Related papers: Exact Sparse Orthogonal Dictionary Learning

Sparse signal representations based on linear combinations of learned atoms have been used to obtain state-of-the-art results in several practical signal processing applications. Approximation methods are needed to process high-dimensional…

Convolutional Sparse Coding (CSC) is an increasingly popular model in the signal and image processing communities, tackling some of the limitations of traditional patch-based sparse representations. Although several works have addressed the…

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is,…

We propose a convolutional recurrent sparse auto-encoder model. The model consists of a sparse encoder, which is a convolutional extension of the learned ISTA (LISTA) method, and a linear convolutional decoder. Our strategy offers a simple…

Sparse coding or sparse dictionary learning has been widely used to recover underlying structure in many kinds of natural data. Here, we provide conditions guaranteeing when this recovery is universal; that is, when sparse codes and…

Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…

We study in this paper the improvement of one-class support vector machines (OC-SVM) through sparse representation techniques for unsupervised anomaly detection. As Dictionary Learning (DL) became recently a common analysis technique that…

In sparse recovery, the unique sparsest solution to an under-determined system of linear equations is of main interest. This scheme is commonly proposed to be applied to signal acquisition. In most cases, the signals are not sparse…

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…

Modeling data with linear combinations of a few elements from a learned dictionary has been the focus of much recent research in machine learning, neuroscience and signal processing. For signals such as natural images that admit such sparse…

Dictionary learning, the problem of recovering a sparsely used matrix $\mathbf{D} \in \mathbb{R}^{M \times K}$ and $N$ $s$-sparse vectors $\mathbf{x}_i \in \mathbb{R}^{K}$ from samples of the form $\mathbf{y}_i = \mathbf{D}\mathbf{x}_i$, 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,…

In this paper, we propose a new sampling strategy for hyperspectral signals that is based on dictionary learning and singular value decomposition (SVD). Specifically, we first learn a sparsifying dictionary from training spectral data using…

Many natural signals exhibit a sparse representation, whenever a suitable describing model is given. Here, a linear generative model is considered, where many sparsity-based signal processing techniques rely on such a simplified model. As…

Sparse representation models a signal as a linear combination of a small number of dictionary atoms. As a generative model, it requires the dictionary to be highly redundant in order to ensure both a stable high sparsity level and a low…

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…

We present theoretical guarantees for an alternating minimization algorithm for the dictionary learning/sparse coding problem. The dictionary learning problem is to factorize vector samples $y^{1},y^{2},\ldots, y^{n}$ into an appropriate…

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…

Mixed dictionaries generated by cosine and B-spline functions are considered. It is shown that, by highly nonlinear approaches such as Orthogonal Matching Pursuit, the discrete version of the proposed dictionaries yields a significant gain…

Data encoded as symmetric positive definite (SPD) matrices frequently arise in many areas of computer vision and machine learning. While these matrices form an open subset of the Euclidean space of symmetric matrices, viewing them through…