Related papers: An Approximate Message Passing Framework for Side …
Solving a large-scale regularized linear inverse problem using multiple processors is important in various real-world applications due to the limitations of individual processors and constraints on data sharing policies. This paper focuses…
In this work we aim to solve the compressed sensing problem for the case of a complex unknown vector by utilizing the Bayesian-optimal structured signal approximate message passing (BOSSAMP) algorithm on the jointly sparse real and…
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. AMP only applies to independent identically distributed (IID) transform…
This work explores multi-modal inference in a high-dimensional simplified model, analytically quantifying the performance gain of multi-modal inference over that of analyzing modalities in isolation. We present the Bayes-optimal performance…
X-ray Computed Tomography (CT) reconstruction from a sparse number of views is a useful way to reduce either the radiation dose or the acquisition time, for example in fixed-gantry CT systems, however this results in an ill-posed inverse…
We study a class of Approximate Message Passing (AMP) algorithms for symmetric and rectangular spiked random matrix models with orthogonally invariant noise. The AMP iterates have fixed dimension $K \geq 1$, a multivariate non-linearity is…
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…
We present a novel compressed sensing recovery algorithm - termed Bayesian Optimal Structured Signal Approximate Message Passing (BOSSAMP) - that jointly exploits the prior distribution and the structured sparsity of a signal that shall be…
We consider the problem of localizing change points in a generalized linear model (GLM), a model that covers many widely studied problems in statistical learning including linear, logistic, and rectified linear regression. We propose a…
We consider the problem of reconstructing the signal and the hidden variables from observations coming from a multi-layer network with rotationally invariant weight matrices. The multi-layer structure models inference from deep generative…
In this paper, we propose an information geometry (IG) framework to solve the standard linear regression problem. The proposed framework is an extension of the one for computing the mean of complex multivariate Gaussian distribution. By…
In cosparse analysis compressive sensing (CS), one seeks to estimate a non-sparse signal vector from noisy sub-Nyquist linear measurements by exploiting the knowledge that a given linear transform of the signal is cosparse, i.e., has…
This paper proposes Bayes-optimal convolutional approximate message-passing (CAMP) for signal recovery in compressed sensing. CAMP uses the same low-complexity matched filter (MF) for interference suppression as approximate message-passing…
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…
As one of the core technologies for 5G systems, massive multiple-input multiple-output (MIMO) introduces dramatic capacity improvements along with very high beamforming and spatial multiplexing gains. When developing efficient physical…
In linear inverse problems, the goal is to recover a target signal from undersampled, incomplete or noisy linear measurements. Typically, the recovery relies on complex numerical optimization methods; recent approaches perform an unfolding…
A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica…
Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed…
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…
Approximate Message Passing (AMP) algorithms have seen widespread use across a variety of applications. However, the precise forms for their Onsager corrections and state evolutions depend on properties of the underlying random matrix…