Related papers: Convergence of algorithms for reconstructing conve…
In this paper we propose a blind deconvolution method which applies to data perturbed by Poisson noise. The objective function is a generalized Kullback-Leibler divergence, depending on both the unknown object and unknown point spread…
A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of…
Processing of Diffusion MRI data obtained from High Angular Resolution measurements consists of a series of steps, starting with the estimation of an orientation distribution function (ODF), which is then used as input for e.g. tractography…
We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…
The paper is devoted to new modifications of recently proposed adaptive methods of Mirror Descent for convex minimization problems in the case of several convex functional constraints. Methods for problems of two classes are considered. The…
This research proposes a novel adjustable algorithm for reconstructing 3D body shapes from front and side silhouettes. Most recent silhouette-based approaches use a deep neural network trained by silhouettes and key points to estimate the…
This paper describes recursive algorithms for state estimation of linear dynamical systems when measurements are noisy with unknown bias and/or outliers. For situations with noisy and biased measurements, algorithms are proposed that…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Restoration of digital images from their degraded measurements has always been a problem of great theoretical and practical importance in numerous applications of imaging sciences. A specific solution to the problem of image restoration is…
This paper is concerned with convergence analysis for the mirror descent (MD) method, a well-known algorithm in convex optimization. An analysis framework via integral quadratic constraints (IQCs) is constructed to analyze the convergence…
This paper considers stochastic subgradient mirror-descent method for solving constrained convex minimization problems. In particular, a stochastic subgradient mirror-descent method with weighted iterate-averaging is investigated and its…
The image restoration problem is one of the popular topics in image processing studied by many authors on account of its applications in various areas. The aim of this paper is to present a new algorithm by using viscosity approximation…
Conventional algorithms for sparse signal recovery and sparse representation rely on $l_1$-norm regularized variational methods. However, when applied to the reconstruction of $\textit{sparse images}$, i.e., images where only a few pixels…
A result of Spencer states that every collection of $n$ sets over a universe of size $n$ has a coloring of the ground set with $\{-1,+1\}$ of discrepancy $O(\sqrt{n})$. A geometric generalization of this result was given by Gluskin (see…
The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it…
Boosting is a popular way to derive powerful learners from simpler hypothesis classes. Following previous work (Mason et al., 1999; Friedman, 2000) on general boosting frameworks, we analyze gradient-based descent algorithms for boosting…
This paper deals with a Tikhonov regularized second-order inertial dynamical system that incorporates time scaling, asymptotically vanishing damping and Hessian-driven damping for solving convex optimization problems. Under appropriate…
High-dimensional linear regression under heavy-tailed noise or outlier corruption is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs,…
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…