Related papers: Sparse Representation in Fourier and Local Bases U…
Given a redundant dictionary $\Phi$, represented by an $M \times N$ matrix ($\Phi \in \mathbb{R}^{M \times N}$) and a target signal $y \in \mathbb{R}^M$, the \emph{sparse approximation problem} asks to find an approximate representation of…
In this work we study convergence properties of sparse polynomial approximations for a class of affine parametric saddle point problems. Such problems can be found in many computational science and engineering fields, including the Stokes…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
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.…
In the synthesis model signals are represented as a sparse combinations of atoms from a dictionary. Dictionary learning describes the acquisition process of the underlying dictionary for a given set of training samples. While ideally this…
In the dictionary learning (or sparse coding) problem, we are given a collection of signals (vectors in $\mathbb{R}^d$), and the goal is to find a "basis" in which the signals have a sparse (approximate) representation. The problem has…
ProSper is a python library containing probabilistic algorithms to learn dictionaries. Given a set of data points, the implemented algorithms seek to learn the elementary components that have generated the data. The library widens the scope…
This paper presents a variational based approach to fusing hyperspectral and multispectral images. The fusion process is formulated as an inverse problem whose solution is the target image assumed to live in a much lower dimensional…
Multivariate global polynomial approximations - such as polynomial chaos or stochastic collocation methods - are now in widespread use for sensitivity analysis and uncertainty quantification. The pseudospectral variety of these methods uses…
Frames are the foundation of the linear operators used in the decomposition and reconstruction of signals, such as the discrete Fourier transform, Gabor, wavelets, and curvelet transforms. The emergence of sparse representation models has…
We study the problem of estimating the best B term Fourier representation for a given frequency-sparse signal (i.e., vector) $\textbf{A}$ of length $N \gg B$. More explicitly, we investigate how to deterministically identify B of the…
Complex-valued sparse coding is a data representation which employs a dictionary of two-dimensional subspaces, while imposing a sparse, factorial prior on complex amplitudes. When trained on a dataset of natural image patches, it learns…
The goal of predictive sparse coding is to learn a representation of examples as sparse linear combinations of elements from a dictionary, such that a learned hypothesis linear in the new representation performs well on a predictive task.…
Term-based sparse representations dominate the first-stage text retrieval in industrial applications, due to its advantage in efficiency, interpretability, and exact term matching. In this paper, we study the problem of transferring the…
This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources…
In this paper we present a theoretical analysis to understand sparse filtering, a recent and effective algorithm for unsupervised learning. The aim of this research is not to show whether or how well sparse filtering works, but to…
Neural networks are among the state-of-the-art techniques for language modeling. Existing neural language models typically map discrete words to distributed, dense vector representations. After information processing of the preceding…
Sparse coding algorithms are about finding a linear basis in which signals can be represented by a small number of active (non-zero) coefficients. Such coding has many applications in science and engineering and is believed to play an…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
Sparse representation has attracted much attention from researchers in fields of signal processing, image processing, computer vision and pattern recognition. Sparse representation also has a good reputation in both theoretical research and…