Related papers: Compressive Detection of Random Subspace Signals
The problem of testing whether a signal lies within a given subspace, also named matched subspace detection, has been well studied when the signal is represented as a vector. However, the matched subspace detection methods based on vectors…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
We consider the problem of deciding whether a highly incomplete signal lies within a given subspace. This problem, Matched Subspace Detection, is a classical, well-studied problem when the signal is completely observed. High- dimensional…
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…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
In 1-bit compressed sensing, the aim is to estimate a $k$-sparse unit vector $x\in S^{n-1}$ within an $\epsilon$ error (in $\ell_2$) from minimal number of linear measurements that are quantized to just their signs, i.e., from measurements…
We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of the signal, we consider the general problem of…
We consider the general problem of matching a subspace to a signal in R^N that has been observed indirectly (compressed) through a random projection. We are interested in the case where the collection of K-dimensional subspaces is…
Results on the spectral behavior of random matrices as the dimension increases are applied to the problem of detecting the number of sources impinging on an array of sensors. A common strategy to solve this problem is to estimate the…
Sensor placement for linear inverse problems is the selection of locations to assign sensors so that the entire physical signal can be well recovered from partial observations. In this paper, we propose a fast sampling algorithm to place…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
Remote sensing hyperspectral sensors collect large volumes of high dimensional spectral and spatial data. However, due to spectral and spatial redundancy the true hyperspectral signal lies on a subspace of much lower dimension than the…
Compressed sensing is a signal processing technique in which data is acquired directly in a compressed form. There are two modeling approaches that can be considered: the worst-case (Hamming) approach and a statistical mechanism, in which…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
In this paper, we consider the problem of detecting signals in multiple, sequentially observed data streams. For each stream, the exact distribution is unknown, but characterized by a parameter that takes values in either of two disjoint…