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The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…
We presented a separation based optimization algorithm which, rather than optimization the entire variables altogether, This would allow us to employ: 1) a class of nonlinear functions with three variables and 2) a convex quadratic…
A new class of disturbance covariance matrix estimators for radar signal processing applications is introduced following a geometric paradigm. Each estimator is associated with a given unitary invariant norm and performs the sample…
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This problem aims to…
Kernel-based methods for support vector machines (SVM) have shown highly advantageous performance in various applications. However, they may incur prohibitive computational costs for large-scale sample datasets. Therefore, data reduction…
We present a computationally-efficient method for recovering sparse signals from a series of noisy observations, known as the problem of compressed sensing (CS). CS theory requires solving a convex constrained minimization problem. We…
A great variety of fundamental optimization and counting problems arising in computer science, mathematics and physics can be reduced to one of the following computational tasks involving polynomials and set systems: given an $m$-variate…
Sparse solution problems play an important role in both signal processing and image restoration. In this paper, we propose a stochastic column-block nonlinear Bregman method for efficiently computing sparse solutions to nonlinear systems.…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
We propose a penalized likelihood framework for estimating multiple precision matrices from different classes. Most existing methods either incorporate no information on relationships between the precision matrices, or require this…
We propose and analyze a variant of Sparse Polyak for high dimensional M-estimation problems. Sparse Polyak proposes a novel adaptive step-size rule tailored to suitably estimate the problem's curvature in the high-dimensional setting,…
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions…
The celebrated sparse representation model has led to remarkable results in various signal processing tasks in the last decade. However, despite its initial purpose of serving as a global prior for entire signals, it has been commonly used…
Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial…
Sparse learning is a very important tool for mining useful information and patterns from high dimensional data. Non-convex non-smooth regularized learning problems play essential roles in sparse learning, and have drawn extensive attentions…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
We propose a two-level nested preconditioned iterative scheme for solving sparse linear systems of equations in which the coefficient matrix is symmetric and indefinite with relatively small number of negative eigenvalues. The proposed…
We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the…