Related papers: Optimal Phase Transitions in Compressed Sensing
Compressed sensing is a promising technique that attempts to faithfully recover sparse signal with as few linear and nonadaptive measurements as possible. Its performance is largely determined by the characteristic of sensing matrix.…
Compressive imaging is an emerging application of compressed sensing, devoted to acquisition, encoding and reconstruction of images using random projections as measurements. In this paper we propose a novel method to provide a scalable…
The process of dynamic state estimation (filtering) based on point process observations is in general intractable. Numerical sampling techniques are often practically useful, but lead to limited conceptual insight about optimal…
The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
Monte Carlo simulations of neutronic systems are computationally intensive and demand significant memory resources for high-fidelity modeling. Compressed sensing enables accurate reconstruction of signals from significantly fewer samples…
We study the use of very sparse random projections for compressed sensing (sparse signal recovery) when the signal entries can be either positive or negative. In our setting, the entries of a Gaussian design matrix are randomly sparsified…
In this paper, we demonstrate some applications of compressive sensing over networks. We make a connection between compressive sensing and traditional information theoretic techniques in source coding and channel coding. Our results provide…
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.…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…
We examine the problem of selecting a small set of linear measurements for reconstructing high-dimensional signals. Well-established methods for optimizing such measurements include principal component analysis (PCA), independent component…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, 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…
The practice of compressed sensing suffers importantly in terms of the efficiency/accuracy trade-off when acquiring noisy signals prior to measurement. It is rather common to find results treating the noise affecting the measurements,…
We develop a Bayesian framework for sensing which adapts the sensing time and/or basis functions to the instantaneous sensing quality measured in terms of the expected posterior mean-squared error. For sparse Gaussian sources a significant…
This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…
Compressed sensing is a theory which guarantees the exact recovery of sparse signals from a small number of linear projections. The sampling schemes suggested by current compressed sensing theories are often of little practical relevance…
Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…
We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…