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Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
Sparse superposition codes, or sparse regression codes (SPARCs), are a recent class of codes for reliable communication over the AWGN channel at rates approaching the channel capacity. Approximate message passing (AMP) decoding, a…
This paper considers the problem of signal decomposition and data visualization. For this purpose, we introduce a new multiscale transform, termed `ensemble patch transformation' that enhances identification of local characteristics…
The sparse Beyesian learning (also referred to as Bayesian compressed sensing) algorithm is one of the most popular approaches for sparse signal recovery, and has demonstrated superior performance in a series of experiments. Nevertheless,…
We consider the problem of recovering a block (or group) sparse signal from an underdetermined set of random linear measurements, which appear in compressed sensing applications such as radar and imaging. Recent results of Donoho,…
Compressed sensing is a technique for recovering an unknown sparse signal from a small number of linear measurements. When the measurement matrix is random, the number of measurements required for perfect recovery exhibits a phase…
The characterisation of time-series data via their most salient features is extremely important in a range of machine learning task, not least of all with regards to classification and clustering. While there exist many feature extraction…
Motivated by the recent application of approximate message passing (AMP) to the analysis of convex optimizations in multi-class classifications [Loureiro, et. al., 2021], we present a convergence analysis of AMP dynamics with non-separable…
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of…
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…
In this paper, we consider the sparse phase retrieval problem, recovering an $s$-sparse signal $\bm{x}^{\natural}\in\mathbb{R}^n$ from $m$ phaseless samples $y_i=|\langle\bm{x}^{\natural},\bm{a}_i\rangle|$ for $i=1,\ldots,m$. Existing…
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 give a fast, spectral procedure for implementing approximate-message passing (AMP) algorithms robustly. For any quadratic optimization problem over symmetric matrices $X$ with independent subgaussian entries, and any separable AMP…
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…
In this paper, we propose a deep learning aided list approximate message passing (AMP) algorithm to further improve the user identification performance in massive machine type communications. A neural network is employed to identify a…
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…
Decentralized generalized approximate message-passing (GAMP) is proposed for compressed sensing from distributed generalized linear measurements in a tree-structured network. Consensus propagation is used to realize average consensus…
In this paper, we propose a general framework for the asymptotic analysis of node-based verification-based algorithms. In our analysis we tend the signal length $n$ to infinity. We also let the number of non-zero elements of the signal $k$…
For the problem of binary linear classification and feature selection, we propose algorithmic approaches to classifier design based on the generalized approximate message passing (GAMP) algorithm, recently proposed in the context of…
Approximate message passing (AMP) algorithms break a (high-dimensional) statistical problem into parts then repeatedly solve each part in turn, akin to alternating projections. A distinguishing feature is their asymptotic behaviours can be…