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.

中文翻译：

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用于反稀疏编码的安全压缩

在数字通信或机器学习等许多应用中，将信息传播到表示的所有系数上是一种理想的特性。这种所谓的反稀疏表示可以通过求解一个涉及 $\ell _\infty$-norm 惩罚和二次差异的凸程序来获得。在本文中，我们提出了一种称为安全挤压的新方法，以加速反稀疏表示的计算。我们描述了一个测试，它允许在优化问题的解决方案中检测饱和条目。这些条目的贡献被压缩到一个向量中，从而实现了一种降维形式。我们提出了两种算法来解决由此产生的低维问题。