相关论文: Some Options for L1-Subspace Signal Processing
This material introduces the D-Subspace algorithm derived on the basis of the centralized algorithm [1], which originally addresses parameter estimation problems under a subspace constraint.
Finding the $r\times r$ submatrix of maximum volume of a matrix $A\in\mathbb R^{n\times n}$ is an NP hard problem that arises in a variety of applications. We propose a new greedy algorithm of cost $\mathcal O(n)$, for the case $A$…
Signal estimation from incomplete observations improves as more signal structure can be exploited in the inference process. Classic algorithms (e.g., Kalman filtering) have exploited strong dynamic structure for time-varying signals while…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
The low-rank matrix approximation problem with respect to the component-wise $\ell_1$-norm ($\ell_1$-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine…
Optimal symbol detection for multiple-input multiple-output (MIMO) systems is known to be an NP-hard problem. Conventional heuristic algorithms are either too complex to be practical or suffer from poor performance. Recently, several…
Functions of interest are often smooth and sparse in some sense, and both priors should be taken into account when interpolating sampled data. Classical linear interpolation methods are effective under strong regularity assumptions, but…
Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…
The aim of sparse approximation is to estimate a sparse signal according to the measurement matrix and an observation vector. It is widely used in data analytics, image processing, and communication, etc. Up to now, a lot of research has…
In the subspace sketch problem one is given an $n\times d$ matrix $A$ with $O(\log(nd))$ bit entries, and would like to compress it in an arbitrary way to build a small space data structure $Q_p$, so that for any given $x \in \mathbb{R}^d$,…
In this paper, we present a method for denoising and reconstruction of low-dimensional manifold in high-dimensional space. We suggest a multidimensional extension of the Locally Optimal Projection algorithm which was introduced by Lipman et…
Batch Normalization (BN) has been proven to be quite effective at accelerating and improving the training of deep neural networks (DNNs). However, BN brings additional computation, consumes more memory and generally slows down the training…
In this work, we study the problem of finding the maximum value of a non-negative submodular function subject to a limit on the number of items selected, a ubiquitous problem that appears in many applications, such as data summarization and…
Recently, the $\l_{p}$-norm regularization minimization problem $(P_{p}^{\lambda})$ has attracted great attention in compressed sensing. However, the $\l_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^{\lambda})$ is nonconvex and…
We introduce a new family of algorithms for detecting and estimating a rank-one signal from a noisy observation under prior information about that signal's direction, focusing on examples where the signal is known to have entries biased to…
In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
This paper focuses on representing the $L^{\infty}$-norm of finite-dimensional linear time-invariant systems with parameter-dependent coefficients. Previous studies tackled the problem in a non-parametric scenario by simplifying it to…
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…
The use of generalized LASSO is a common technique for recovery of structured high-dimensional signals. Each generalized LASSO program has a governing parameter whose optimal value depends on properties of the data. At this optimal value,…