Related papers: Compressed Sensing by Shortest-Solution Guided Dec…
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 is a signal processing method that acquires data directly in a compressed form. This allows one to make less measurements than what was considered necessary to record a signal, enabling faster or more precise measurement…
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…
Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…
Coded compressed sensing is an algorithmic framework tailored to sparse recovery in very large dimensional spaces. This framework is originally envisioned for the unsourced multiple access channel, a wireless paradigm attuned to…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this paper, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via multiplicative…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…
We study the reconstruction of discrete-valued sparse signals from underdetermined systems of linear equations. On the one hand, classical compressed sensing (CS) is designed to deal with real-valued sparse signals. On the other hand,…
Compressed sensing (CS) is a signal processing framework for efficiently reconstructing a signal from a small number of measurements, obtained by linear projections of the signal. In this paper we present an end-to-end deep learning…
Modern compression algorithms exploit complex structures that are present in signals to describe them very efficiently. On the other hand, the field of compressed sensing is built upon the observation that "structured" signals can be…
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…
In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
Compressed sensing is a technique to sample compressible signals below the Nyquist rate, whilst still allowing near optimal reconstruction of the signal. In this paper we present a theoretical analysis of the iterative hard thresholding…
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…
Compressed sensing (CS) is an innovative technique allowing to represent signals through a small number of their linear projections. Hence, CS can be thought of as a natural candidate for acquisition of multidimensional signals, as the…