相关论文: Convex Optimization Approach for Stable Decomposit…

This paper considers the problem of recovering the delays and amplitudes of a weighted superposition of pulses. This problem is motivated by a variety of applications such as ultrasound and radar. We show that for univariate and bivariate…

This paper considers the problem of estimating the delays of a weighted superposition of pulses, called stream of pulses, in a noisy environment. We show that the delays can be estimated using a tractable convex optimization problem with a…

The problem of estimating the delays and amplitudes of a positive stream of pulses appears in many applications, such as single-molecule microscopy. This paper suggests estimating the delays and amplitudes using a convex program, which is…

The signal demixing problem seeks to separate a superposition of multiple signals into its constituent components. This paper studies a two-stage approach that first decompresses and subsequently deconvolves the noisy and undersampled…

The problem of resolving the fine details of a signal from its coarse scale measurements or, as it is commonly referred to in the literature, the super-resolution problem arises naturally in engineering and physics in a variety of settings.…

In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…

Clustering is a fundamental tool for analyzing large data sets. A rich body of work has been devoted to designing data-stream algorithms for the relevant optimization problems such as $k$-center, $k$-median, and $k$-means. Such algorithms…

Optimized Pulse Patterns (OPPs) are gaining increasing popularity in the power electronics community over the well-studied pulse width modulation due to their inherent ability to provide the switching instances that optimize current…

We propose a convex formulation of the fused lasso signal approximation problem consisting of non-convex penalty functions. The fused lasso signal model aims to estimate a sparse piecewise constant signal from a noisy observation.…

A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled,…

Demixing refers to the challenge of identifying two structured signals given only the sum of the two signals and prior information about their structures. Examples include the problem of separating a signal that is sparse with respect to…

Decentralized optimization is well studied for smooth unconstrained problems. However, constrained problems or problems with composite terms are an open direction for research. We study structured (or composite) optimization problems, where…

We estimate $n$ phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex…

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…

We consider a linear inverse problem whose solution is expressed as a sum of two components: one smooth and the other sparse. This problem is addressed by minimizing an objective function with a least squares data-fidelity term and a…

In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…

We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes…

Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…

In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…