Related papers: A Concise Tutorial on Approximate Message Passing
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…
Optimal data detection in multiple-input multiple-output (MIMO) communication systems with a large number of antennas at both ends of the wireless link entails prohibitive computational complexity. In order to reduce the computational…
The denoising-based approximate message passing (D-AMP) methodology, recently proposed by Metzler, Maleki, and Baraniuk, allows one to plug in sophisticated denoisers like BM3D into the AMP algorithm to achieve state-of-the-art compressive…
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…
Approximate Message Passing (AMP), originally designed to solve high-dimensional linear inverse problems, has found broad applications in signal processing and statistical inference. Among its key variants, Vector Approximate Message…
To improve the convergence property of approximate message-passing (AMP), convolutional AMP (CAMP) has been proposed. CAMP replaces the Onsager correction in AMP with a convolution of messages in all preceding iterations while it uses the…
This paper presents a unified framework for constructing Approximate Message Passing (AMP) algorithms for rotationally-invariant models. By employing a general iterative algorithm template and reducing it to long-memory Orthogonal AMP…
In a recent article (Proc. Natl. Acad. Sci., 110(36), 14557-14562), El Karoui et al. study the distribution of robust regression estimators in the regime in which the number of parameters p is of the same order as the number of samples n.…
Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP)…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…
We consider large-scale linear inverse problems in Bayesian settings. Our general approach follows a recent line of work that applies the approximate message passing (AMP) framework in multi-processor (MP) computational systems by storing…
We consider a class of approximated message passing (AMP) algorithms and characterize their high-dimensional behavior in terms of a suitable state evolution recursion. Our proof applies to Gaussian matrices with independent but not…
Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and…
Approximate message passing (AMP) algorithms have shown great promise in sparse signal reconstruction due to their low computational requirements and fast convergence to an exact solution. Moreover, they provide a probabilistic framework…
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…
Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
Generalized approximate message passing (GAMP) is a computationally efficient algorithm for estimating an unknown signal $w_0\in\mathbb{R}^N$ from a random linear measurement $y= Xw_0 + \epsilon\in\mathbb{R}^M$, where…
Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems. However, prior AMP theory -- which focused mostly on high-dimensional asymptotics -- fell short of predicting…