Safe squeezing for antisparse coding
This work addresses a computational bottleneck in antisparse coding for applications like digital communication and machine learning, but it is incremental as it builds on existing convex optimization methods.
The paper tackles the problem of accelerating the computation of antisparse representations, which spread information across all coefficients, by proposing a safe squeezing methodology that detects saturated entries and reduces dimensionality, resulting in computational gains as shown in numerical experiments.
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.