We present explicit worst case degree and height bounds for the rational univariate representation of the isolated roots of polynomial systems based on mixed volume. We base our estimations on height bounds of resultants and we consider the case of 0-dimensional, positive dimensional, and parametric polynomial systems. CCS Concepts •Computing methodologies→ Symbolic calculus algorithms;

Sparsity-based models have proven to be very effective in most image processing applications. The notion of sparsity has recently been extended to structured sparsity models where not only the number of components but also their support is important. This paper goes one step further and proposes a new model where signals are composed of a small number of molecules, which are each linear combina...

original LPP SRLP LLE SRE Figure 1: SwissRoll 2D projections form 3D We adapt the Locality Preserving Projections (LPP)[4] and Locally Linear Embedding (LLE)[5] techniques to preserve the sparse representation property in the embedded space. The resulting techniques are Sparse Representation based Linear Projections (SRLP) and Sparse Representation based Embedding (SRE). We compare them to the ...

Given an overcomplete dictionary A and a signal b that is a linear combination of a few linearly independent columns of A, classical sparse recovery theory deals with the problem of recovering the unique sparse representation x such that b = Ax. It is known that under certain conditions on A, x can be recovered by the Basis Pursuit (BP) and the Orthogonal Matching Pursuit (OMP) algorithms. In t...