相关论文: SAFIP: a streaming algorithm for inverse problems

In large-scale applications including medical imaging, collocation differential equation solvers, and estimation with differential privacy, the underlying linear inverse problem can be reformulated as a streaming problem. In theory, the…

We propose a prototypical Split Inverse Problem (SIP) and a new variational problem, called the Split Variational Inequality Problem (SVIP), which is a SIP. It entails finding a solution of one inverse problem (e.g., a Variational…

Solving inverse problems with diffusion models has shown promise in tasks such as image restoration. A common approach is to formulate the problem in a Bayesian framework and sample from the posterior by combining the prior score with the…

We introduce a new computational model for data streams: asymptotically exact streaming algorithms. These algorithms have an approximation ratio that tends to one as the length of the stream goes to infinity while the memory used by the…

A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…

This paper presents a first-order distributed algorithm for solving a convex semi-infinite program (SIP) over a time-varying network. In this setting, the objective function associated with the optimization problem is a summation of a set…

We show a dichotomy result for $p$-pass streaming algorithms for all CSPs and for up to polynomially many passes. More precisely, we prove that for any arity parameter $k$, finite alphabet $\Sigma$, collection $\mathcal{F}$ of $k$-ary…

The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…

This work present an affine map approximation for solving the inverse scattering problem related to the nonlinear Schr\"odinger model of signal propagation in high-speed coherent optical communication. Numerical simulations indicate that…

We present an algorithm for solving inverse problems on graphs analogous to those arising in diffuse optical tomography for continuous media. In particular, we formulate and analyze a discrete version of the inverse Born series, proving…

In this paper, we propose an exact general algorithm for solving non-convex optimization problems, where the non-convexity arises due to the presence of an inverse S-shaped function. The proposed method involves iteratively approximating…

Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…

Stimulated by practical applications arising from viral marketing. This paper investigates a novel Budgeted $k$-Submodular Maximization problem defined as follows: Given a finite set $V$, a budget $B$ and a $k$-submodular function $f:…

We shall investigate randomized algorithms for solving large-scale linear inverse problems with general regularizations. We first present some techniques to transform inverse problems of general form into the ones of standard form, then…

We give efficient deterministic one-pass streaming algorithms for finding an ellipsoidal approximation of a symmetric convex polytope. The algorithms are near-optimal in that their approximation factors differ from that of the optimal…

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

Obtaining meaningful solutions for inverse problems has been a major challenge with many applications in science and engineering. Recent machine learning techniques based on proximal and diffusion-based methods have shown promising results.…

This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…