Related papers: Perfect reconstruction of sparse signals using non…
We consider the design and analysis of spatially coupled sparse regression codes (SC-SPARCs), which were recently introduced by Barbier et al. for efficient communication over the additive white Gaussian noise channel. SC-SPARCs can be…
Approximate Message Passing (AMP), originally designed to solve high-dimensional linear inverse problems, has found broad applications in signal processing and statistical inference. Among its key variants, Vector Approximate Message…
The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each…
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…
We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the…
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,…
Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…
The mathematical theory of super-resolution developed recently by Cand\`{e}s and Fernandes-Granda states that a continuous, sparse frequency spectrum can be recovered with infinite precision via a (convex) atomic norm technique given a set…
Compressed sensing (CS) demonstrates that sparse signals can be recovered from underdetermined linear measurements. We focus on the joint sparse recovery problem where multiple signals share the same common sparse support sets, and they are…
The ubiquity of approximately sparse data has led a variety of com- munities to great interest in compressed sensing algorithms. Although these are very successful and well understood for linear measurements with additive noise, applying…
Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…
One-bit compressed sensing (1bCS) is a method of signal acquisition under extreme measurement quantization that gives important insights on the limits of signal compression and analog-to-digital conversion. The setting is also equivalent to…
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 establish exact asymptotic expressions for the normalized mutual information and minimum mean-square-error (MMSE) of sparse linear regression in the sub-linear sparsity regime. Our result is achieved by a generalization of the adaptive…
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…
As an emerging communication auxiliary technology, reconfigurable intelligent surface (RIS) is expected to play a significant role in the upcoming 6G networks. Due to its total reflection characteristics, it is challenging to implement…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
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…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
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…