Related papers: Stable Recovery with Analysis Decomposable Priors
Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated…
A linear stochastic transport equation with non-regular coefficients is considered. Under the same assumption of the deterministic theory, all weak $L^\infty$-solutions are renormalized. But then, if the noise is nondegenerate, uniqueness…
We study the stability of regularization by projection for solving linear inverse problems if the forward operator is given indirectly but specified via some input-output training pairs. We extend the approach in "Data driven regularization…
We show that perturbing ill-posed differential equations with (potentially very) smooth random processes can restore well-posedness -- even if the perturbation is (potentially much) more regular than the drift component of the solution. The…
We consider multilevel decompositions of piecewise constants on simplicial meshes that are stable in $H^{-s}$ for $s\in (0,1)$. Proofs are given in the case of uniformly and locally refined meshes. Our findings can be applied to define…
Separable nonlinear least squares problems appear in many inverse problems, including semi-blind image deblurring. The variable projection (VarPro) method provides an efficient approach for solving such problems by eliminating linear…
Stability is a key property of both forward models and inverse problems, and depends on the norms considered in the relevant function spaces. For instance, stability estimates for hyperbolic partial differential equations are often based on…
This paper is devoted to the stability analysis of spatially interconnected systems (SISs) via the sum-of-squares (SOS) decomposition of positive trigonometric polynomials. For each spatial direction of SISs, three types of interconnected…
We revisit the classic stability problem of the buckling of an inextensible, axially compressed beam on a nonlinear elastic foundation with a semi-analytical approach to understand how spatially localized deformation solutions emerge in…
Regularized inversion methods for image reconstruction are used widely due to their tractability and ability to combine complex physical sensor models with useful regularity criteria. Such methods motivated the recently developed…
Regularization by denoising (RED) is a widely-used framework for solving inverse problems by leveraging image denoisers as image priors. Recent work has reported the state-of-the-art performance of RED in a number of imaging applications…
This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its…
This paper introduces the concept of renormalized solution for a general class of non-coercive nonlinear parabolic problems, including both singularities and unbounded lower order terms. We prove existence and uniqueness of renormalized…
In this paper, we prove the uniform stability of the Hochstadt-Lieberman problem, which consists in the recovery of the Sturm-Liouville potential on a half-interval from the spectrum and the known potential on the other half-interval. For…
Solving inverse problems requires appropriate regularization techniques to ensure well-posedness and stability. In recent years, denoiser-driven methods have emerged as effective regularization strategies, achieving state-of-the-art…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory.…
This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…