Many questions of fundamental interest in today's science can be formulated as inference
problems: some partial, or noisy, observations are performed over a set of variables and the …

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 …

The goal of this paper is to present a non-iterative and more importantly an extremely fast
algorithm to reconstruct images from compressively sensed (CS) random measurements. To …

A denoising algorithm seeks to remove noise, errors, or perturbations from a signal.
Extensive research has been devoted to this arena over the last several decades, and as a …

Regularization by denoising (RED), as recently proposed by Romano, Elad, and Milanfar, is
powerful image-recovery framework that aims to minimize an explicit regularization objective …

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

This paper presents a framework for compressed sensing that bridges a gap between
existing theory and the current use of compressed sensing in many real-world applications …

In phase retrieval, the goal is to recover a signal x∈ CN from the magnitudes of linear
measurements Ax∈ C M. While recent theory has established that M≈ 4N intensity …

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 …

Given a high-dimensional data matrix, approximate message passing (AMP) algorithms
construct sequences of vectors,, indexed by by iteratively applying or and suitable nonlinear …