Related papers: Minimal lensing solutions in the singular perturba…
The task of finding a sparse signal decomposition in an overcomplete dictionary is made more complicated when the signal undergoes an unknown modulation (or convolution in the complementary Fourier domain). Such simultaneous sparse recovery…
Reactive synthesis is concerned with finding a correct-by-construction controller from formal specifications, typically expressed in Linear Temporal Logic (LTL). The specifications describe assumptions about an environment and guarantees to…
We review connections between coding-theoretic objects and sparse learning problems. In particular, we show how seemingly different combinatorial objects such as error-correcting codes, combinatorial designs, spherical codes, compressed…
The inability of standard models to explain the flux ratios in many 4-image gravitational lenses has been cited as evidence for significant small-scale structure in lens galaxies. That claim has generally relied on detailed lens modeling,…
In this paper, motivated by diffraction of traveling light waves, a simple mathematical model is proposed, both for the multivariate super-resolution problem and the problem of blind-source separation of real-valued exponential sums. This…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
Many problems give rise to polynomial systems. These systems often have several parameters and we are interested to study how the solutions vary when we change the values for the parameters. Using predictor-corrector methods we track the…
We introduce a method that automatically and jointly updates both continuous and discrete parameters of a compound lens design, to improve its performance in terms of sharpness, speed, or both. Previous methods for compound lens design use…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
Achieving high spatial resolution is the goal of many imaging systems. Designing a high-resolution lens with diffraction-limited performance over a large field of view remains a difficult task in imaging system design. On the other hand,…
We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…
We consider a separation problem where the observation consists of the sum of a high amplitude smooth signal and a low amplitude transient signal. We propose a method for decomposition that relies on solving instances of a `constrained…
The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…
In this paper, we develop a new decomposition technique for solving bi-objective linear programming problems. The proposed methodology combines the bi-objective simplex algorithm with Benders decomposition and can be used to obtain a…
Model generation is a problem complementary to theorem proving and is important for fault analysis and debugging of formal specifications of security protocols, programs and terminological definitions. This paper discusses several ways of…
Various approaches to iterative refinement (IR) for least-squares problems have been proposed in the literature and it may not be clear which approach is suitable for a given problem. We consider three approaches to IR for least-squares…
We explore connections between the approach of solving the rational interpolation problem via resolutions of ideals and syzygies with the standard method provided by the Extended Euclidean Algorithm. As a consequence, we obtain explicit…
Biadjoint scalar field theories are increasingly important in the study of scattering amplitudes in various string and field theories. Recently, some first exact nonperturbative solutions of biadjoint scalar theory were presented, with a…
Gravitational lens modeling of spatially resolved sources is a challenging inverse problem with many observational constraints and model parameters. We examine established pixel-based source reconstruction algorithms for de-lensing the…