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We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
Subset repair is an important data cleaning technique that enforces integrity constraints by deleting a minimal number of conflicting tuples, yet multiple minimal repairs often exist. Density-based methods address this ambiguity by favoring…
We study statistical inverse learning in the context of nonlinear inverse problems under random design. Specifically, we address a class of nonlinear problems by employing gradient descent (GD) and stochastic gradient descent (SGD) with…
The aim of this Lecture Note is to introduce the Signal Processing (SP) community to a powerful yet still under-utilised tool: the semiparametric statistics. In short, the semiparametric framework allows us to estimate or perform hypothesis…
Computed tomography (CT) relies on precise patient immobilization during image acquisition. Nevertheless, motion artifacts in the reconstructed images can persist. Motion compensation methods aim to correct such artifacts post-acquisition,…
A new higher-order accurate method is proposed that combines the advantages of the classical $p$-version of the FEM on body-fitted meshes with embedded domain methods. A background mesh composed by higher-order Lagrange elements is used.…
In this work, we address the solution of both linear and nonlinear ill-posed inverse problems by developing a novel graph-based regularization framework, where the regularization term is formulated through an iteratively updated graph…
We study iterative signal reconstruction in computed tomography (CT), wherein measurements are produced by a linear transformation of the unknown signal followed by an exponential nonlinear map. Approaches based on pre-processing the data…
In this paper, we consider nonparametric estimation over general Dirichlet metric measure spaces. Unlike the more commonly studied reproducing kernel Hilbert space, whose elements may be defined pointwise, a Dirichlet space typically only…
Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…
This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…
In this paper, a topology optimization framework utilizing automatic differentiation is presented as an efficient way for solving 2D density-based topology optimization problem by calculating gradients through the fully differentiable…
In this work, we investigate the inverse problem of recovering a potential coefficient in an elliptic partial differential equation from the observations at deterministic sampling points in the domain subject to random noise. We employ a…
Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
This contribution proposes a recursive set-membership method for the ellipsoidal state characterization for discrete-time linear time-varying models with additive unknown disturbances vectors, bounded by possibly degenerate zonotopes and…
Two-phase random textures abound in a host of contexts, porous and composite media, ecological structures, biological media and astrophysical structures. Questions surrounding the spatial structure of such textures continue to pose many…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…
Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…