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Compressed Sensing (CS) is a novel technique for simultaneous signal sampling and compression based on the existence of a sparse representation of signal and a projected dictionary $PD$, where $P\in\mathbb{R}^{m\times d}$ is the projection…
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…
In the theory of compressed sensing, restricted isometry analysis has become a standard tool for studying how efficiently a measurement matrix acquires information about sparse and compressible signals. Many recovery algorithms are known to…
Blind Compressed Sensing (BCS) is an extension of Compressed Sensing (CS) where the optimal sparsifying dictionary is assumed to be unknown and subject to estimation (in addition to the CS sparse coefficients). Since the emergence of BCS,…
We provide two novel adaptive-rate compressive sensing (CS) strategies for sparse, time-varying signals using side information. Our first method utilizes extra cross-validation measurements, and the second one exploits extra low-resolution…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…
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…
Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity…
Sparse signals, encountered in many wireless and signal acquisition applications, can be acquired via compressed sensing (CS) to reduce computations and transmissions, crucial for resource-limited devices, e.g., wireless sensors. Since the…
Parsimony in signal representation is a topic of active research. Sparse signal processing and representation is the outcome of this line of research which has many applications in information processing and has shown significant…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…
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…
Compressive sensing (CS) allows for acquisition of sparse signals at sampling rates significantly lower than the Nyquist rate required for bandlimited signals. Recovery guarantees for CS are generally derived based on the assumption that…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Phase modulation is a commonly used modulation mode in digital communication, which usually brings phase sparsity to digital signals. It is naturally to connect the sparsity with the newly emerged theory of compressed sensing (CS), which…
A {\em universal 1-bit compressive sensing (CS)} scheme consists of a measurement matrix $A$ such that all signals $x$ belonging to a particular class can be approximately recovered from $\textrm{sign}(Ax)$. 1-bit CS models extreme…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
Compressive sensing (CS) is a data acquisition technique that measures sparse or compressible signals at a sampling rate lower than their Nyquist rate. Results show that sparse signals can be reconstructed using greedy algorithms, often…