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We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…
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…
In this survey paper, our goal is to discuss recent advances of compressive sensing (CS) based solutions in wireless sensor networks (WSNs) including the main ongoing/recent research efforts, challenges and research trends in this area. In…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Many applications from camera arrays to sensor networks require efficient compression and processing of correlated data, which in general is collected in a distributed fashion. While information-theoretic foundations of distributed…
Data compression capability of "Compressed sensing (sampling)" in signal discretization is numerically evaluated and found to be far from the theoretical upper bound defined by signal sparsity. It is shown that, for the cases when ordinary…
Compressed sensing in MRI enables high subsampling factors while maintaining diagnostic image quality. This technique enables shortened scan durations and/or improved image resolution. Further, compressed sensing can increase the diagnostic…
The problem of compressing a real-valued sparse source using compressive sensing techniques is studied. The rate distortion optimality of a coding scheme in which compressively sensed signals are quantized and then reconstructed is…
This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…
Ubiquitous sensing is tightly coupled with activity recognition. This survey reviews recent advances in Ubiquitous sensing and looks ahead on promising future directions. In particular, Ubiquitous sensing crosses new barriers giving us new…
Compressive sensing is a sensing protocol that facilitates reconstruction of large signals from relatively few measurements by exploiting known structures of signals of interest, typically manifested as signal sparsity. Compressive…
Compressed sensing is a scheme that allows for sparse signals to be acquired, transmitted and stored using far fewer measurements than done by conventional means employing Nyquist sampling theorem. Since many naturally occurring signals are…
Recent years have witnessed a growing interest in understating the limitations imposed by quantum noise in precision measurements and devising techniques to reduce it. The attention is currently turning to the simultaneously estimation of…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
Recent advances in signal processing have focused on the use of sparse representations in various applications. A new field of interest based on sparsity has recently emerged: compressed sensing. This theory is a new sampling framework that…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Most of compressed sensing (CS) theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications,…
The Herschel Space Observatory of ESA was launched in May 2009 and is in operation since. From its distant orbit around L2 it needs to transmit a huge quantity of information through a very limited bandwidth. This is especially true for the…
A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…