Related papers: Phase diagram of matrix compressed sensing
We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…
We consider the problems of compressed sensing and optimal denoising for signals $\mathbf{x_0}\in\mathbb{R}^N$ that are monotone, i.e., $\mathbf{x_0}(i+1) \geq \mathbf{x_0}(i)$, and sparsely varying, i.e., $\mathbf{x_0}(i+1) >…
Many practical sensing applications involve multiple sensors simultaneously acquiring measurements of a single object. Conversely, most existing sparse recovery guarantees in compressed sensing concern only single-sensor acquisition…
Quantized maximum a posteriori (Q-MAP) is a recently-proposed Bayesian compressed sensing algorithm that, given the source distribution, recovers $X^n$ from its linear measurements $Y^m=AX^n$, where $A\in R^{m\times n}$ denotes the known…
Compressive sampling offers a new paradigm for acquiring signals that are compressible with respect to an orthonormal basis. The major algorithmic challenge in compressive sampling is to approximate a compressible signal from noisy samples.…
Compressed sensing posits that, within limits, one can undersample a sparse signal and yet reconstruct it accurately. Knowing the precise limits to such undersampling is important both for theory and practice. We present a formula that…
In this paper, the `Approximate Message Passing' (AMP) algorithm, initially developed for compressed sensing of signals under i.i.d. Gaussian measurement matrices, has been extended to a multi-terminal setting (MAMP algorithm). It has been…
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. In this correspondence, a $K \times N$ measurement matrix for compressed sensing is deterministically constructed via additive…
We introduce the bilinear generalized vector approximate message passing (BiG-VAMP) algorithm which jointly recovers two matrices U and V from their noisy product through a probabilistic observation model. BiG-VAMP provides computationally…
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…
The problem of identifying sparse solutions for the link structure and dynamics of an unknown linear, time-invariant network is posed as finding sparse solutions x to Ax=b. If the sensing matrix A satisfies a rank condition, this problem…
We study the problem of estimating low-rank matrices from linear measurements (a.k.a., matrix sensing) through nonconvex optimization. We propose an efficient stochastic variance reduced gradient descent algorithm to solve a nonconvex…
We study the low-rank phase retrieval problem, where we try to recover a $d_1\times d_2$ low-rank matrix from a series of phaseless linear measurements. This is a fourth-order inverse problem, as we are trying to recover factors of matrix…
We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover…
Bayesian approximate message passing (BAMP) is an efficient method in compressed sensing that is nearly optimal in the minimum mean squared error (MMSE) sense. Bayesian approximate message passing (BAMP) performs joint recovery of multiple…
Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic…
This paper proposes a fast approximate message-passing (AMP) algorithm for solving compressed sensing (CS) recovery problems with 1D-finite-difference sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD, is…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
Limited measurement availability at the distribution grid presents challenges for state estimation and situational awareness. This paper combines the advantages of two sparsity-based state estimation approaches (matrix completion and…