相关论文: Concise Derivation of Complex Bayesian Approximate…
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…
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-Nyquist signal acquisition. When a statistical…
This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…
This paper tackles the problem of millimeter-Wave (mmWave) channel estimation in massive MIMO communication systems. A new Bayes-optimal channel estimator is derived using recent advances in the approximate belief propagation (BP) Bayesian…
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…
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…
We introduce an iterative optimization scheme for convex objectives consisting of a linear loss and a non-separable penalty, based on the expectation-consistent approximation and the vector approximate message-passing (VAMP) algorithm.…
We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…
The denoising-based approximate message passing (D-AMP) methodology, recently proposed by Metzler, Maleki, and Baraniuk, allows one to plug in sophisticated denoisers like BM3D into the AMP algorithm to achieve state-of-the-art compressive…
Approximate message passing (AMP) is a family of iterative algorithms that generalize matrix power iteration. AMP algorithms are known to optimally solve many average-case optimization problems. In this paper, we show that a large class of…
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…
We consider the problem of signal estimation in a generalized linear model (GLM). GLMs include many canonical problems in statistical estimation, such as linear regression, phase retrieval, and 1-bit compressed sensing. Recent work has…
In order to reduce hardware complexity and power consumption, massive multiple-input multiple-output (MIMO) systems employ low-resolution analog-to-digital converters (ADCs) to acquire quantized measurements $\boldsymbol y$. This poses new…
Recovering complex-valued image recovery from noisy indirect data is important in applications such as ultrasound imaging and synthetic aperture radar. While there are many effective algorithms to recover point estimates of the magnitude,…
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…
Approximate message passing (AMP) emerges as an effective iterative paradigm for solving high-dimensional statistical problems. However, prior AMP theory -- which focused mostly on high-dimensional asymptotics -- fell short of predicting…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
We study the problem of estimating a rank-$1$ signal in the presence of rotationally invariant noise-a class of perturbations more general than Gaussian noise. Principal Component Analysis (PCA) provides a natural estimator, and sharp…
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)…