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This paper considers the problem of recovering either a low rank matrix or a sparse vector from observations of linear combinations of the vector or matrix elements. Recent methods replace the non-convex regularization with $\ell_1$ or…

We start out by demonstrating that an elementary learning task, corresponding to the training of a single linear neuron in a convolutional neural network, can be solved for feature spaces of very high dimensionality. In a second step,…

Atomic norm methods have recently been proposed for spectral super-resolution with flexibility in dealing with missing data and miscellaneous noises. A notorious drawback of these convex optimization methods however is their lower…

There has been tremendous research on the design of image regularizers over the years, from simple Tikhonov and Laplacian to sophisticated sparsity and CNN-based regularizers. Coupled with a model-based loss function, these are typically…

We develop spectral methods for ODEs and operator eigenvalue problems that are based on a least-squares formulation of the problem. The key tool is a method for rectangular generalized eigenvalue problems, which we extend to quasimatrices…

We propose a flexible machine-learning framework for solving eigenvalue problems of diffusion operators in moderately large dimension. We improve on existing Neural Networks (NNs) eigensolvers by demonstrating our approach ability to…

Hyperspectral Imaging is a crucial tool in remote sensing which captures far more spectral information than standard color images. However, the increase in spectral information comes at the cost of spatial resolution. Super-resolution is a…

In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…

Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More…

The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive…

We consider the problem of efficiently solving large-scale linear least squares problems that have one or more linear constraints that must be satisfied exactly. Whilst some classical approaches are theoretically well founded, they can face…

A number of inference problems with sensor networks involve projecting a measured signal onto a given subspace. In existing decentralized approaches, sensors communicate with their local neighbors to obtain a sequence of iterates that…

Investigating the stability of nonlinear waves often leads to linear or nonlinear eigenvalue problems for differential operators on unbounded domains. In this paper we propose to detect and approximate the point spectra of such operators…

Joint radar receive filter and waveform design is non-convex, but is individually convex for a fixed receiver filter while optimizing the waveform, and vice versa. Such classes of problems are fre- quently encountered in optimization, and…

We consider the minimization of a continuous function over the intersection of a regular cone with an affine set via a new class of adaptive first- and second-order optimization methods, building on the Hessian-barrier techniques introduced…

This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…

Phase retrieval has been an attractive but difficult problem rising from physical science, and there has been a gap between state-of-the-art theoretical convergence analyses and the corresponding efficient retrieval methods. Firstly, these…

A simple procedure for the design of recursive digital filters with an infinite impulse response (IIR) and non-recursive digital filters with a finite impulse response (FIR) is described. The fixed-lag smoothing filters are designed to…

Efficiently solving sparse linear algebraic equations is an important research topic of numerical simulation. Commonly used approaches include direct methods and iterative methods. Compared with the direct methods, the iterative methods…