Related papers: Towards Learning Sparsely Used Dictionaries with A…

Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…

Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned…

Sparse representation, which uses dictionary atoms to reconstruct input vectors, has been studied intensively in recent years. A proper dictionary is a key for the success of sparse representation. In this paper, an active dictionary…

Learning optimal dictionaries for sparse coding has exposed characteristic sparse features of many natural signals. However, universal guarantees of the stability of such features in the presence of noise are lacking. Here, we provide very…

Recent work has demonstrated that using a carefully designed dictionary instead of a predefined one, can improve the sparsity in jointly representing a class of signals. This has motivated the derivation of learning methods for designing a…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints.…

We consider the dictionary learning problem, where the aim is to model the given data as a linear combination of a few columns of a matrix known as a dictionary, where the sparse weights forming the linear combination are known as…

Dictionary learning consists of finding a sparse representation from noisy data and is a common way to encode data-driven prior knowledge on signals. Alternating minimization (AM) is standard for the underlying optimization, where gradient…

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The…

Sparse dictionary learning (SDL) is a fundamental technique that is useful for many image processing tasks. As an example we consider here image recovery, where SDL can be cast as a nonsmooth optimization problem. For this kind of problems,…

We study the Dictionary Learning (aka Sparse Coding) problem of obtaining a sparse representation of data points, by learning \emph{dictionary vectors} upon which the data points can be written as sparse linear combinations. We view this…

In conventional sparse representations based dictionary learning algorithms, initial dictionaries are generally assumed to be proper representatives of the system at hand. However, this may not be the case, especially in some systems…

We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…

Distributional models are derived from co-occurrences in a corpus, where only a small proportion of all possible plausible co-occurrences will be observed. This results in a very sparse vector space, requiring a mechanism for inferring…

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…

Disentangled representation learning aims to uncover latent variables underlying the observed data, and generally speaking, rather strong assumptions are needed to ensure identifiability. Some approaches rely on sufficient changes on the…

The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix, has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference…

Sparse Representation (SR) of signals or data has a well founded theory with rigorous mathematical error bounds and proofs. SR of a signal is given by superposition of very few columns of a matrix called Dictionary, implicitly reducing…

Many techniques in computer vision, machine learning, and statistics rely on the fact that a signal of interest admits a sparse representation over some dictionary. Dictionaries are either available analytically, or can be learned from a…