Related papers: Data Separation by Sparse Representations
Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using fewer elementary components than the number of intensity points in the 3D array.…
Deep neural networks have emerged as powerful tools for learning operators defined over infinite-dimensional function spaces. However, existing theories frequently encounter difficulties related to dimensionality and limited…
The estimation of covariance operators of spatio-temporal data is in many applications only computationally feasible under simplifying assumptions, such as separability of the covariance into strictly temporal and spatial factors.Powerful…
Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is done by solving an l_1-regularized linear regression problem, usually called Lasso. In this work we first combine the…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
Data dispersed across multiple files are commonly integrated through probabilistic linkage methods, where even minimal error rates in record matching can significantly contaminate subsequent statistical analyses. In regression problems, we…
This paper is based on a chapter of a new book on Machine Learning, by the first and third author, which is currently under preparation. We provide an overview of the major theoretical advances as well as the main trends in algorithmic…
We propose a scheme for multi-layer representation of images. The problem is first treated from an information-theoretic viewpoint where we analyze the behavior of different sources of information under a multi-layer data compression…
This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold…
A simple sparse coding mechanism appears in the sensory systems of several organisms: to a coarse approximation, an input $x \in \R^d$ is mapped to much higher dimension $m \gg d$ by a random linear transformation, and is then sparsified by…
The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…
Hyperspectral unmixing, the process of estimating a common set of spectral bases and their corresponding composite percentages at each pixel, is an important task for hyperspectral analysis, visualization and understanding. From an…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
Deep representation learning has become one of the most widely adopted approaches for visual search, recommendation, and identification. Retrieval of such representations from a large database is however computationally challenging.…
High-dimensional data often lie in low-dimensional subspaces corresponding to different classes they belong to. Finding sparse representations of data points in a dictionary built using the collection of data helps to uncover…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…
Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…
Singing voice separation attempts to separate the vocal and instrumental parts of a music recording, which is a fundamental problem in music information retrieval. Recent work on singing voice separation has shown that the low-rank…