Related papers: Basis pursuit by inconsistent alternating projecti…
In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…
Many real world data sets exhibit an embedding of low-dimensional structure in a high-dimensional manifold. Examples include images, videos and internet traffic data. It is of great significance to reduce the storage requirements and…
In this paper, we propose a unified theoretical and practical spherical approximation framework for functional inverse problems on the hypersphere. More specifically, we consider recovering spherical fields directly in the continuous domain…
This thesis investigates optimal trajectory tracking of nonlinear dynamical systems with affine controls. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible. The concept of…
Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…
Overparameterized neural networks can interpolate a given dataset in many different ways, prompting the fundamental question: which among these solutions should we prefer, and what explicit regularization strategies will provably yield…
Sparse Bayesian Learning (SBL) is a powerful framework for attaining sparsity in probabilistic models. Herein, we propose a coordinate ascent algorithm for SBL termed Relevance Matching Pursuit (RMP) and show that, as its noise variance…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
In this paper, we consider the problem of minimizing the sum of two convex functions subject to linear linking constraints. The classical alternating direction type methods usually assume that the two convex functions have relatively easy…
We study the tracking problem, namely, estimating the hidden state of an object over time, from unreliable and noisy measurements. The standard framework for the tracking problem is the generative framework, which is the basis of solutions…
In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. The proposed PDE has the form of continuity equation that arises in various research areas, e.g. fluid dynamics and…
Total variation (TV) regularization has proven effective for a range of computer vision tasks through its preferential weighting of sharp image edges. Existing TV-based methods, however, often suffer from the over-smoothing issue and…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and…
In this paper, we consider a well-known sparse optimization problem that aims to find a sparse solution of a possibly noisy underdetermined system of linear equations. Mathematically, it can be modeled in a unified manner by minimizing…
Isometry pursuit is a convex algorithm for identifying orthonormal column-submatrices of wide matrices. It consists of a novel normalization method followed by multitask basis pursuit. Applied to Jacobians of putative coordinate functions,…
In this paper, we propose a novel sparse coding and counting method under Bayesian framwork for visual tracking. In contrast to existing methods, the proposed method employs the combination of L0 and L1 norm to regularize the linear…
Projection pursuit is used to find interesting low-dimensional projections of high-dimensional data by optimizing an index over all possible projections. Most indexes have been developed to detect departure from known distributions, such as…
We propose a new gradient projection algorithm that compares favorably with the fastest algorithms available to date for $\ell_1$-constrained sparse recovery from noisy data, both in the compressed sensing and inverse problem frameworks.…