Projection-Based and Look Ahead Strategies for Atom Selection

TL;DR

This paper introduces two novel atom selection strategies for greedy algorithms, including a look ahead approach, and combines them into a cascade method to balance performance and computational complexity.

Contribution

The paper proposes two new atom selection schemes and a cascade algorithm, enhancing greedy search methods with improved accuracy and efficiency.

Findings

The cascade algorithm outperforms traditional greedy methods in accuracy.

Look ahead strategy improves future iteration decisions at higher computational cost.

Experimental results show competitive performance with existing algorithms.

Abstract

In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of potential atoms in each iteration. The two new schemes lead to two new algorithms. For both the algorithms, in each iteration, the set of potential atoms is found using a standard matched filter. In case of the first scheme, we propose an orthogonal projection strategy that selects an atom from the set of potential atoms. Then, for the second scheme, we propose a look ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations. The use of look ahead strategy requires a higher computational resource. To achieve a trade-off between performance and complexity, we use the two new schemes in cascade and develop a third new algorithm. Through experimental evaluations, we compare the proposed algorithms with existing greedy search and convex relaxation algorithms.