This chapter surveys recent work in applying ideas from graphical models and message
passing algorithms to solve large-scale regularized regression problems. In particular, the …

We consider the estimation of a random vector observed through a linear transform followed
by a componentwise probabilistic measurement channel. Although such linear mixing …

“Approximate message passing”(AMP) algorithms have proved to be effective in
reconstructing sparse signals from a small number of incoherent linear measurements …

A popular approach for estimating an unknown signal x 0∈ ℝ n from noisy, linear
measurements y= Ax 0+ z∈ ℝ m is via solving a so called regularized M-estimator: x̂:= arg …

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. The …

We consider the problem of learning a coefficient vector x ο∈ RN from noisy linear
observation y= Ax o+∈ R n. In many contexts (ranging from model selection to image …

Compressive sensing (CS) is an emerging field based on the revelation that a small
collection of linear projections of a sparse signal contains enough information for stable, sub …

Compressed sensing is a signal processing method that acquires data directly in a
compressed form. This allows one to make fewer measurements than were considered …

Compressed sensing has triggered a major evolution in signal acquisition. It consists of
sampling a sparse signal at low rate and later using computational power for the exact …

Unsourced random-access (U-RA) is a type of grant-free random access with a virtually
unlimited number of users, of which only a certain number K a are active on the same time …