相关论文: Bayes-Optimal Convolutional AMP

We consider large-scale linear inverse problems in Bayesian settings. We follow a recent line of work that applies the approximate message passing (AMP) framework to multi-processor (MP) computational systems, where each processor node…

We consider sparse signal reconstruction via minimization of the smoothly clipped absolute deviation (SCAD) penalty, and develop one-step replica-symmetry-breaking (1RSB) extensions of approximate message passing (AMP), termed 1RSB-AMP.…

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…

Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector $\mathbf{x}$ observed through a linear transform $\mathbf{A}$. In the case of large…

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing…

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.…

In this paper, we consider a general form of noisy compressive sensing (CS) where the sensing matrix is not precisely known. Such cases exist when there are imperfections or unknown calibration parameters during the measurement process.…

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…

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 so-called Turbo approximate message passing…

Compressed sensing, allows to acquire compressible signals with a small number of measurements. In applications, a hardware implementation often requires a calibration as the sensing process is not perfectly known. Blind calibration, that…

We study mean-field variational Bayesian inference using the TAP approach, for Z2-synchronization as a prototypical example of a high-dimensional Bayesian model. We show that for any signal strength $\lambda > 1$ (the weak-recovery…

The learned denoising-based approximate message passing (LDAMP) algorithm has attracted great attention for image compressed sensing (CS) tasks. However, it has two issues: first, its global measurement model severely restricts its…

Computing maximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise…

Sparse Bayesian learning (SBL) can be implemented with low complexity based on the approximate message passing (AMP) algorithm. However, it does not work well for a generic measurement matrix, which may cause AMP to diverge. Damped AMP has…

Previous partial permutation synchronization (PPS) algorithms, which are commonly used for multi-object matching, often involve computation-intensive and memory-demanding matrix operations. These operations become intractable for large…

In this paper, we bring together two trends that have recently emerged in sparse signal recovery: the problem of sparse signals that stem from finite alphabets and the techniques that introduce concave penalties. Specifically, we show that…

The standard linear regression (SLR) problem is to recover a vector $\mathbf{x}^0$ from noisy linear observations $\mathbf{y}=\mathbf{Ax}^0+\mathbf{w}$. The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki,…

Spike and Slab priors have been of much recent interest in signal processing as a means of inducing sparsity in Bayesian inference. Applications domains that benefit from the use of these priors include sparse recovery, regression and…

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 \cite{DMM}. The new algorithms are broadly referred to as AMP,…

The Approximate Message Passing (AMP) algorithm efficiently reconstructs signals which have been sampled with large i.i.d. sub-Gaussian sensing matrices. Central to AMP is its "state evolution", which guarantees that the difference between…