相关论文: Tensor Matched Kronecker-Structured Subspace Detec…
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 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…
We consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors that admit a known multilinear decomposition. We leverage the multidomain structure of tensor signals and…
We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a…
Kronecker compressed sensing refers to using Kronecker product matrices as sparsifying bases and measurement matrices in compressed sensing. This work focuses on the Kronecker compressed sensing problem, encompassing three sparsity…
In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities.…
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…
We consider two hypothesis testing problems for low-rank and high-dimensional tensor signals, namely the tensor signal alignment and tensor signal matching problems. These problems are challenging due to the high dimension of tensors and…
In this paper, we exhibit the tradeoffs between the (training) sample, computation and storage complexity for the problem of supervised classification using signal subspace estimation. Our main tool is the use of tensor subspaces, i.e.…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…
This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$th-order tensor data. Tensor observations are assumed to be generated from…
Kronecker regression is a highly-structured least squares problem $\min_{\mathbf{x}} \lVert \mathbf{K}\mathbf{x} - \mathbf{b} \rVert_{2}^2$, where the design matrix $\mathbf{K} = \mathbf{A}^{(1)} \otimes \cdots \otimes \mathbf{A}^{(N)}$ is…
The problem of compressive detection of random subspace signals is studied. We consider signals modeled as $\mathbf{s} = \mathbf{H} \mathbf{x}$ where $\mathbf{H}$ is an $N \times K$ matrix with $K \le N$ and $\mathbf{x} \sim…
Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to…
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…
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…
Consider a data set collected by (individuals-features) pairs in different times. It can be represented as a tensor of three dimensions (Individuals, features and times). The tensor biclustering problem computes a subset of individuals and…
Higher-order tensors have received increased attention across science and engineering. While most tensor decomposition methods are developed for a single tensor observation, scientific studies often collect side information, in the form of…
Topological spaces, represented by simplicial complexes, capture richer relationships than graphs by modeling interactions not only between nodes but also among higher-order entities, such as edges or triangles. This motivates the…
Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…