Related papers: On Approximate Message Passing for Unsourced Acces…
Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…
Approximate message passing (AMP) is an effective iterative sparse recovery algorithm for linear system models. Its performance is characterized by the state evolution (SE) which is a simple scalar recursion. However, depending on a…
Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…
We consider the problem of signal estimation in generalized linear models defined via rotationally invariant design matrices. Since these matrices can have an arbitrary spectral distribution, this model is well suited for capturing complex…
Xampling generalizes compressed sensing (CS) to reduced-rate sampling of analog signals. A unified framework is introduced for low rate sampling and processing of signals lying in a union of subspaces. Xampling consists of two main blocks:…
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…
Compressive imaging is an emerging application of compressed sensing, devoted to acquisition, encoding and reconstruction of images using random projections as measurements. In this paper we propose a novel method to provide a scalable…
Efficient signal detectors are rather important yet challenging to achieve satisfactory performance for large-scale communication systems. This paper considers a non-orthogonal sparse code multiple access (SCMA) configuration for…
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain…
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…
Network coding is famous for significantly improving the throughput of networks. The successful decoding of the network coded data relies on some side information of the original data. In that framework, independent data flows are usually…
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…
We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The CASSI imaging process can be…
Approximate message passing (AMP) is a scalable, iterative approach to signal recovery. For structured random measurement ensembles, including independent and identically distributed (i.i.d.) Gaussian and rotationally-invariant matrices,…
In this letter, we propose a turbo compressed sensing algorithm with partial discrete Fourier transform (DFT) sensing matrices. Interestingly, the state evolution of the proposed algorithm is shown to be consistent with that derived using…
Compressed sensing (CS) demonstrates that a sparse, or compressible signal can be acquired using a low rate acquisition process below the Nyquist rate, which projects the signal onto a small set of vectors incoherent with the sparsity…
Both theoretical analysis and empirical evidence confirm that the approximate message passing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise…
The idea that compressed sensing may be used to encrypt information from unauthorised receivers has already been envisioned, but never explored in depth since its security may seem compromised by the linearity of its encoding process. In…
We show how the notion of message passing can be used to streamline the algebra and computer coding for fast approximate inference in large Bayesian semiparametric regression models. In particular, this approach is amenable to handling…
We propose tensor-network compressed sensing (TNCS) by combining the ideas of compressed sensing, tensor network (TN), and machine learning, which permits novel and efficient quantum communications of realistic data. The strategy is to use…