Related papers: When can dictionary learning uniquely recover spar…
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…
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.…
A dictionary is a database of standard vectors, so that other vectors / signals are expressed as linear combinations of dictionary vectors, and the task of learning a dictionary for a given data is to find a good dictionary so that the…
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…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
It is now well established that sparse signal models are well suited to restoration tasks and can effectively be learned from audio, image, and video data. Recent research has been aimed at learning discriminative sparse models instead of…
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…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
Sparse recovery is widely applied in many fields, since many signals or vectors can be sparsely represented under some frames or dictionaries. Most of fast algorithms at present are based on solving $l^0$ or $l^1$ minimization problems and…
Audio events are quite often overlapping in nature, and more prone to noise than visual signals. There has been increasing evidence for the superior performance of representations learned using sparse dictionaries for applications like…
Sparse coding approximates the data sample as a sparse linear combination of some basic codewords and uses the sparse codes as new presentations. In this paper, we investigate learning discriminative sparse codes by sparse coding in a…
The efficient sparse coding and reconstruction of signal vectors via linear observations has received a tremendous amount of attention over the last decade. In this context, the automated learning of a suitable basis or overcomplete…
Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…
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…
We consider the problem of sparse coding, where each sample consists of a sparse linear combination of a set of dictionary atoms, and the task is to learn both the dictionary elements and the mixing coefficients. Alternating minimization is…
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,…
This article presents novel results concerning the recovery of signals from undersampled data in the common situation where such signals are not sparse in an orthonormal basis or incoherent dictionary, but in a truly redundant dictionary.…
We consider the problem of dictionary learning under the assumption that the observed signals can be represented as sparse linear combinations of the columns of a single large dictionary matrix. In particular, we analyze the minimax risk of…
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…
Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…