Related papers: User Manual for Model-based Imaging Inverse Proble…
The image reconstruction problem of the tomographic imaging technique magnetic particle imaging (MPI) requires the solution of a linear inverse problem. One prerequisite for this task is that the imaging operator that describes the mapping…
Inverse kinematics is an important and challenging problem in the operation of industrial manipulators. This study proposes a simple inverse kinematics calculation scheme for an industrial serial manipulator. The proposed technique can…
Most of the optimal guidance problems can be formulated as nonconvex optimization problems, which can be solved indirectly by relaxation, convexification, or linearization. Although these methods are guaranteed to converge to the global…
Motivation: Medical image analysis involves tasks to assist physicians in qualitative and quantitative analysis of lesions or anatomical structures, significantly improving the accuracy and reliability of diagnosis and prognosis.…
The classical approach to inverse problems is based on the optimization of a misfit function. Despite its computational appeal, such an approach suffers from many shortcomings, e.g., non-uniqueness of solutions, modeling prior knowledge,…
The study of solving the inverse eigenvalue problem for nonnegative matrices has been around for decades. It is clear that an inverse eigenvalue problem is trivial if the desirable matrix is not restricted to a certain structure. Provided…
A complete solution for an inverse problem needs five main steps: choice of basis functions for discretization, determination of the order of the model, estimation of the hyperparameters, estimation of the solution, and finally,…
In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…
A wide range of applications arising in machine learning and signal processing can be cast as convex optimization problems. These problems are often ill-posed, i.e., the optimal solution lacks a desired property such as uniqueness or…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
The optical resolution of a digital camera is one of its most crucial parameters with broad relevance for consumer electronics, surveillance systems, remote sensing, or medical imaging. However, resolution is physically limited by the…
Image registration is the basis for many applications in the fields of medical image computing and computer assisted interventions. One example is the registration of 2D X-ray images with preoperative three-dimensional computed tomography…
Topological concepts open many new horizons for photonic devices, from integrated optics to lasers. The complexity of large scale topological devices asks for an effective solution of the inverse problem: how best to engineer the topology…
These lecture notes evolve around mathematical concepts arising in inverse problems. We start by introducing inverse problems through examples such as differentiation, deconvolution, computed tomography and phase retrieval. This then leads…
Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML)…
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…