Article ID Journal Published Year Pages File Type
567153 Signal Processing 2008 15 Pages PDF
Abstract

Sparsity plays an important role in many fields of engineering. The cardinality penalty function, often used as a measure of sparsity, is neither continuous nor differentiable and therefore smooth optimization algorithms cannot be applied directly. In this paper we present a continuous yet non-differentiable sparsity function which constitutes a tight lower bound on the cardinality function. The novelty of this approach is that we cast the problem of minimizing the new sparsity function as a problem with a bilinear objective function. We present a numerical comparison to other sparsity encouraging penalty functions for several applications. Additionally, we apply the techniques developed to minimize an objective function with a truncated hinge loss function. We present highly competitive results for all of the applications.

Related Topics
Physical Sciences and Engineering Computer Science Signal Processing
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