Non-convex P-Norm Projection for Robust Sparsity

Mithun Das Gupta, Sanjeev Kumar

Abstract: In this paper, we investigate the properties of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm (p ≤1) within a projection framework. We start with the KKT equations of the non-linear optimization problem and then use its key properties to arrive at an algorithm for L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> norm projection on the non-negative simplex. We compare with L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> projection which needs prior knowledge of the true norm, as well as hard thresholding based sparsification proposed in recent compressed sensing literature. We show performance improvements compared to these techniques across different vision applications.