Related papers: High Dimensional Robust M-Estimation: Asymptotic V…
Iterative thresholding algorithms are well-suited for high-dimensional problems in sparse recovery and compressive sensing. The performance of this class of algorithms depends heavily on the tuning of certain threshold parameters. In…
Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of \emph{multiple statistically asymmetric signal sources}, we introduce a multi-source AMP framework in which…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
Purpose: For quantitative susceptibility mapping (QSM), the lack of ground-truth in clinical settings makes it challenging to determine suitable parameters for the dipole inversion. We propose a probabilistic Bayesian approach for QSM with…
Estimation of a vector from quantized linear measurements is a common problem for which simple linear techniques are suboptimal -- sometimes greatly so. This paper develops generalized approximate message passing (GAMP) algorithms for…
This paper introduces a framework for approximate message passing (AMP) in dynamic settings where the data at each iteration is passed through a linear operator. This framework is motivated in part by applications in large-scale,…
Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional asymptotic regime where the sample size $n$ and the number…
The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of $x$ observed from a noisy version of the transform coefficients $z = Ax$. In fact, for large zero-mean i.i.d…
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID)…
Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to…
In the pooled data problem, the goal is to identify the categories associated with a large collection of items via a sequence of pooled tests. Each pooled test reveals the number of items of each category within the pool. We study an…
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,…
This paper considers a discrete-valued signal estimation scheme based on a low-complexity Bayesian optimal message passing algorithm (MPA) for solving massive linear inverse problems under highly correlated measurements. Gaussian belief…
Approximate message passing (AMP) is a class of efficient algorithms for solving high-dimensional linear regression tasks where one wishes to recover an unknown signal \beta_0 from noisy, linear measurements y = A \beta_0 + w. When applying…
Approximate Message Passing (AMP) algorithms are a family of iterative algorithms based on large random matrices with the special property of tracking the statistical properties of their iterates. They are used in various fields such as…
Approximate message passing (AMP) is an algorithmic framework for solving linear inverse problems from noisy measurements, with exciting applications such as reconstructing images, audio, hyper spectral images, and various other signals,…
Generalised approximate message passing (GAMP) is an approximate Bayesian estimation algorithm for signals observed through a linear transform with a possibly non-linear subsequent measurement model. By leveraging prior information about…
This paper concerns the performance of the LASSO (also knows as basis pursuit denoising) for recovering sparse signals from undersampled, randomized, noisy measurements. We consider the recovery of the signal $x_o \in \mathbb{R}^N$ from $n$…
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.…
Asymmetry along with heteroscedasticity or contamination often occurs with the growth of data dimensionality. In ultra-high dimensional data analysis, such irregular settings are usually overlooked for both theoretical and computational…