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Speed-of-sound is a biomechanical property for quantitative tissue differentiation, with great potential as a new ultrasound-based image modality. A conventional ultrasound array transducer can be used together with an acoustic mirror, or…
Deciding whether the union of two convex polyhedra is itself a convex polyhedron is a basic problem in polyhedral computations; having important applications in the field of constrained control and in the synthesis, analysis, verification…
3D image reconstruction from a set of X-ray projections is an important image reconstruction problem, with applications in medical imaging, industrial inspection and airport security. The innovation of X-ray emitter arrays allows for a…
X-ray computed tomographic infrastructures are medical imaging modalities that rely on the acquisition of rays crossing examined objects while measuring their intensity decrease. Physical measurements are post-processed by mathematical…
This paper addresses the challenge of 3D human pose estimation from a single color image. Despite the general success of the end-to-end learning paradigm, top performing approaches employ a two-step solution consisting of a Convolutional…
In this paper we address the basic geometric question of when a given convex set is the image under a linear map of an affine slice of a given closed convex cone. Such a representation or 'lift' of the convex set is especially useful if the…
This paper presents a selected tour through the theory and applications of lifts of convex sets. A lift of a convex set is a higher-dimensional convex set that projects onto the original set. Many convex sets have lifts that are…
Purpose: To develop a general phase regularized image reconstruction method, with applications to partial Fourier imaging, water-fat imaging and flow imaging. Theory and Methods: The problem of enforcing phase constraints in reconstruction…
The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps: (1) We cut every edge of G into two halves, thus obtaining a…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
We present some complexity results concerning the problems of covering a graph with $p$ convex sets and of partitioning a graph into $p$ convex sets. The following convexities are considered: digital convexity, monophonic convexity,…
Discrete tomography deals with the reconstruction of images from projections collected along a few given directions. Different approaches can be considered, according to different models. In this paper we adopt the grid model, where pixels…
This article describes a method to compute successive convex approximations of the convex hull of a set of points in R^n that are the solutions to a system of polynomial equations over the reals. The method relies on sums of squares of…
Reconstructing images from very long baseline interferometry (VLBI) data with sparse sampling of the Fourier domain (uv-coverage) constitutes an ill-posed deconvolution problem. It requires application of robust algorithms maximizing the…
High resolution reconstruction of complicated objects from incomplete and noisy data can be achieved by solving modulation equations iteratively under physical constraints. This direct demodulation method is a powerful technique for dealing…
We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a…
Computed Tomography (CT) is an essential non-destructive three dimensional imaging modality used in medicine, security screening, and inspection of manufactured components. Typical CT data acquisition entails the collection of a thousand or…
3D reconstruction from single view images is an ill-posed problem. Inferring the hidden regions from self-occluded images is both challenging and ambiguous. We propose a two-pronged approach to address these issues. To better incorporate…
Convex maximization encompasses a broad class of optimization problems and is generally NP-hard, even for low-rank objectives. This paper investigates structural conditions under which convex maximization becomes polynomially solvable. From…