  Spreading the information over all coefficients of a representation is a
desirable property in many applications such as digital communication or
machine learning. This so-called antisparse representation can be obtained by
solving a convex program involving an $\ell_\infty$-norm penalty combined with
a quadratic discrepancy. In this paper, we propose a new methodology, dubbed
safe squeezing, to accelerate the computation of antisparse representation. We
describe a test that allows to detect saturated entries in the solution of the
optimization problem. The contribution of these entries is compacted into a
single vector, thus operating a form of dimensionality reduction. We propose
two algorithms to solve the resulting lower dimensional problem. Numerical
experiments show the effectiveness of the proposed method to detect the
saturated components of the solution and illustrates the induced computational
gains in the resolution of the antisparse problem.
