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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)…

Information Theory · Computer Science 2015-01-27 Burak Çakmak , Ole Winther , Bernard H. Fleury

A concise expectation propagation (EP) based message passing algorithm (MPA) is derived for the general measurement channel. By neglecting some high-order infinitesimal terms, the EP-MPA is proven to be equivalent to the Generalized…

Information Theory · Computer Science 2019-07-11 Lei Liu , Ying Li , Chongwen Huang , Chau Yuen , Yong Liang Guan

In phase retrieval, the goal is to recover a signal $\mathbf{x}\in\mathbb{C}^N$ from the magnitudes of linear measurements $\mathbf{Ax}\in\mathbb{C}^M$. While recent theory has established that $M\approx 4N$ intensity measurements are…

Information Theory · Computer Science 2015-06-19 Philip Schniter , Sundeep Rangan

Approximate message passing (AMP) has emerged both as a popular class of iterative algorithms and as a powerful analytic tool in a wide range of statistical estimation problems and statistical physics models. A well established line of AMP…

Statistics Theory · Mathematics 2025-07-22 Zhigang Bao , Qiyang Han , Xiaocong Xu

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…

Probability · Mathematics 2010-11-10 Holger Rauhut , Karin Schnass , Pierre Vandergheynst

With a unified belief propagation (BP) and mean field (MF) framework, we propose an iterative message passing receiver, which performs joint channel state and noise precision (the reciprocal of noise variance) estimation and decoding for…

Information Theory · Computer Science 2017-11-13 Zhengdao Yuan , Chuanzong Zhang , Zhongyong Wang , Qinghua Guo , Sheng Wu , and Xingye Wang

High-dimensional time series appear in many scientific setups, demanding a nuanced approach to model and analyze the underlying dependence structure. Theoretical advancements so far often rely on stringent assumptions regarding the sparsity…

Information Theory · Computer Science 2025-03-20 Daria Tieplova , Samriddha Lahiry , Jean Barbier

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2016-01-19 Puxiao Han , Junan Zhu , Ruixin Niu , Dror Baron

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…

Information Theory · Computer Science 2015-04-30 Christophe Schülke , Francesco Caltagirone , Florent Krzakala , Lenka Zdeborová

Due to the massive number of devices in the M2M communication era, new challenges have been brought to the existing random-access (RA) mechanism, such as severe preamble collisions and resource block (RB) wastes. To address these problems,…

Information Theory · Computer Science 2019-10-09 Zhaoji Zhang , Ying Li , Lei Liu , Huimei Han

Both theoretical analysis and empirical evidence confirm that the approximate message passing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise…

Information Theory · Computer Science 2015-06-22 Chunli Guo , Mike E. Davies

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…

Information Theory · Computer Science 2016-11-07 Philip Schniter , Sundeep Rangan , Alyson Fletcher

Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that…

Machine Learning · Computer Science 2025-09-16 Shane Stevenson , Maryam Sabagh

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…

Information Theory · Computer Science 2017-06-20 Alyson K. Fletcher , Mojtaba Sahraee-Ardakan , Philip Schniter , Sundeep Rangan

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…

Information Theory · Computer Science 2015-04-28 Ljubisa Stankovic , Milos Dakovic

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…

Statistics Theory · Mathematics 2024-12-03 Songbin Liu , Junjie Ma

We introduce the sparse direct sampling method (DSM) to estimate properties of a region from signals that probe the region. We demonstrate the sparse-DSM on two separate problems: estimating both the angle-of-arrival of a radio wave…

Analysis of PDEs · Mathematics 2020-10-19 Isaac Harris , Jacob D Rezac

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…

Statistics Theory · Mathematics 2023-02-08 Gen Li , Wei Fan , Yuting Wei

This paper studies the problem of power allocation in compressed sensing when different components in the unknown sparse signal have different probability to be non-zero. Given the prior information of the non-uniform sparsity and the total…

Information Theory · Computer Science 2014-05-12 Xiaochen Zhao , Wei Dai

Sparse regression codes with approximate message passing (AMP) decoding have gained much attention in recent times. The concepts underlying this coding scheme extend to unsourced random access with coded compressed sensing (CCS), as first…

Information Theory · Computer Science 2020-10-12 Vamsi K. Amalladinne , Asit Kumar Pradhan , Cynthia Rush , Jean-Francois Chamberland , Krishna R. Narayanan