Related papers: Sampling in the Analysis Transform Domain
A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…
Sampling techniques are used in many fields, including design of experiments, image processing, and graphics. The techniques in each field are designed to meet the constraints specific to that field such as uniform coverage of the range of…
The sampling of graph signals has recently drawn much attention due to the wide applications of graph signal processing. While a lot of efficient methods and interesting results have been reported to the sampling of band-limited or smooth…
In this paper, we present an approach to the reconstruction of signals exhibiting sparsity in a transformation domain, having some heavily disturbed samples. This sparsity-driven signal recovery exploits a carefully suited random sampling…
We survey a new paradigm in signal processing known as "compressive sensing". Contrary to old practices of data acquisition and reconstruction based on the Shannon-Nyquist sampling principle, the new theory shows that it is possible to…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
In compressive sensing, a small collection of linear projections of a sparse signal contains enough information to permit signal recovery. Distributed compressive sensing (DCS) extends this framework by defining ensemble sparsity models,…
Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This…
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…
Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
Frame is the corner stone for designing decomposition and reconstruction operations in signal processing. Famous frames include wavelets, curvelets,and Gabor. A celebrated result indicates that if a synthesis frame is chosen for…
Sparsity-based approaches have been popular in many applications in image processing and imaging. Compressed sensing exploits the sparsity of images in a transform domain or dictionary to improve image recovery from undersampled…
Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…
The success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
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…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…