Related papers: On Convergence of Approximate Message Passing
Message passing (MP) is a computational technique used to find approximate solutions to a variety of problems defined on networks. MP approximations are generally accurate in locally tree-like networks but require corrections to maintain…
Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…
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…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…
We propose and analyze an approximate message passing (AMP) algorithm for the matrix tensor product model, which is a generalization of the standard spiked matrix models that allows for multiple types of pairwise observations over a…
Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…
We study the problem of estimating a rank one signal matrix from an observed matrix generated by corrupting the signal with additive rotationally invariant noise. We develop a new class of approximate message-passing algorithms for this…
Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in…
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of…
For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with…
Compressed sensing (CS) is a concept that allows to acquire compressible signals with a small number of measurements. As such it is very attractive for hardware implementations. Therefore, correct calibration of the hardware is a central…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
The problem of estimating a random vector x from noisy linear measurements y = A x + w with unknown parameters on the distributions of x and w, which must also be learned, arises in a wide range of statistical learning and linear inverse…
Approximate Message Passing (AMP) algorithms are a class of iterative procedures for computationally-efficient estimation in high-dimensional inference and estimation tasks. Due to the presence of an 'Onsager' correction term in its…
This paper studies the convergence properties the well-known message-passing algorithm for convex optimisation. Under the assumption of pairwise separability and scaled diagonal dominance, asymptotic convergence is established and a simple…
We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $K \geq 1$, a multivariate non-linearity is…
This paper is concerned with the problem of reconstructing an unknown rank-one matrix with prior structural information from noisy observations. While computing the Bayes-optimal estimator seems intractable in general due to its nonconvex…
Approximate message passing (AMP) is a scalable, iterative approach to signal recovery. For structured random measurement ensembles, including independent and identically distributed (i.i.d.) Gaussian and rotationally-invariant matrices,…
In this paper, a communication-efficient multi-processor compressed sensing framework based on the approximate message passing algorithm is proposed. We perform lossy compression on the data being communicated between processors, resulting…