Related papers: Decoupled Solution for Composite Sparse-plus-Smoot…
A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
We consider the problem of super-resolving the line spectrum of a multisinusoidal signal from a finite number of samples, some of which may be completely corrupted. Measurements of this form can be modeled as an additive mixture of a…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…
In this paper, we propose and analyze a two-point gradient method for solving inverse problems in Banach spaces which is based on the Landweber iteration and an extrapolation strategy. The method allows to use non-smooth penalty terms,…
Blind deconvolution and demixing is the problem of reconstructing convolved signals and kernels from the sum of their convolutions. This problem arises in many applications, such as blind MIMO. This work presents a separable approach to…
This paper introduces a novel double regularization scheme for bilevel optimization problems whose lower-level problem is composite and convex, but not necessarily strongly convex, in the lower-level variable. The analysis focuses on the…
Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for…
In this paper, we develop a randomized algorithm and theory for learning a sparse model from large-scale and high-dimensional data, which is usually formulated as an empirical risk minimization problem with a sparsity-inducing regularizer.…
This paper studies sparse spikes deconvolution over the space of measures. We focus our attention to the recovery properties of the support of the measure, i.e. the location of the Dirac masses. For non-degenerate sums of Diracs, we show…
We present a method for supervised learning of sparsity-promoting regularizers for denoising signals and images. Sparsity-promoting regularization is a key ingredient in solving modern signal reconstruction problems; however, the operators…
In compressed sensing one uses known structures of otherwise unknown signals to recover them from as few linear observations as possible. The structure comes in form of some compressibility including different notions of sparsity and low…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
In this work we consider, in a Banach space framework, the regularization of linear ill-posed problems. Our focus is on the recovery of solutions that have a logarithmic source representation. Such cases typically occur in exponentially…
In the first part of this paper, we consider nonlinear extension of frame theory by introducing bi-Lipschitz maps $F$ between Banach spaces. Our linear model of bi-Lipschitz maps is the analysis operator associated with Hilbert frames,…
A general stochastic algorithm for solving mixed linear and nonlinear problems was introduced in [11]. We show in this paper how it can be used to solve the fault inverse problem, where a planar fault in elastic half-space and a slip on…
We propose an adaptive regularization scheme in a variational framework where a convex composite energy functional is optimized. We consider a number of imaging problems including denoising, segmentation and motion estimation, which are…
We study the solutions of infinite dimensional linear inverse problems over Banach spaces. The regularizer is defined as the total variation of a linear mapping of the function to recover, while the data fitting term is a near arbitrary…
A numerical method is developed for recovering both the source locations and the obstacle from the scattered Cauchy data of the time-harmonic acoustic field. First of all, the incident and scattered components are decomposed from the…