Related papers: Perfect reconstruction of sparse signals using non…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
We address the problem of reconstructing a multi-band signal from its sub-Nyquist point-wise samples. To date, all reconstruction methods proposed for this class of signals assumed knowledge of the band locations. In this paper, we develop…
Noiseless compressive sensing is a two-steps setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on $\lone$ regularization, provides an efficient and…
Approximate message passing (AMP) refers to a class of efficient algorithms for statistical estimation in high-dimensional problems such as compressed sensing and low-rank matrix estimation. This paper analyzes the performance of AMP in the…
In many real-world problems, recovering sparse signals from underdetermined linear systems remains a fundamental challenge. Although $\ell_1$ norm minimization is widely used, it suffers from estimation bias that prevents it from reaching…
We study compressed sensing (CS) signal reconstruction problems where an input signal is measured via matrix multiplication under additive white Gaussian noise. Our signals are assumed to be stationary and ergodic, but the input statistics…
This paper focuses on the asymptotic analysis of a class of nonlinear one-bit precoding schemes under Rayleigh fading channels. The considered scheme employs a convex-relaxation-then-quantization (CRQ) approach to the well-known minimum…
In a recent paper, the authors proposed a new class of low-complexity iterative thresholding algorithms for reconstructing sparse signals from a small set of linear measurements \cite{DMM}. The new algorithms are broadly referred to as AMP,…
Designing efficient sparse recovery algorithms that could handle noisy quantized measurements is important in a variety of applications -- from radar to source localization, spectrum sensing and wireless networking. We take advantage of the…
This paper considers the massive connectivity application in which a large number of potential devices communicate with a base-station (BS) in a sporadic fashion. The detection of device activity pattern together with the estimation of the…
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…
We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and…
A common sparse linear regression formulation is the l1 regularized least squares, which is also known as least absolute shrinkage and selection operator (LASSO). Approximate message passing (AMP) has been proved to asymptotically achieve…
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…
Purpose: Undersampling is used to reduce the scan time for high-resolution 3D magnetic resonance imaging. In order to achieve better image quality and avoid manual parameter tuning, we propose a probabilistic Bayesian approach to recover…
Analysis based reconstruction has recently been introduced as an alternative to the well-known synthesis sparsity model used in a variety of signal processing areas. In this paper we convert the analysis exact-sparse reconstruction problem…
Sparse superposition codes, also called sparse regression codes (SPARCs), are a class of codes for efficient communication over the AWGN channel at rates approaching the channel capacity. In a standard SPARC, codewords are sparse linear…
We propose a probabilistic framework for interpreting and developing hard thresholding sparse signal reconstruction methods and present several new algorithms based on this framework. The measurements follow an underdetermined linear model,…
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…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…