相关论文: Optimal dictionary for least squares representatio…

Dictionaries are collections of vectors used for representations of elements in Euclidean spaces. While recent research on optimal dictionaries is focussed on providing sparse (i.e., $\ell_0$-optimal,) representations, here we consider the…

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…

This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms,…

We consider the minimization of the number of non-zero coefficients (the $\ell_0$ "norm") of the representation of a data set in terms of a dictionary under a fidelity constraint. (Both the dictionary and the norm defining the constraint…

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…

Dictionary learning is a classic representation learning method that has been widely applied in signal processing and data analytics. In this paper, we investigate a family of $\ell_p$-norm ($p>2,p \in \mathbb{N}$) maximization approaches…

We provide the construction of a set of square matrices whose translates and rotates provide a Parseval frame that is optimal for approximating a given dataset of images. Our approach is based on abstract harmonic analysis techniques.…

The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical…

Finding an optimal word representation algorithm is particularly important in terms of domain specific data, as the same word can have different meanings and hence, different representations depending on the domain and context. While…

This paper studies the question of how well a signal can be reprsented by a sparse linear combination of reference signals from an overcomplete dictionary. When the dictionary size is exponential in the dimension of signal, then the exact…

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…

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…

Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…

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…

In signal analysis and synthesis, linear approximation theory considers a linear decomposition of any given signal in a set of atoms, collected into a so-called dictionary. Relevant sparse representations are obtained by relaxing the…

We describe a new construction of an incoherent dictionary, referred to as the oscillator dictionary, which is based on considerations in the representation theory of finite groups. The oscillator dictionary consists of order of p^5 unit…

Sparse representation over redundant dictionaries constitutes a good model for many classes of signals (e.g., patches of natural images, segments of speech signals, etc.). However, despite its popularity, very little is known about 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…

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…

A choice dictionary is a data structure that can be initialized with a parameter $n\in\{1,2,\ldots\}$ and subsequently maintains an initially empty subset $S$ of $\{1,\ldots,n\}$ under insertion, deletion, membership queries and an…