Related papers: Learning computationally efficient dictionaries an…
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…
Dictionary learning aims to find a dictionary that can sparsely represent the training data. Methods in the literature typically formulate the dictionary learning problem as an optimisation with respect to two variables, i.e., dictionary…
Dictionary learning is a popular approach for inferring a hidden basis or dictionary in which data has a sparse representation. Data generated from the dictionary A (an n by m matrix, with m > n in the over-complete setting) is given by Y =…
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…
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…
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing…
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…
Dictionary learning is a widely used technique in signal processing and machine learning that aims to represent data as a linear combination of a few elements from an overcomplete dictionary. In this work, we propose a generalization of the…
We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class…
In this paper we consider the dictionary learning problem for sparse representation. We first show that this problem is NP-hard by polynomial time reduction of the densest cut problem. Then, using successive convex approximation strategies,…
The dictionary learning problem concerns the task of representing data as sparse linear sums drawn from a smaller collection of basic building blocks. In application domains where such techniques are deployed, we frequently encounter…
Dictionary learning aims at seeking a dictionary under which the training data can be sparsely represented. Methods in the literature typically formulate the dictionary learning problem as an optimization w.r.t. two variables, i.e.,…
In this paper, we propose and investigate algorithms for the structured orthogonal dictionary learning problem. First, we investigate the case when the dictionary is a Householder matrix. We give sample complexity results and show…
Dictionary learning algorithms have been successfully used for both reconstructive and discriminative tasks, where an input signal is represented with a sparse linear combination of dictionary atoms. While these methods are mostly developed…
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…
In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent…
This work proposes kernel transform learning. The idea of dictionary learning is well known; it is a synthesis formulation where a basis is learnt along with the coefficients so as to generate or synthesize the data. Transform learning is…
Sparse representations using learned dictionaries are being increasingly used with success in several data processing and machine learning applications. The availability of abundant training data necessitates the development of efficient,…
In dictionary learning, also known as sparse coding, the algorithm is given samples of the form $y = Ax$ where $x\in \mathbb{R}^m$ is an unknown random sparse vector and $A$ is an unknown dictionary matrix in $\mathbb{R}^{n\times m}$…
Dictionary learning is a versatile method to produce an overcomplete set of vectors, called atoms, to represent a given input with only a few atoms. In the literature, it has been used primarily for tasks that explore its powerful…