Related papers: An Analysis of State Evolution for Approximate Mes…
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.…
We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The CASSI imaging process can be…
Gradient-descent-based algorithms and their stochastic versions have widespread applications in machine learning and statistical inference. In this work we perform an analytic study of the performances of one of them, the Langevin…
The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based…
Deep learning has gained great popularity due to its widespread success on many inference problems. We consider the application of deep learning to the sparse linear inverse problem, where one seeks to recover a sparse signal from a few…
Purpose: Undersampling is used to reduce the scan time for high-resolution 3D magnetic resonance imaging. In order to achieve better image quality and avoid manual parameter tuning, we propose a probabilistic Bayesian approach to recover…
We consider the problem of recovering a block (or group) sparse signal from an underdetermined set of random linear measurements, which appear in compressed sensing applications such as radar and imaging. Recent results of Donoho,…
We propose a scheme to estimate the parameters $b_i$ and $c_j$ of the bilinear form $z_m=\sum_{i,j} b_i z_m^{(i,j)} c_j$ from noisy measurements $\{y_m\}_{m=1}^M$, where $y_m$ and $z_m$ are related through an arbitrary likelihood function…
In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits…
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…
This paper addresses the reconstruction of sparse signals from spatially coupled, linear, and noisy measurements. A unified framework of rigorous state evolution is established for developing long-memory message-passing (LM-MP) in spatially…
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…
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…
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.…
Semantic communication (SemComm) has emerged as new paradigm shifts.Most existing SemComm systems transmit continuously distributed signals in analog fashion.However, the analog paradigm is not compatible with current digital communication…
This paper considers a discrete-valued signal estimation scheme based on a low-complexity Bayesian optimal message passing algorithm (MPA) for solving massive linear inverse problems under highly correlated measurements. Gaussian belief…
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…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
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…
This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under…