Related papers: Approximate Message Passing with Spectral Initiali…
This article addresses the problem of multiple preamble detection in random access systems based on orthogonal time frequency space (OTFS) signaling. This challenge is formulated as a structured sparse recovery problem in the complex…
Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable…
Practical systems often suffer from hardware impairments that already appear during signal generation. Despite the limiting effect of such input-noise impairments on signal processing systems, they are routinely ignored in the literature.…
Maximum a posteriori (MAP) inference in discrete-valued Markov random fields is a fundamental problem in machine learning that involves identifying the most likely configuration of random variables given a distribution. Due to the…
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…
Given a high-dimensional data matrix ${\boldsymbol A}\in{\mathbb R}^{m\times n}$, Approximate Message Passing (AMP) algorithms construct sequences of vectors ${\boldsymbol u}^t\in{\mathbb R}^n$, ${\boldsymbol v}^t\in{\mathbb R}^m$, indexed…
We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm.…
We consider the linear regression problem, where the goal is to recover the vector $\boldsymbol{x}\in\mathbb{R}^n$ from measurements $\boldsymbol{y}=\boldsymbol{A}\boldsymbol{x}+\boldsymbol{w}\in\mathbb{R}^m$ under known matrix…
We consider communication over the Gaussian multiple-access channel in the regime where the number of users grows linearly with the codelength. In this regime, schemes based on sparse superposition coding can achieve a near-optimal tradeoff…
In order to reduce hardware complexity and power consumption, massive multiple-input multiple-output (MIMO) systems employ low-resolution analog-to-digital converters (ADCs) to acquire quantized measurements $\boldsymbol y$. This poses new…
We consider the problem of recovering a vector $\beta_o \in \mathbb{R}^p$ from $n$ random and noisy linear observations $y= X\beta_o + w$, where $X$ is the measurement matrix and $w$ is noise. The LASSO estimate is given by the solution to…
The generalized linear system (GLS) has been widely used in wireless communications to evaluate the effect of nonlinear preprocessing on receiver performance. Generalized approximation message passing (AMP) is a state-of-the-art algorithm…
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study…
This is Part II of a two-part work on the estimation for a multi-layer generalized linear model (ML-GLM) in large system limits. In Part I, we had analyzed the asymptotic performance of an exact MMSE estimator, and obtained a set of coupled…
Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean.…
We consider the problem of reconstructing rank-one matrices from random linear measurements, a task that appears in a variety of problems in signal processing, statistics, and machine learning. In this paper, we focus on the Alternating…
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…
This paper considers probabilistic estimation of a low-rank matrix from non-linear element-wise measurements of its elements. We derive the corresponding approximate message passing (AMP) algorithm and its state evolution. Relying on…
The linear model uses the space defined by the input to project the target or desired signal and find the optimal set of model parameters. When the problem is nonlinear, the adaption requires nonlinear models for good performance, but it…
In phase retrieval, the goal is to recover a complex signal from the magnitude of its linear measurements. While many well-known algorithms guarantee deterministic recovery of the unknown signal using i.i.d. random measurement matrices,…