相关论文: An Information Theoretic Study for Noisy Compresse…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
We are motivated by problems that arise in a number of applications such as Online Marketing and Explosives detection, where the observations are usually modeled using Poisson statistics. We model each observation as a Poisson random…
Recent interest has developed around the problem of dynamic compressed sensing, or the recovery of time-varying, sparse signals from limited observations. In this paper, we study how the dynamics of recurrent networks, formulated as general…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
Compressed sensing (CS) demonstrates that sparse signals can be estimated from under-determined linear systems. Distributed CS (DCS) further reduces the number of measurements by considering joint sparsity within signal ensembles. DCS with…
This paper proposes a verification-based decoding approach for reconstruction of a sparse signal with incremental sparse measurements. In its first step, the verification-based decoding algorithm is employed to reconstruct the signal with a…
In this paper we theoretically study exact recovery of sparse vectors from compressed measurements by minimizing a general nonconvex function that can be decomposed into the sum of single variable functions belonging to a class of smooth…
This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…
We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
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…
Recent advances in unsupervised learning have highlighted the possibility of learning to reconstruct signals from noisy and incomplete linear measurements alone. These methods play a key role in medical and scientific imaging and sensing,…
Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…
In this paper, we study the sparse nonnegative tensor factorization and completion problem from partial and noisy observations for third-order tensors. Because of sparsity and nonnegativity, the underlying tensor is decomposed into the…
The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…
Consider the problem of recovering an unknown signal from undersampled measurements, given the knowledge that the signal has a sparse representation in a specified dictionary $D$. This problem is now understood to be well-posed and…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
We present reconstruction algorithms for smooth signals with block sparsity from their compressed measurements. We tackle the issue of varying group size via group-sparse least absolute shrinkage selection operator (LASSO) as well as via…