample-dependent patterns to be captured, while the resultant model can still be efficiently learned by online learning. Ext…
In this article, we present a denoising algorithm to improve the interpretation and quality of scanning tunneling microscopy (STM) images. Given the high level of self-similarity of STM images, we propose a denoising algorithm by reformulating the true estimation problem as a sparse regression, often termed sparse coding. We introduce modifications to the algorithm to cope with the existence of artifacts, mainly dropouts, which appear in a structured way as consecutive line segments on the scanning direction. The resulting algorithm treats the artifacts as missing data, and the estimated value…
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…
University of Maryland（马里兰大学）；General Electric Global Research（通用电气全球研究中心）
In real-world visual recognition problems, the assumption that the training data (source domain) and test data (target domain) are sampled from the same distribution is often violated. This is known as the domain adaptation problem. In this work, we propose a novel domain-adaptive dictionary learning framework for cross-domain visual recognition. Our method generates a set of intermediate domains. These intermediate domains form a smooth path and bridge the gap between the source and target domains. Specifically, we not only learn a common dictionary to encode the domain-shared features, but a…
With the development of range sensors such as LIDAR and time-of-flight cameras, 3D point cloud scans have become ubiquitous in computer vision applications, the most prominent ones being gesture recognition and autonomous driving. Parsimony-based algorithms have shown great success on images and videos where data points are sampled on a regular Cartesian grid. We propose an adaptation of these techniques to irregularly sampled signals by using continuous dictionaries. We present an example application in the form of point cloud denoising.
Xiamen University（厦门大学）；University of Waterloo（滑铁卢大学）；The Hong Kong Polytechnic University（香港理工大学）
In this paper, we propose an effective scene text recognition method using sparse coding based features, called Histograms of Sparse Codes (HSC) features. For character detection, we use the HSC features instead of using the Histograms of Oriented Gradients (HOG) features. The HSC features are extracted by computing sparse codes with dictionaries that are learned from data using K-SVD, and aggregating per-pixel sparse codes to form local histograms. For word recognition, we integrate multiple cues including character detection scores and geometric contexts in an objective function. The final r…
Duke University（杜克大学）；University of Maryland（马里兰大学）
We present a dictionary learning approach to compensate for the transformation of faces due to changes in view point, illumination, resolution, etc. The key idea of our approach is to force domain-invariant sparse coding, i.e., design a consistent sparse representation of the same face in different domains. In this way, classifiers trained on the sparse codes in the source domain consisting of frontal faces for example can be applied to the target domain (consisting of faces in different poses, illumination conditions, etc) without much loss in recognition accuracy. The approach is to first le…
Indian Institute of Information Technology Vadodara（瓦多达拉印度信息技术学院）
Medical image acquisition is often intervented by unwanted noise that corrupts the information content. This paper introduces an unsupervised medical image denoising technique that learns noise characteristics from the available images and constructs denoised images. It comprises of two blocks of data processing, viz., patch-based dictionaries that indirectly learn the noise and residual learning (RL) that directly learns the noise. The model is generalized to account for both 2D and 3D images considering different medical imaging instruments. The images are considered one-by-one from the stac…
University of Basel（巴塞尔大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
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 rel…
Nanjing University of Science and Technology（南京理工大学）
Sparse coding can learn good robust representation to noise and model more higher-order representation for image classification. However, the inference algorithm is computationally expensive even though the supervised signals are used to learn compact and discriminative dictionaries in sparse coding techniques. Luckily, a simplified neural network module (SNNM) has been proposed to directly learn the discriminative dictionaries for avoiding the expensive inference. But the SNNM module ignores the sparse representations. Therefore, we propose a sparse SNNM module by adding the mixed-norm regula…
Sparse coding is a proven principle for learning compact representations of images. However, sparse coding by itself often leads to very redundant dictionaries. With images, this often takes the form of similar edge detectors which are replicated many times at various positions, scales and orientations. An immediate consequence of this observation is that the estimation of the dictionary components is not statistically efficient. We propose a factored model in which factors of variation (e.g. position, scale and orientation) are untangled from the underlying Gabor-like filters. There is so muc…
University College London（伦敦大学学院）；Technion -- Israel Institute of Technology（以色列理工学院）；Heriot-Watt University（赫瑞-瓦特大学）
Medical imaging tasks often involve multiple contrasts, such as T1- and T2-weighted magnetic resonance imaging (MRI) data. These contrasts capture information associated with the same underlying anatomy and thus exhibit similarities. In this paper, we propose a Coupled Dictionary Learning based multi-contrast MRI reconstruction (CDLMRI) approach to leverage an available guidance contrast to restore the target contrast. Our approach consists of three stages: coupled dictionary learning, coupled sparse denoising, and $k$-space consistency enforcing. The first stage learns a group of dictionaries…
Despite the fact that different objects possess distinct class-specific features, they also usually share common patterns. Inspired by this observation, we propose a novel method to explicitly and simultaneously learn a set of common patterns as well as class-specific features for classification. Our dictionary learning framework is hence characterized by both a shared dictionary and particular (class-specific) dictionaries. For the shared dictionary, we enforce a low-rank constraint, i.e. claim that its spanning subspace should have low dimension and the coefficients corresponding to this dic…
Hierarchical Sparse Coding (HSC) is a powerful model to efficiently represent multi-dimensional, structured data such as images. The simplest solution to solve this computationally hard problem is to decompose it into independent layer-wise subproblems. However, neuroscientific evidence would suggest inter-connecting these subproblems as in the Predictive Coding (PC) theory, which adds top-down connections between consecutive layers. In this study, a new model called 2-Layers Sparse Predictive Coding (2L-SPC) is introduced to assess the impact of this inter-layer feedback connection. In partic…
Wasserstein dictionary learning is an unsupervised approach to learning a collection of probability distributions that generate observed distributions as Wasserstein barycentric combinations. Existing methods for Wasserstein dictionary learning optimize an objective that seeks a dictionary with sufficient representation capacity via barycentric interpolation to approximate the observed training data, but without imposing additional structural properties on the coefficients associated to the dictionary. This leads to dictionaries that densely represent the observed data, which makes interpretat…
Learning dictionaries suitable for sparse coding instead of using engineered bases has proven effective in a variety of image processing tasks. This paper studies the optimization of dictionaries on image data where the representation is enforced to be explicitly sparse with respect to a smooth, normalized sparseness measure. This involves the computation of Euclidean projections onto level sets of the sparseness measure. While previous algorithms for this optimization problem had at least quasi-linear time complexity, here the first algorithm with linear time complexity and constant space com…
