Related papers: Reconstruction Algorithms for Sums of Affine Power…
If g and h are functions over some field, we can consider their composition f = g(h). The inverse problem is decomposition: given f, determine the ex- istence of such functions g and h. In this thesis we consider functional decom- positions…
This paper addresses the robust counterparts of optimization problems containing sums of maxima of linear functions. These problems include many practical problems, e.g.~problems with sums of absolute values, and arise when taking the…
To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…
The Waring Problem over polynomial rings asks for how to decompose an homogeneous polynomial of degree $d$ as a finite sum of $d^{th}$ powers of linear forms. First, we give a constructive method to obtain a real Waring decomposition of any…
Recently there has been much interest in "sparsifying" sums of rank one matrices: modifying the coefficients such that only a few are nonzero, while approximately preserving the matrix that results from the sum. Results of this sort have…
We present a new probabilistic algorithm that characterizes the equidimensional components of the affine algebraic variety defined by an arbitrary sparse polynomial system with prescribed supports. For each equidimensional component, the…
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging…
We aim at the solution of inverse problems in imaging, by combining a penalized sparse representation of image patches with an unconstrained smooth one. This allows for a straightforward interpretation of the reconstruction. We formulate…
Most integers are composite and most univariate polynomials over a finite field are reducible. The Prime Number Theorem and a classical result of Gau{\ss} count the remaining ones, approximately and exactly. For polynomials in two or more…
Symmetric tensor decomposition is an important problem with applications in several areas for example signal processing, statistics, data analysis and computational neuroscience. It is equivalent to Waring's problem for homogeneous…
Designing and implementing systems as an interconnection of smaller subsystems is a common practice for modularity and standardization of components and design algorithms. Although not typically cast in this framework, many of these…
Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data, and can…
We give new algorithms based on the sum-of-squares method for tensor decomposition. Our results improve the best known running times from quasi-polynomial to polynomial for several problems, including decomposing random overcomplete…
We consider algorithms and recovery guarantees for the analysis sparse model in which the signal is sparse with respect to a highly coherent frame. We consider the use of a monotone version of the fast iterative shrinkage- thresholding…
We exhibit an algorithm to compute the strongest polynomial (or algebraic) invariants that hold at each location of a given affine program (i.e., a program having only non-deterministic (as opposed to conditional) branching and all of whose…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
In this paper, we derive a new reconstruction method for real non-harmonic Fourier sums, i.e., real signals which can be represented as sparse exponential sums of the form $f(t) = \sum_{j=1}^{K} \gamma_{j} \, \cos(2\pi a_{j} t + b_{j})$,…
Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
We consider elliptic partial differential equations with diffusion coefficients that depend affinely on countably many parameters. We study the summability properties of polynomial expansions of the function mapping parameter values to…