Fast Algorithms for Delta-Separated Sparsity Projection

TL;DR

This paper introduces a fast approximation algorithm for the $\Delta$-separated sparsity projection problem, enabling efficient recovery of sparse signals in large datasets with improved speed.

Contribution

It presents a linear-time, head and tail approximation algorithm for $\Delta$-separated sparsity projection, solving an open problem and enhancing sparse signal recovery methods.

Findings

Algorithm runs in linear time for fixed precision.

Provides both head and tail approximation guarantees.

Enables faster sparse signal recovery in large datasets.

Abstract

We describe a fast approximation algorithm for the $\Delta$-separated sparsity projection problem. The $\Delta$-separated sparsity model was introduced by Hegde, Duarte and Cevher (2009) to capture the firing process of a single Poisson neuron with absolute refractoriness. The running time of our projection algorithm is linear for an arbitrary (but fixed) precision and it is both a head and a tail approximation. This solves a problem of Hegde, Indyk and Schmidt (2015). We also describe how our algorithm fits into the approximate model iterative hard tresholding framework of Hegde, Indyk and Schmidt (2014) that allows to recover $\Delta$-separated sparse signals from noisy random linear measurements. The resulting recovery algorithm is substantially faster than the existing one, at least for large data sets.