相关论文: Noisy 1-Bit Compressed Sensing Embeddings Enjoy a …

In this letter, we consider the problem of detecting a high dimensional signal based on compressed measurements with physical layer secrecy guarantees. We assume that the network operates in the presence of an eavesdropper who intends to…

The fields of compressed sensing (CS) and matrix completion have shown that high-dimensional signals with sparse or low-rank structure can be effectively projected into a low-dimensional space (for efficient acquisition or processing) when…

In this paper, we study a support set reconstruction problem in which the signals of interest are jointly sparse with a common support set, and sampled by joint sparsity model-2 (JSM-2) in the presence of noise. Using mathematical tools, we…

We present a simple and effective algorithm for the problem of \emph{sparse robust linear regression}. In this problem, one would like to estimate a sparse vector $w^* \in \mathbb{R}^n$ from linear measurements corrupted by sparse noise…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

This paper provides performance bounds for compressed sensing in the presence of Poisson noise using expander graphs. The Poisson noise model is appropriate for a variety of applications, including low-light imaging and digital streaming,…

Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind…

Oversampling combined with low quantization resolutions has been shown to be a viable option when aiming for energy efficiency in multigigabit/s communications systems. This work considers the case of 1-bit quantization combined with…

This paper addresses the topic of robust Bayesian compressed sensing over finite fields. For stationary and ergodic sources, it provides asymptotic (with the size of the vector to estimate) necessary and sufficient conditions on the number…

In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is…

The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…

Snapshot compressed sensing (CS) refers to compressive imaging systems in which multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a noisy linear mapping of the corresponding pixels in the frames…

The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the…

Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…

Sign truncated matching pursuit (STrMP) algorithm is presented in this paper. STrMP is a new greedy algorithm for the recovery of sparse signals from the sign measurement, which combines the principle of consistent reconstruction with…

As shown in [Blumensath and Davies 2009, Baraniuk et al. 2010], signals whose wavelet coefficients exhibit a rooted tree structure can be recovered using specially-adapted compressed sensing algorithms from just n=O(k) measurements, where k…

A simple hard-thresholding operation is shown to be able to recover $L$ signals $\mathbf{x}_1,...,\mathbf{x}_L \in \mathbb{R}^n$ that share a common support of size $s$ from $m = \mathcal{O}(s)$ one-bit measurements per signal if $L \ge…

$\ell_1$ minimization is often used for finding the sparse solutions of an under-determined linear system. In this paper we focus on finding sharp performance bounds on recovering approximately sparse signals using $\ell_1$ minimization,…

Sub-bit model compression seeks storage below one bit per weight; as magnitudes are aggressively compressed, the sign bit becomes a fixed-cost bottleneck. Across Transformers, CNNs, and MLPs, learned sign matrices resist low-rank…

We give some new results on sparse signal recovery in the presence of noise, for weighted spaces. Traditionally, were used dictionaries that have the norm equal to 1, but, for random dictionaries this condition is rarely satisfied.…